A S T R O N O M Y 1 1

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1 A S T R O N O M Y Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Getting Your Bearings, The Sizes of Things Math Review The Constellations Constellation List Star Maps Star Songs How Earth and Sky Work- Effects of Latitude How Earth and Sky Work -The Effect of Time Positions of the Sun and Moon Eclipse Tables and Map History of Astronomy -Ancient Times through Galileo History Timeline Calendars and Time The Start of Modern Physics Using Equations and Formulae Illuminating Light Solar System Overview Chapter 10 Earth, Our Point of Reference History of Earth Chapter 11 Comparative Planetology Test 1 Review Test 2 Review Final Review THE VISIBLE UNIVERSE 2012 karen g castle

2 Chapter I Getting Your Bearings, Math Skills and The Sizes of Things 2 Finding sizes: As part of the first assignment, you will be finding sizes of things. You might need to find mass or radius or lifetime. The assignment is geared to your textbook, although you may use the internet to find the information. Be very careful to get what is requested. Download and save the Internet reference if you want to be able to show that the answer is correct. Part of what we are learning is how to convert units and how to use a logarithmic plot. So don t spend a lot of time searching for the exact units (e.g. finding meters vs Earth radii). Converting Units: We compare the sizes of objects in order to get a concept of the Universe. The term size is somewhat vague. It might mean mass, radius, area, circumference, duration in time etc. Generally these features are not interchangeable. They have different meanings and refer to different features. Even when we have comparable measurements e.g. lengths, the values all need to be in the same units so that we can understand what is larger. If the information isn t all in the same units, it is necessary to convert it so that they can be compared. What if we don t have the information in the same units? It is necessary to convert them to the same units. For the first homework, we will find a dimension: that is, a length, width, diameter etc. Other forms of size, such as mass, area, or volume are useful, but not directly comparable. To decide whether you have found the proper dimension, the values must be in units of length e.g. meters, miles, kilometers etc. There may not be one exact answer for each item. For example, you might be seeking the size of an automobile. Possible answers would be the length of a Mini Cooper, about 97 inches long (2.46x10 0 meters in scientific notation) and 55.4 inches (1.47 x10 0 meters) high. A Hummer H3 might be 6.7x10 0 meters long and about 1.85 meters high. We can convert the lengths or heights of the vehicles to the same units to see which is larger. On the other hand, the mass of the auto, or the surface area are different from one another and different from the length or height. They cannot be compared directly. They need to be in the same units. Units In science (and almost everywhere but the USA) the metric system is used. So lengths should be in centimeters, meters, or kilometers. Time is usually in seconds. Mass would be in grams or kilograms. In astronomy there are some other, unique, units you will be seeing. These include Astronomical Unit distance between the Earth and Sun=1.496x10 8 km=1.496x10 11 m Light Year(ly), distance light travels in a year=9.46x10 12 km=9.46x10 15 m Parsec(pc) = 3.26 light years= Astronomical Units=3.0856x10 13 km=3.0856x10 16 m (a parsec is the distance of a body whose parallax is 1 second of arc) Your book has quite a few relations between units (appendix and inside front cover). For example 100 centimeters (cm)=1 meters (m) 1000 meters (m) = 1 kilometers (km) 1 mile (mi)= km 1 meter = inches (beware, meter is abbreviated m and mile is abbreviated mi) It is handy to write down all the conversion factors in one place, like a page of your notebook, so you don t need to search.. Converting units does not change their meaning. But, as you know from algebra class, the only things that can be done to a number without changing its value are to add 0 or to multiply by 1. To convert multiply by 1. This may sound useless, how can multiplying by 1 do anything at all? To convert units, you might use any of the following. They are all equal to 1, since they are the same on the top and bottom. Chapter I Getting Your Bearings, The Sizes of Things 1

3 x10 15 m 1 light year x10 11 m 1AU x10 16 m 1 pc 1km 3.937x10 4 in 1 in.0254 m All of these values are equally true, but each is most useful when the units of the denominator (bottom of the fraction) are the same as the units of the value you want to convert, so that the units cancel. Read through the examples to see how it works. Example: Saturn s orbit has a semimajor axis of AU. How large is the semimajor axis in meters? To get from AU to meters, look up 1 AU = 1.496x10 11 m Since these values are equal, they can be placed, one over the other, to make a form of 1. How should it be done? The units of the previous value (the AU) should be on the bottom, to cancel AU " = 9.539AU x x 1011 m% $ ' # 1 AU & = x1.496 x m =1.427x10 12 m Cancel the AU to get Example: Sirius is 2.7 parsecs away from the Sun. How far away is this in meters? The parsecs cancel. 3 Example: The distance to Vega is 2.39x10 17 m. How many light years is that? " 1 light year % Multiply the distance by$ ', with the meters on the bottom to cancel the units. So # 9.46x10 15 m& # 1 light year & m % ( $ m' # = light year& Since 9.46x10 15 was on the bottom of the fraction, we divide BY it to get % ( $ ' = light years When you start, there is no equation. You just write the number and equate it to itself times ONE. You can tell that the conversion is correct if the units (just the names like parsec or km) cancel top and bottom. Find these same values from a textbook or the work book. You do not need to memorize the number values. Often, you will not find a single equation relating the original units to the final value. In that case, find relations between the current units and some other, then between that unit and another, etc. etc. until you have steps relating one unit to the next, without skipping any steps. In this case you will be multiplying by 1 several times. It is generally better to write out ALL the terms, cancel the units (to be certain that the correct values are being used) and only then to multiply all the values together. Example: A football field is 300 feet. How many kilometers is that? Find the conversion factors to go from the original units, step by step, to the units you want. # 300feet 12inches & # % ( m & # % ( 1km & % ( $ 1foot ' $ 1inch ' $ 1000m' # = 3600 inches m & # % ( 1km & % ( $ 1inch ' $ 1000m' # = km & % ( $ 1000m' = km Check yourself: Convert each of the following a) 1.7x10 11 inches to m b) 14 yards to miles c) Convert 13 Mpc to m d) 14kpc to m e) 3.4 ft to m Chapter I Getting Your Bearings, The Sizes of Things 2

4 4 a) 1.7x10 11 inches=4.318x10 9 " m b) 3ft % " 14yd x $ ' x 1mi % $ ' = 7.95x10 3 mi c) # 1yd& # 5280ft & d) 14 kpc = 4.326x10 20 m e) 3.4 ft = 1.04x10 0 m Calculator Note: The order of multiplication and division doesn t matter. On the other hand, many calculators will need more parentheses than you might think. Example: If you type 6/5x7 into a calculator, you get 8.4 not The calculator will divide 6 by 5 and then multiply the answer by 7. To divide 6 by 5x7, you need to type 6/(5x7) or 6/5=/7=. Scientific Notation; This is a style of numbers. Scientific notation does not change the information, but does make it easier to compare values and eliminates the need to write out many zeroes. In Scientific Notation the value is written as a number between 1 and times an integer power of 10. So the following are written in scientific notation: 5x10 1, 4.23x10-6, 1.09 x 10 4 while the following are not: 50, 43.9x10-7, x 10 7 although these numbers represent the same values. When operating with scientific notation, the easiest thing is to load the values (in whatever format) into your calculator, find the answer, and then write the answer in scientific notation. To put a number into scientific notation, move the decimal point until it is to the right of the first non-zero digit and count how many places you have moved it. Then multiply by 10 to the power equal to the number of places that you moved the decimal. If you moved the decimal to the left, making the number smaller, then multiply by 10 to a positive power. If you moved it to the right, making the number larger, then multiply by 10 to a negative power. If there is no decimal showing, it is past the last digit to the right. For example 5234.=5.234x =3.4x10-3 Calculator Note: Calculators express the power of 10 using a key that says EE or EXP or ee. The ee key is usually a second function (above the actual keys). These keys tell the calculator that the next number will be the power of 10 that is part of the number. e.g x10 3 is EE3 or EXP 3 3.4x10-3 is 3.4 EE-3 When you want to enter the -3, it is necessary to use the +/- key. Things that don t give the right answer include: a) typing x10 as part of the number b) using the e key or e x key for a power of 10 c) using the - key to get a negative number. Plotting: We want to plot the sizes of astronomical objects to compare them. The wide range of sizes doesn t usually fit on a single plot, so we use a logarithmic plot, like the following. A logarithmic plot gives equal space to equal powers of 10, rather than giving equal space to equal size intervals. The major divisions start at 1 times a power of 10. Numbers that are not exactly powers of 10 (e.g. 4 x 10 3, 3.8 x10 5 etc) are plotted between the major divisions. The tiny numbers 2, 3,5,8 show which mark to use for 2 times the power of 10 that is immediately below, 3 times, etc. The tic marks show all of the multipliers (2x, 3x, 4x etc). They are not all labeled because there is too little space. To use the graph, each number must be in scientific notation first (a value between 1 and times an integer power of 10). Since the number is LARGER than the power of 10, its value will be plotted ABOVE the power of 10, at the position indicated by the leading number. For example 8x10 9 km Chapter I Getting Your Bearings, The Sizes of Things 3

5 Sizes in Meters 5 1.0x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x Chapter I Getting Your Bearings, The Sizes of Things 4

6 appears above the 1x10 9 line at the value 8. The value 1.2x10 19 appears slightly above the 1x10 19 line, but below the 2x10 19 line. When you plot the values you have found on the logarithmic graph provided and label them with the name of the object. The vertical coordinate on the plot is the size of the object in kilometers. The horizontal coordinate on this graph has no meaning (although it does on other graphs). Theory Note: How is spacing of the numbers decided? Every positive number can be represented by 10 raised to some power. This power is called the logarithm of the number. The power is not usually an integer. The spacing is determined by this power. So, for example, 4=10 log (4) =10.602, so the 4 is about 0.6 of the way from the bottom of the interval to the top. The spacing of the small marks takes the logarithms into account. 6 Math Notes Order of Operations Do whatever is within parentheses first. Then: Raise to powers (i.e. evaluate the effect of the exponent) Multiply and divide (order doesn t matter) Add and Subtract (order doesn t matter between these) So, for example x5/17 =? would be evaluated as follows. Do powers first, then multiplication and division, then addition and subtraction. (6 3 ) + (9 2 )+{4x(5/17)} or (6 3 )x(9 2 )+{(4x5)/17} = /17= /17 = = When using a calculator, be prepared to use parentheses in more places that you might expect. For example, the expression, 6x 7 should come out as 3.5. The order of multiplication and division doesn t 4x 3 matter, but the expression includes dividing by 3. A calculator may give (6x7/4)x3 = 31.5, depending on how the information is entered. The calculator needs to be told explicitly to divide by 3. Exponential Notation The symbols 10 3, 1E3, and 10**3 all mean 10 to the third power i.e. 10 x 10 x 10. The first way of writing is used if the writer can do superscripts, the other ways are used in some computer notations where superscripts are not available More generally 10 n means 10 multiplied together n times, i.e. 10x10x10...x10 where there are n repetitions of 10 (or equivalently 1 with n zeroes following it.). To multiply together two numbers of the form 10 n x 10 m, the exponents are added, e.g. 10 n x 10 m =10 m+n Similarly, 14 5 means 14 x 14 x 14 x 14 x 14 = not 14x10 5. A negative exponent, means 1 divided by the number raised to the power given. e.g means 1/ means 1/2 2 =1/ means (1/10) multiplied together twice, i.e =1/10 2 = (1/10) x (1/10) = 0.01 Similarly, 17-3 = 1/(17 x 17 x 17) = 2.035x10-4 = Chapter I Getting Your Bearings, The Sizes of Things 5

7 7 The rule of adding the exponents when multiplying numbers of the form 10 -n x 10 m holds so 10 -n x 10 m =10 -n+m =10 m-n or subtract the exponent on the bottom when dividing. For example 10 m /10 n =10 m-n In math, two negatives cancel (or two wrongs make a right, if you like), so 10 m /10 -n =10 m (-n) =10 m +n Examples 10 9 / = = /10-12 = 10 9-(-12) =10 21 Addition/Subtraction The calculator will take any combination, but there is no simple way to add exponential numbers, by hand. You need to either write them out explicitly or factor them e.g = =10100 =10 2 x ( )=10 2 x (1+100)= 10 2 x (101)=10100 Computing with Scientific Notation and Similar Forms Because the order of multiplication and division doesn t matter, scientific notation can be used in computation as follows. 3.1x10 6 x 7.5x 10 9 = 3.1 x 7.5 x = x =2.325 x in scientific notation. It is necessary to increase the exponent to compensate for decreasing the value to and increasing the exponent. It is NOT necessary to separate the powers of 10 from the rest of the computation. It is helpful if you are doing the computation by hand, because it is easy to compute the powers of 10 and estimate the rest. In the computation about, the 3x7 part could be estimated as 21. That would not be final answer, but it would give a rough idea of the result. Solving Equations Often we have a formula where we know values for some, but not all, of the variables. For example Distance =Rate xtime Distance= 340 kilometers, Time= 3 hours The goal is to rearrange the values so that an unknown value appears on one side, alone, and only known values appear on the other. The way to do this without destroying the information embodied in the equation is to use EQUAL TREATMENT for both sides of the equation You can do the following without making an equation untrue: Substitute a numerical value for a variable, if you know the value Multiply or Divide by something, both sides (using zero here is legal, but it destroys the process) Add or Subtract something, both sides Raise something to a power (like square it, take the square root) Clear parentheses, for example a(b+c) = ab + bc and you should do one or another of the above (or several) if it helps to get all the known things on one side, and the unknown things on the other. Looking back at the problem, Distance =Rate xtime Distance = 340 kilometers, Time= 3 hours Chapter I Getting Your Bearings, The Sizes of Things 6

8 8 We know the distance and the time and want to find the rate. So divide both sides by Time, to get rate by itself (1/Rate) x Distance =Rate x Time x (1/Rate) The point was to be able to cancel the Rate, so we do to get (1/Rate) x Distance =Rate x Time x (1/Rate) Distance/ Time = Rate Now it is easy to substitute, (Distance = 340 kilometers, Time= 3 hours) 340 km/3 hr = Rate km/ hr = Rate Algebra Advice Solutions in algebra are not very intuitive. Don t expect to know the answer automatically, no matter how brilliant you are. It is rather like fixing a car or cooking. No matter how smart you are, it still takes all the steps and a bunch of time. It doesn t mean that you are dumb or bad at math. It just works slowly and systematically. It is best to write out EVERY step completely. Be sure that each line is a repetition of a true equation. That way, you can understand what you have done if you come back. Not every legal thing you may do will help isolate the unknown. If it doesn t help, it may be necessary to start again. Even if it seems to have helped, it may be worthwhile to put the problem away. A good way to check your work is to put the answer aside, separate from the problem. Come back to it when you have not thought about it for a while. Redo the problem. NOW compare your results. If they are different, at least one must be incorrect. If you are working with a friend, compare methods, each reading the other person s. Or read the work out loud to someone, even if they have not done the problem. It will make you go over the information slowly and often help you to notice an error. It is hard to read your own work and find the error. We all want to be right and that gets in our way as we look at our own results. Uncertainty and Number of Significant Figures Most numbers we use are the results of measurements. That means that they are not perfectly accurate. Unfortunately not all textbooks tell you how accurate the values are and it is not true that the last digit is the only one that is uncertain, Consider a value like 3.88x10-9. The range of values really might really be from 4.03 x10-9 to 3.5x10-9 with probability 95% (typically the exponent would not change). Another way that this can be written is 3.88 x10-9 ( +0.15, -0.38, 2σ). There is no way for you to know the uncertainty is unless the author specifies it. In this case, we would say that the value has 1 significant figure, since the range of values from largest to smallest leaves only one digit unchanged. If we don t have detailed information about the measurement uncertainty, the number of significant figures is used to estimate the error. When computing with measurement values, you should get a result only as good as the LEAST accurate of the numbers included. If the only operations are multiplication and division, and the values are all expressed in scientific notation, the number of figures in a number is the number of digits in the number before the power of 10. The power of 10 does NOT affect the number of significant figures. If the number is NOT in scientific notation, leading zeroes do not count as significant figures, but trailing zeroes do. Examples: 0.09 has 1 significant figure (9. x 10-2 ) has 2 significant figures since the 0 following the 1 indicates that you know the next digit. You could write it as 1.0 x The leading zero(s) indicate the power of 10, but is (are) not considered to be significant figures 9.87 x 10 9 has 3 significant figures Thus, the result 0.09 x 0.010/9.87x10 9 = 9x10-14 should have ONLY 1 significant figure, the same as the least accurate value in the computation. Chapter I Getting Your Bearings, The Sizes of Things 7

9 9 If addition or subtraction is involved in a computation, the numbers need to be written out, and digits should be kept so long as they are the result of known values. Example 3.24 x = Adding 3240 ( actually we don t know the 0, but it is needed to keep the columns straight) This value does not include the correct number of significant figures. If we write it in scientific notation the result becomes x10 3, with all the digits, and 3.51 x10 3 with the correct number of digits. The two 6 s resulted from addition of some uncertain values. The final answer was rounded up to get the best value Conversion Factors 1 meter = in (meter is abbreviated m) 1 foot = 12 in 1 in = 2.54 cm 1 mile = km 1 statute mile=5280 feet (this is the normal kind of mile, it would be abbreviate mi, NOT m) 1 nautical mile= 6080 feet 1 nautical mile= km 1 m = 100 cm 1 km = 1000 m 1 µ = 10 6 m ( the symbol µ, like m in the Greek alphabet, stands for micron unit) 1 nm = 10-9 m 1 Å = 10 8 cm=10-10 m (the symbol Å stands for Ångstrom units) 1 AU = 1.496x10 8 km (AU stands for Astronomical Unit, the average distance from the Earth to the Sun) 1 ly = 9.46x10 12 km (ly stands for light year, the distance that light would travel in a year) 1 pc = 3.26 ly 1 pc = x10 13 km (pc stands for parsec, the distance at which parallax shift due to the observer moving by 1 AU is one second of arc) 1 kpc = 10 3 pc 1 Mpc = 10 6 pc Triangles If you know two sides and one angle, you can finish drawing the triangle. Which means, the triangle is known. e.g. If you know all three sides, you can also finish the triangle, i.e. draw and stick it together in only one way. So you know the entire triangle On the other hand, if you know all the angles, you know the shape of the triangle, but not its size. Triangles with the same shape as one another are called similar, like the following three triangles. Chapter I Getting Your Bearings, The Sizes of Things 8

10 10 The angles in any plane triangle always add up to 180 degrees. Angles 360 o in a circle, 180 o in the angles of a triangle or on one side of a straight line 1 o =1 degree=60' ( minutes of arc) 1'=60" (seconds of arc) Areas Triangle Area = 1/2 Base x Height Rectangle Area = Base x Height Circle Area = π Radius 2, where π = The circumference of a circle is Circumference = 2 π Radius. The number of degrees in a circle is 360. Trigonometry, just so you know A special, useful class of triangles is the right triangle. Since one of the angles in it is always 90 degrees, the right angle, and there are 180 degrees total, there are 90 degrees left among the other two angles. Once one of the angles is known, the other is simply the remainder of the 180 degrees. Since the shape of a right triangle is known once one of the smaller angles is known, we can understand the relations between the lengths of the sides. The relations are tabulated as the functions shown above. The ratios of the lengths of the sides can be found in books or on scientific calculators. Be sure that the calculator is in degrees mode to use it to find a trigonometric function. One more quick trick. If an angle is smaller than about o, then sine or tangent of the angle is about the same as the size of the angle in radians. Angles 360 o in a circle, 180 o in the angles of a triangle or on one side of a straight line 1 o =1 degree=60' ( minutes of arc) 1'=60" (seconds of arc) 1 radian = o 2 π radians =360 o Areas Triangle Area = 1/2 Base x Height Rectangle Area = Base x Height Circle Area = π Radius 2, where π = Sphere Area = 4π Radius 2 The circumference of a circle is Circumference = 2 π Radius. Chapter I Getting Your Bearings, The Sizes of Things 9

11 11 Chapter 2 The Constellations The constellations are formally named patterns and areas of the sky. Ancient people named patterns they found from their locations. Different peoples found very different patterns and named them differently. Even the choice of stars to combine varied. Many of the constellations we use today first started with the Babylonians and were modified by the Greeks. The Romans seem to have adopted the Greeks apprach. During the Dark Ages in western Europe, the Islamic world maintained the knowledge of astronomy developed by the Greeks. Most of our common star names are Arabic names developed during this time. Not every visible star was used to make the named pattern. The Greeks and Romans had no names for stars or patterns too far south to be seen from the Mediterranean area. Native people in Africa, Polynesia and Australia had star and star pattern names, but we have not adopted them. Europe awoke from the Dark Ages and became reacquainted with the Greeks knowledge starting around 1000CE (Common Era). The works of Plato and Aristotle were translated into Latin (from Arabic). These authors were more advanced than the Europeans of the day. So they were studied, not challenged. By the 1600 s and 1700 s CE, astronomers realized that there were unnamed parts of the sky and that use of the telescope would lead them to find increasing numbers of stars. They proceeded to name constellations covering all regions of the sky. Some of the names they chose, such as Telescopium, attest to the modern origin of these constellations. Astronomers extended the definition of a constellation to include a region of the sky and any stars found within the region. The stars making up the traditional pattern (if any) are included in the boundaries, as are any additional objects found within the boundaries. These constellation boundaries are shown in Figure 2-5. A total of 88 constellations cover all directions. These constellations are used by astronomers planetwide. Stars in a constellation are not normally associated in three dimensional space. Other apparent star groupings are called asterisms. The stars in an asterism can belong to one or several constellations. Asterisms can be likened to nicknames or names for neighborhoods. Many, including the Big Dipper, Little Dipper, and Summer Triangle are very famous. Additional asterisms can be created at will, but changing constellations requires the decision of the International Astronomical Union (IAU). You will be learning to recognize some of the more prominent constellations visible from the USA. The list of constellations and asterisms we may cover follows. After we have covered each constellation or asterism in class, you will be responsible to know a) Official name of the constellation (or asterism) 1 st column b) Official meaning of the name (not what we think it looks like) 1 st column c) Name(s) of first magnitude and other stars in the constellation 2 nd colunm (Star names are bold. The other information in this block is for your observing pleasure) d) Find the constellation or any of the stars on a star map with no lines e) Circle the stars in the constellation f) Read the Right Ascension and Declination of a star or constellation from the map. In a test or quiz There will be no lines, no numbers, but tic marks to indicate where the lines would be. The data in the last column of the tables expresses coordinates of (roughly) the middle of the constellation. There is nothing official about them. They are not the coordinates of any particular star in the constellation. Their purpose is to allow the reader to find the constellation (or to explain to another where it is) if he had no idea. There is no reason to memorize these values if you can find the constellation on a map. Do NOT use these coordinates for stars. You will be using these names and positions in some of the exercises concerning what can and cannot be seen from different locations and at different times. As you use these stars, you will be expected to be able to find them on a map without lines. Constellations retain their positions relative to one another, but their position relative to the horizon changes as the Earth spins. So it is handy to use one to find another, rather than to count on using the horizon or land-based references to find them. Chapter 2 Constellations 1

12 12 Name/ meaning Andromeda (And) name (daughter of Cassiopeia) Aquila (Aql) eagle Auriga (Aur) charioteer Boötes (Boo) herdsman Cancer (Cnc) crab Canis Major (CMa) large dog Canis Minor (CMi) small dog Cassiopeia (Cas) Her name (a queen) Cepheus(Cep) His name(a king) Corona Borealis (CrB) northern crown Cygnus (Cyg) swan Delphinus (Del) dolphin Draco (Dra) dragon Gemini (Gem) twins (Castor and Pollux ) Hercules (Her)His name Leo (Leo) Lion Lepus (Lep) hare Libra (Lib) balance scale Features and Bright Stars Approx Location M31 Andromeda Galaxy at RA 00 hr 42.7 min, Dec RA 1 hr, ', Naked Eye Dec +40 Andromeda's head is shared with Pegasus And (Almak) Bright Binary K2 and A0, Eastern "foot" Aquilae is Altair, First Magnitude from Flying Eagle, RA 19hr 30min Southernmost part of Summer Triangle Dec +5 Aurigae is Capella First Magnitude RA 5 hr 30 min M36(RA 5 hr 36.1m, Dec +34 8') and nearby M37, M38 Dec +40 Open Clusters Boötis is Arcturus, find Using Big Dipper Handle, Kite RA 15hr 30min Shaped, is triple, incl. visual Binary "Pulchrissima" Dec +30 M 44, Praesepe (RA 8 hr 40.1m, Dec ') a star RA 8 hr 30 min cluster best seen in binoculars Dec +20 Canis Majoris is Sirius brightest apparent, Double with RA 7 hr White Dwarf Dec-25 M41(RA 6 hr 47.0m, Dec ') open cluster Canis Minoris is Procyon first magnitude, with white RA 7 hr 30 min dwarf companion Dec + 5 Relatively bright is a Variable star changing from 1.6 to3. RA 1 hr mag (middle of W) Dec +60 M103 (RA 1 hr 33.2m, Dec ') open cluster is near Tycho Brahe found a Supernova here Not Bright, Cepheii is variable and is distance RA 22 hr benchmark Dec +70 T Cor Bor, (not naked eye) has brightened twice(1945, RA 15 hr ) to mag 2, drops to 15 near Cor Bor min Dec + 30 Cygni is Deneb, "bird's tail", first Mag is northernmost, Southern end ( ) is Albireo fine blue and yellow binary North America Nebula 3 E of Deneb East of Summer Triangle, No bright stars, but distinct pattern RA 20 hr 30 min Dec +40 RA 20 hr30min Dec +15 Extends between Ursa Major and Ursa Minor, all faint stars RA 10 to 21 hr Dec +65 Geminorum, the fainter, is Castor, is Westward and RA 7 hr triple, Dec +25 Geminorum, the brighter, is Pollux is Eastward, both first magnitude M35 (RA 6 hr 8.9m, Dec ') M13 (RA 16 hr 41.7m, Dec ') fine globular cluster Leontis is Regulus, first magnitude, the Stella Regina for Greeks, many occultations, Leontis is Denebola, Arabic for "Lions Tail" M65(RA 11 hr 18.9m, Dec ') Spiral Galaxy M66(RA 11 hr 20.2m, Dec ') Spiral Galaxy M95(RA 10 hr 44.9m, Dec ') Spiral Galaxy M96(RA 10 hr 46.8m, Dec ') Spiral Galaxy No bright stars, below Orion M79 (RA 5 hr 24.5m, Dec ')rich globular star cluster Faint stars, was part of Scorpius (a claw), renamed in honor of Augustus Caesar for justice and reform of Law RA 17 hr Dec +30 RA 11 hr Dec +17 RA 5 hr 30 min Dec -20 RA 15 hr, Dec-15 Chapter 2 Constellations 2

13 13 Lyra (Lyr) lyre Monoceros (Mon) Unicorn Orion (Ori) name (a hunter) Lyrae is Vega, first magnitude; will be pole star in ~ 13,000 years, Lyrae is eclipsing binary, with gas shells M57 (RA 18 hr 53.6m, Dec +33 2')planetary nebula Faint, between Orion and Canis Major Orionis, Betelgeuse, is reddish Orionis, Rigel, is a bluish system of five stars M42 (RA 5 hr 35.4m, Dec -5 27' diffuse nebula, naked eye RA 19 hr, Dec 38 RA 7 hr Dec -5 RA 5 hr 30 min Dec 0 Pegasus (Peg) His name, (winged horse) Perseus (Per) His name (a hero) Pisces (Psc) fish Sagittarius (Sgr) archer (anatomically a centaur) Scorpius (Sco) scorpion Taurus (Tau) bull Ursa Major (UMa) great bear No first magnitude stars, Large square with stars interior, Looks like Baseball diamond M15 (RA 21 hr 30.0m, Dec ') globular cluster is Algol an eclipsing binary with 2.87 day period Double Cluster h and young open clusters in Milky Way NGC 869 (RA 2 hr 19m, Dec ') =h Persii NGC 884 (RA 2 hr 22m, Dec ') = Persii All faint stars. Trifid Nebula = M20=NGC6514 (RA 18 hr 2.6m, Dec ') diffuse nebula Lagoon Nebula=M8=NGC6523 (RA 18 hr 3.8m, Dec ') diffuse nebula Omega Nebula = M17=NGC6618 (RA 18 hr 20.8m, Dec ') diffuse nebula Scorpii is Antares Temperature~3500 K, double M4=NGC6121 (RA 16 hr 23.6m, Dec ') globular cluster M6=NGC6405 (RA 17 hr 40.1m, Dec ') open cluster M7=NGC6475 (RA 17 hr 53.9m, Dec ') open cluster Tauri is Aldebaran, about 3000 K Pleiades=M45, open cluster (RA 3 hr 47.0m, Dec+24 07') M1=Crab Nebula,Supernova remnant (RA 5 hr 34.5m, Dec+22 01') Hyades naked eye V shape, nearby galactic cluster Ursa Maoris is Dubhe, pointer nearer Polaris (double) Ursa Majoris is Merak, the other pointer, a single A1 star Mizar, at the bend in the handle of the dipper, is triple. The visible dimmer companion Alcor (the rider) is binary as well Ursa Minoris is Polaris (other name Cynosura), variable by 0.1 magnitude with day period Virginis is Spica, "ear of grain". Large cluster of distant Ursa Minor (UMi) small bear Virgo (Vir) virgin galaxies in constellation Asterisms: Summer Triangle (Deneb, Altair, Vega), Big Dipper (in Ursa Major), Little Dipper (in Ursa Minor), and Winter Triangle (Betelgeuse, Procyon, Sirius) RA 23 hr, Dec +20 RA 3 hr 30 min Dec +45 RA 1 hr, Dec +10 RA 19 hr Dec-25 RA 16 hr 45 min Dec-30 RA 4 hr 30 min Dec +15 Extends RA 8-14 hr Dec +60 RA 16 hr Dec +80 RA 13 hr Dec +0 from Chapter 2 Constellations 3

14 Chapter 2 Constellations h -60 4h -60 6h -60 8h h h h h h h h -30 2h -30 4h -30 6h -30 8h h h h h h h h 0 2h 0 4h 0 6h 0 8h 0 10h 0 12h 0 14h 0 16h 0 18h 0 20h 0 22h 30 2h 30 4h 30 6h 30 8h 30 10h 30 12h 30 14h 30 16h 30 18h 30 20h 30 22h 60 2h 60 4h 60 6h 60 8h 60 10h 60 12h 60 14h 60 16h 60 18h 60 20h 60 22h And Ant Aps Aqr Aql Ara Ari Aur Boo Cae Cam Cnc CVn CMa CMi Cap Car Cas Cen Cep Cet Cha Cir Col Com CrA CrB Crv Crt Cru Cyg Del Dor Dra Equ Eri For Gem Gru Her Hor Hya Hyi Ind Lac Leo LMi Lep Lib Lup Lyn Lyr Men Mic Mon Mus Nor Oct Oph Ori Pav Peg Per Phe Pic Psc PsA Pup Pyx Ret Sge Sgr Sco Scl Sct Ser Sex Tau Tel Tri TrA Tuc UMa UMi Vel Vir Vol Vul Figure 2-1 Entire Sky, Mercator Projection with Labels 14

15 15 Figure 2-2 Entire Sky, Mercator Projection No Labels Chapter 2 Constellations 5

16 Figure 2-3 Northern Hemisphere with Labels Chapter 2 Constellations 6 16

17 17 Figure 2-4 Northern Hemisphere No Labels Chapter 2 Constellations 7

18 18 Cep Dra UMi Cam Cas UMa Lac Peg Aqr Cyg Vul Sge Del Equ Aql Cap Lyr Sct Her Oph CrB Ser Lib Boo CVn Com Vir Crv Crt LMi Leo Sex Hya Cnc Lyn Gem CMi Mon CMa Aur Ori Lep Tau Eri Per Ari Tri Cet And Psc Tuc PsA Gru Oct Ind Mic Pav CrA Tel Sgr Ara Sco Nor TrA Aps Lup Cir Cen Cru Mus Cha Ant Vel Pyx Pup Car Vol Col Pic Dor Men Cae Ret Hor For Hyi Scl Phe Figure 2-5 Constellation Boundaries (with Milky Way shaded)- Entire Sky Chapter 2 Constellations 8

19 19 Figure 2-6 Southern Hemisphere with Labels Chapter 2 Constellations 9

20 20 Figure 2-7 Constellations of the Zodiac, the Constellations Along the Ecliptic Chapter 2 Constellations 10

21 21 Studying the Constellations Don t expect to ignore the constellations until the day before the test and then read and remember the maps. Do repeat the constellations several times a week, if not every day. It will only take a few minutes. Don t just look at the constellations and hope they will sink in. Use as many of your senses as possible. Make lots of copies of the blank maps. As we learn a few more constellations in class, study them, then fill in the blank map over and over until you can do it from memory. Start with the same parts each time, so you can build on what you already know. The next time we learn a few more constellations, repeat the process. Drawing the constellations involves you visually and kinesthetically (moving your body as you draw). Say the names out loud and use the mnemonics or sing the constellation songs to involve your aural (hearing) memory. You should have two goals as you study the constellations, to do well on the tests and to learn the constellations so that you can find them in the sky. These are somewhat different because the test will be from the fixed maps, while the orientation of the constellations in the sky changes. What doesn t change is the relative positions of the stars and constellations. So it is helpful to go from one recognizable constellation to the next. This section shows how to go from the most obvious constellations to others. The mercator projection is broken up as follows. The polar map has a separate sequence of constellations. Tuc Cep Cep 2 2 h2 2 h Lac Lac Peg 2 2 h 2 2 h Peg A qr Eq u Del 2 Eq 2 h u h A qr h PsA -3Cap h PsA Gru -3 0 Gru Tuc Mic Ind 2 2 h -6 0 Ind 2 2 h -6 0 Oct Oct h h Cyg Cyg Lyr 20 h Lyr 2030 h V ul 30 V ul Sg e Cap Mic Del Sg e Aql 20 h Aql 0 20 h 0 20 h h -3 0 CrA Sgr Tel CrA 20 h -6 0 Pav Tel 20 h -6 0 Pav Sct Sgr Dra Dra 1 8h h h Her h Her hoph hoph h h -30 Ara 1 8 h Sco Ara 1 8 h Sco Nor UMi UMi 16 h16 h Summer Triangle Region Sct Se r 16 h 0 Se r 16 h 0 16 h h Lib 16Lu hp Cir TrA Nor Aps 16 h -6 0 Cir TrA Aps 1 4h 1 4h h h -6 0 CVn CVn 1 4h 0 Vir 1 4h 0 Vir Crv 1 4h -3 0 Cen 1 4h h 6 0 CrB16 h 1 4h 1 2 h 30 CrB Boo 16 h h Boo Com Com Lib Lu p Arc to Arcturus 1 Crv 2 h h h h 1 0h 0 Se 0 x 1 2 h Crt h Cru Cen -60 Mus Cru Mus 1 2 h 6 0 UMa 1 2 h 3 0 Leo Hya Crt 1 0h A nt Pyx -3 0 Hya 1 2 h h -60 Cha LMi UMa Leo 1 0h h 8 h LMi 8 h 1 0h Gem Cnc 1 0h Se 0 x 1 0h A nt -3 0 V el Cha CMi 8 h 0 8 h -3 0 Pu p Car 8 h -6 0 V el V ol 1 0h -6 0 Cnc CMa Car Cam 8 h6h Lyn Lyn Orient to Aur Orion Pyx 6h 8 h Tau Gem 6h CMi Ori Mo n 0 8 h 0 Mo n V ol Lep 6h -3 0 Col 8 h -3 0 Pu p CMa Cae Pic 6h Dor h -6 0 Men Cam 6h 4 h h 6h h 0 6h Ori 0 Eri Per Aur 4Lep h -3 0 For 6h -3 0 Col Ho r Cae 4 h Re -6 t 0 2 h4 h Cas Tri2 h 3 04 h 3 0 Ari Tau 2 h 0 Cet 4 h 0 2 h Eri h Per And 4 h Ho r Pic Hyi 6h Dor 4 h -6 0 Re -6 t 0 Men Psc For P Ari Hyi 2 h 6 0 Tri2 h h 0 Cet 2 h h -60 Cas And Psc P Chapter 2 Constellations 11

22 22 Orient to Orion 1 Find Orion and note his stars 2 Follow OrionÕs belt south to Canis Major, his large dog Betelgeuse Orion Rigel Sirius Canis Major 3 Slide along OrionÕs Collar Bone to Canis Minor, the smaller dog 4 Go Diagonally up Orion to the Dancing Twins, Gemini Castor Pollux Gemini Canis Minor Procyon 5 Go Straight up OrionÕs Body to reach Auriga, the Charioteer Auriga Capella 6 Going West Along OrionÕs Belt Reveals Taurus Taurus Pleiades star cluster Aldebaran Chapter 2 Constellations 12

23 23 7 Little Lepus Hides beneath OrionÕs Feet 8 Questioning Leo follows Gemini Leo Lepus the Hare 9 Crabby Cancer lies between Pollux and Leo 10 Monoceros, the secretive Unicorn slinks behind Orion Cancer the Crab Monoceros 11 Perseus treds on TaurusÕ Horn Perseus Chapter 2 Constellations 13

24 Arc to Arcturus 1 Find Big Dipper part of Ursa Major 2 Extend the curve of the Handle to ARCTURUS, the first bright star 24 Big Dipper, part of Ursa Major Arc to Arcturus.. 3 Draw in Bootes, the Herdsman Shaped like a Kite 4 Continue the Curve through Arcturus, but straighten to Speed to Spica.. Bootes Spica Chapter 2 Constellations 14

25 Fill in Virgo, lying on her back 6 Corona Borealis Nestles Near Bootes Corona Borealis Virgo 7 Leo lies above VirgoÕs Head 8 Scorpius and Libra lie below VirgoÕs Leg Leo Scorpius Libra Chapter 2 Constellations 15

26 26 Deneb Summer Triangle Region 1 Summer Triangle joins stars from three constellations Vega 2 Deneb is the tail of Cygnus the Swan CygnusÕ head is in the middle of the triangle Altair D A V e l e n t g e a a b i r 3 Altair is in Aquila the Eagle D A V goes to C e l e y n t g g e a a n b i u r s 4 Vega,brightest star in the triangle is part of Lyra, the lyre Aquila D A V goes to C A L e l e y q n t g g u e a a n i b i u l r s a D A V goes to C A L e l e y q y n t g g u r e a a n i a b i u l r s a Chapter 2 Constellations 16

27 27 5 ScorpiusÕ tail scoops south of the Summer Triangle 6 Libra, the scales stands where ScorpiusÕ claws once were Arcturus Find Libra on a line from Antares to Spica or Arcturus Antares Libra Spica Scorpius the Scorpion Antares 7 Sagittarius the Archer follows ScorpiusÕ Tail 8 Sagittarius the Archer is Supposed to be a Centaur Sagittarius can look like a teapot Sagittarius Chapter 2 Constellations 17

28 Chapter 2 Constellations 18 28

29 29 Polar Polka tune of Beer Barrel Polka chorus Roll out the Pole Star We ll have Polaris all night Spin out the Mom Bear She ll put you all in a fright Follow Merak to Dubhe, they ll put you right on the pole Always roll out the pole star and you ll sail all right. Point through Polaris, you will find Cephe us hat Keep on a curving, to find where Cassiopeia s at If you are clever, Andromeda hides behind Her mother s chair where she s chained and she s stuck all night If you would save her, look for Perseus her beau. He stands awaiting right near Andromeda s toes Perseus comes riding upon his flying horse, Pegasus squares up the family and makes the story come out right. And that s the way of the stars The head star points to the Chariot eer The Bull is charging the Orion s shield And the Hare is curling up Un derfoot And that s the way of the stars. Refrain The lion lurks left of Little Dog The Crab crawls after Milky Ways Unicorns utterly unseen And that s the way of the stars Refrain Aldebaran bashes Betelgeuse And Betelgeuse chases Capella Capella coaxes Castor West And that s the way of the stars. Refrain Castor partners Pollux And Pollux pulls on Procyon The puppy pleases Sirius And that s the way of the stars. Stars Near Orion Sung to the tune of Dry Bones The belt stars connected to the Big Dog And the shoulder stars connected to the Little Dog, The twins dance on the diagonal And that s the way of the stars. Refrain: Them stars, them stars goin to wheel around Them stars, them stars goin to rise and set, Them stars, them stars goin light the night Refrain Sirius snips at Rigel Regulus returns to questioning The beehive buzzes the crabmeat And that s the way of the stars. Refrain Summer Sky Mneumonics Arc to Arcturus, bound up in Boötes Chapter 2 Constellations 19

30 30 Speed on to Spica sweet Virgo s waistband Curve back to Corona butting up to Boötes. Traipse the Triangle where DAV goes to CAL Swoop to southern Scorpius tail. Scorpius claws at Libra s steady balance, While Sagittarius arches to pour tea on his tail Hercules Huddles tween herdsman and Vega, flying upended o re Ophiuchus and snake The sea nymphs did hear her and weren t amused They complained to Neptune, that they were abused. So Neptune took umbrage and went to their aid He stole poor Andromeda from her mother s side Behind Cassiopeia s Double U, her daughter doth hide Andromeda s so timid cause to rock she s tied. She s tied to the rock awaiting her fate To be eaten by Cetus, who is lying in wait The Sad Song of Cepheus et al (To the tune of On Top of Old Smokey On top of the North Pole, The small bear does roll Sep rated from Mo-ther For safety of all The Mom Bear points to him, With stars in her back Old Merak and Dubhe Will show you how to react Past Arcas pole star, Polaris by name We find a fami- lee of mythical fame Continue on further to Cepheus the sad A king with a ha-at, he married for bad. His bride Cassiopeia, who one daughter had She ll kick her poor hubby, in hi-s left ear Because she s so gorgeous, her daughter s in fear Her daughter Andromeda is lovely it s true, And Ms Cassiopeia told all whom she knew. Bragged about her own offspring, as a true peach E en prettier than sea nymphs as Cassiopeia did preach A fore evil Cetus could rip out her patella The hero Perseus heard of her dilemma Perseus was famous, quite famous afore For slaying Medusa, a monster of yore Perseus went to poor Cepheus and to him he said May I please save her lest, she end up dead? So what do you think that poor Cepheus did? He said, Please, please Mr Perseus, go save my one kid. Perseus said, Yes, fine, but what s the quid pro the quo? If I can save her, can married we go? Of course, my dear Perseus, quoth the worried dad, Just prevent her from being eaten and I will be glad. So Perseus he whistled, and forth came a horse, Flying Pegasus arrived in a froth. Armed with Medusa, her head in his hand, And aboard swift Pegasus, he flew o re the land Perseus succeeded in freeing the girl And carried her off with skirts in a whirl. The all were as happy, as happy can be That this song is over and lived happ i ly. Chapter 2 Constellations 20

31 31 Chapter 3 How Earth and Sky Work- Effects of Latitude In chapters 3 and 4 we will learn why our view of the heavens depends on our position on the Earth, the time of day, and the day of the year. We will explore views of the Earth, the sky, and an observer as seen from space and as seen from the surface of the Earth. Today we know that the Earth is a sphere and we are tiny by comparison. The distance to every other celestial body is MUCH larger than the diameter of the Earth. Because we are so much smaller than the Earth, the Earth appears to take up half of all the directions we can look The Earth and the other planets orbit the Sun, while stars are at various distances and orbit the Milky Way galaxy. But we can use the idea of the Celestial Sphere to describe the appearance of the sky. The Celestial Sphere is an imaginary sphere surrounding the Earth. Stars, the Moon, the planets, the Sun, galaxies etc appear to be pasted on the Celestial Sphere. Straight up from Earth s north pole is the North Celestial Pole. The Earth pole and Celestial Pole are lined up and remain lined up. The same for the Earth s South Pole and the South Celestial Pole. The figure shows our relation to the Celestial Sphere. The observer stands on the Earth. The patterned surface is the apparent (flat) surface of the Earth, bounding the half of the sky visible to the observer. As the Earth spins, different parts of the Celestial Sphere may become visible. When the Earth turns so that a body comes onto the visible half of the Celestial Sphere, we say that it rises. When the Earth turns so that a body becomes blocked by the Earth, we say it has set. The Sun has no effect. We define the zenith, the horizon, and the celestial meridian to describe what an observer can see. These reference points depend on the observer s position. As Earth spins, the zenith and meridian change as the person moves with the Earth. Meridian Circle through Zenith, North Celestial Pole, South Celestial Pole North Pole South Pole Observer Zenith Direction Straight Up from Observer Observer CAN see Observer Horizon Boundary between Visible and Invisible We have been CAN NOT see considering what the observer can see. The Earth spins and the observer moves with it, changing what is visible. The stars move but they do not go around the Sun or the Earth. Because stars are so far away, none of their individual motions of the stars is noticeable. Astronomers measure stars motions by photographing them and comparing their relative positions over many years. Chapter 3 How Earth and Sky Work -The Effect of Latitude 1

32 32 Because the stars move slowly it is useful to define stars' positions and patterns on the Celestial Sphere and to learn how the positions relate to their visibility. We do this using coordinates that are similar to Latitude and Longitude on Earth (other planets, moons and the Sun are also assigned their own Latitude and Longitude systems. So first review Latitude and Longitude as shown in the figure. Latitude is zero at the equator and ±90 o at the poles. Longitude is zero at the Prime Meridian in Greenwich England. It goes East for 180 o and west for 180 o. The International Date Lines is approximately at the 180 o line. The coordinates for the Celestial Sphere are called Right Ascension and Declination. They are similar to latitude and longitude on the Earth. Each location on the Celestial Sphere, that is each direction in the sky, can be identified by its Right Ascension and Declination. North Pole Earth South Pole Parallels of Latitude Run E-W They tell the N-S position Starts at the Equator On Earth Meridians of Longitude Run N-S They tell the E-W position Starts at Greenwich, England North Pole Earth South Pole North Pole On Celestial Sphere Meridians of Right Ascension Run N-S They tell the E-W position Start at Vernal Equinox Run Parallel to Longitude Lines South Pole North Celestial Pole Parallels of Declination Run E-W They tell the N-S position Start at the Celestial Equator Line up with Earth Latitudes North Pole South Pole South Celestial Pole We think of the Celestial Sphere as fixed and the Earth spinning. As the Earth moves orbits and spins, the Earth s poles remain aligned with the poles of the Celestial Sphere and the parallels of latitude remain aligned with the parallels of declination. Meridians of longitude and of Right Ascension are parallel, but there is no one-to-one alignment. You may be wondering how the imaginary Celestial Sphere fits with the overall concept of the Universe, where the Earth orbits the Sun. The overall concept is in the figure below. Chapter 3 How Earth and Sky Work -The Effect of Latitude 2

33 33 The Celestial Sphere is so large that the Earth's orbital motion is insignificant by comparison. The Earth moves in three dimensions, but to make it easier to draw, we will consider the appearance two dimensions at a time. First we will consider the view from the right of the image. When viewed from this direction, we see the effect of latitude on what can EVER be viewed. Then we will look from above the North Pole of the Solar System. This will tell what can be seen at a given time and date, but will ignore the effect of latitude. The visibility curves at the end of chapter 4, combine both effects. In each situation, we will learn to compute what can be seen. Finding the Effect of Latitude Latitude on the Earth (or another object) is the angle between the direction to a location on the object and the equator of that object. Chapter 3 How Earth and Sky Work -The Effect of Latitude 3

34 34 Let s zoom out away from the Earth and the Celestial Sphere and see what happens as the Earth spins (every 23 hr 56 minutes) and the Celestial Sphere stays still, the observer and her/his horizon and meridian are carried along. Some stars rise and set, others are always seen. Even though the Earth is really spinning, the appearance is that the sky is moving. If the figure were redrawn to show the Celestial sphere moving, it would appear as follows. In 12 hours, the sphere moves half way around. Ignoring the depth, the stars, the Sun, the Moon and the planets appear to move horizontally from one side of the figure to the other, keeping the same declination. Over the next 12 hours they move back to their original positions. Bodies at some positions remain visible the entire time (circumpolar for this latitude); others remain invisible (never seen); yet others change from visible to invisible. Bodies at these positions are said to rise and set. These pictures show the apparent motion of the sky, but do not provide a way to compute whether a star will be visible all the time, some of the time, or none of the time. To find this, we need to relate the declination horizon position on the sky and the observer s latitude. The observer s latitude tells the angle from the equator to the observer. If we draw the Earth flat on and label the declinations above it, the following picture results. North is toward the top. South is toward the bottom. The Declination values start at +90 o at the northernmost point and progress lower and lower until they reach -90 o. Chapter 3 How Earth and Sky Work -The Effect of Latitude 4

35 35 The Latitudes on the Earth and the Declinations on the Celestial Sphere line up, so Latitude =Declination at Zenith The observer always stands perpendicular (at a 90 o angle) to his/her horizon. The part of the Celestial Sphere on the side of the horizon with the observer s head can be seen. The rest is blocked by the horizon and invisible. In this picture, North is up and South down on the paper. The declinations where the horizon cuts the Celestial Sphere, are 90 o away from the observer s zenith. To find the declinations at the ends, count off the 90 degrees from the horizon. This isn t the same as adding or subtracting 90 o, since the Declination system goes only from +90 o to 90 o. The declination values where the horizon cuts the Celestial Sphere are equal values, but opposite signs. So Declination at ends of Horizon = ±( 90- latitude ) Either you know the observer s latitude and can find the horizon, or you know something about the horizon so you can draw the horizon and can draw the observer 90 o away. There are standard questions that you can answer when the observer s latitude is known. These questions follow. The blank would have a number in it. What is the furthest north that an observer at latitude can see? What is the furthest south that an observer at latitude can see? What is the range of declinations that an observer at latitude can see? What is the range of declinations that an observer at latitude can NEVER see? What is the range of circumpolar declinations for an observer at latitude? What are these questions asking and how can they be answered? Circumpolar, the part of the sky that is always above the horizon from your location- The circumpolar region starts at either +90 o or -90 o, whichever is above the horizon for the observer. The circumpolar region extends to the closest end of the horizon. The circumpolar region NEVER crosses the equator. The observer s latitude and the boundaries of the circumpolar region all have the same sign. Example. For an observer at +60 o, the circumpolar region is +30 o to +90 o. If Chapter 3 How Earth and Sky Work -The Effect of Latitude 5

36 36 declination is within the circumpolar region for an observer, EVERY location with that declination number is circumpolar. Never seen-that is, never comes above the horizon Starts either -90 o or +90 o, whichever is not visible to the observer. It extends to the closest end of the horizon, the one with sign opposite the observer s latitude. It is just the opposite of the circumpolar region (that is the declination values are -1 times the values for the circumpolar region). For the observer at 60 o, the never seen region would be -30 o to -90 o. Rise and Set-Between (90 o - latitude ) and -(90 o - latitude ) This is what remains when the circumpolar and never seen regions are excluded. Furthest North Seen If the observer is in the northern hemisphere, +90 o, If the observer is in the southern hemisphere (90 o - latitude ) Furthest South Seen - If the observer is in the northern hemisphere, -90 o +latitude If the observer is in the southern hemisphere -90 o. Range of Declinations Which Can be Seen or Range of Declinations Visible - This is the summation of declinations that are Always Seen plus the declinations that are Sometimes Seen If the observer is in the northern hemisphere, +90 o to (90 o -latitude) If the observer is in the southern hemisphere -90 o to (90 o - latitude ) The observer in the previous figure is at latitude 60 o, so her zenith is at declination 60 o. Her horizon is at 90 o from the zenith at declinations ± 30 o. So what is the Furthest north that an observer at latitude 60 o _ can see? +90 o Furthest south that an observer at latitude 60 o can see? -30 o Range of declinations that an observer at latitude 60 o _can see? From +90 o to -30 o Range of declinations that an observer at latitude 60 o _can NEVER see? From -30 o to +90 o Range of circumpolar declinations for an observer at latitude 60 o _? From +90 o to +30 o To determine whether a body can be seen some, none, or all the time, compare the declination to the limits of the circumpolar, never seen, and rise and set regions. Or use the diagram as follows. You will be drawing something like the letter Z. Chapter 3 How Earth and Sky Work -The Effect of Latitude 6

37 37 A. Draw the horizon. It goes though the center of the picture and through ±(90 - latitude ) The horizon is always at 90 o, a right angle, to the observer s body. It does NOT matter whether observer and the horizon are on the right or left of the picture so long as they are at 90 o to one another. B. Draw horizontal lines from the points where the horizon touches the Celestial Sphere to the Celestial Sphere on the other side of the picture. The declination is the SAME number at each end of the line. Your lines and the horizon make the shape Z or a reversed Z (NOT a sideward Z). These lines are the boundaries of the circumpolar and never seen regions. C. Draw a horizontal line representing the daily apparent motion of the body the declination D. Check whether the path of the star crosses the Z you drew before. If so, it rises and sets. If the path does not cross the Z and is always above the horizon as seen by the observer, it is circumpolar. If the path does not cross the Z and is never above the horizon as seen by the observer, it is Never Seen. Lost at Sea- Finding Where You Are From What You Can See In the problems we have been considering, there is only one free parameter, the observer's latitude. If we know the latitude, then we know the horizon and what can be seen, the circumpolar region etc. There is little variety. On the other hand, an observer can find his latitude by noting the range of circumpolar bodies, the furthest south or north that can be seen etc. It is just a matter of using the information to find the horizon, then finding the location of the observer (90 o from the horizon) Example: You notice Vega at your Zenith, what is your latitude? Vega is a star and you can find its declination from a star map. Answer: You know that Latitude of observer = Declination of zenith and the problem says that Vega, is at the zenith. So Vega s declination = declination at the observer s zenith=observer s latitude =39 o Example: If you can see as far north as 20 o, what is your latitude? Answer:The words imply that the horizon goes through 20 o. It also goes through the center of the Earth and -20 o. So draw the horizon. Draw the observer perpendicular to the horizon on the side such that he can see 20 o and south of 20 o, but NOT see north of 20 o. If you are unsure of which observer, draw both (the one at 20 o and the one at -20 o ) and check which one can NOT see further north than 20 o. The latitude of the observer equals the declination at the observer's zenith. How do you know whether the observer is in the North or the South? Be sure that your observer cannot see further north than 20 o Ans 70 o Chapter 3 How Earth and Sky Work -The Effect of Latitude 7

38 38 Example: You notice that Vega is circumpolar, but nothing further south is. What is your latitude? Look up Vega s declination on a star map. If Vega is circumpolar, its entire path is above the horizon. Since nothing further south than Vega is circumpolar, the horizon must touch Vega s path on one side. It doesn t matter which side. So draw the horizon though Vega s declination, the center of the Earth, and the negative of Vega s declination. The observer will be perpendicular to the horizon. In this case, the observer will be in the northern hemisphere, since Vega is. When you draw the line representing Vega s motion, you can simply draw the observer such that the entire path is above the horizon. The Sky as We See It We have been making diagrams as though we are outside the Celestial Sphere. But how does the path of a star really look from the ground? The figure below shows how celestial objects appear to move through the sky. It is drawn for a mid northern latitude location. Circumpolar objects appear to circle the pole, always remaining above the horizon. Objects that rise and set make arcs starting in the East and ending in the West. The never seen objects are, of course, never seen. The filled ellipse represents the ground. As time goes by, the position of each object normally changes compared to the horizon and to the cardinal points (the N, E, S, W positions on the horizon). The only points that don t appear to move are the North Celestial and the South Celestial poles. The North star, Polaris, is about 5/6 of a degree from the North Celestial Pole, changes its position a little. There is no bright star near the South Celestial Pole. Altitude/Azimuth System Chapter 3 How Earth and Sky Work -The Effect of Latitude 8

39 39 Right Ascension and Declination are useful because they tell the position of a location on a star map. They don t correspond to a fixed direction compared to the observer s horizon and meridian. The Altitude and Azimuth system does. Altitude is the angle from body to horizon. Altitude is 90 o at the zenith, 0 o at the horizon. Negative altitudes are sometimes used to describe positions below the horizon (invisible). Azimuth is the angle from north to the point on the horizon below the object. is as it moves across the sky. Altitude of the Celestial Pole Azimuth runs from 0 o at the North Cardinal Point, through 90 o eastward and 180 o to the south. Altitude and Azimuth change as the objects rise and set. So there are no books of Altitude and Azimuth coordinates. But these coordinates are very useful for pointing out objects in the sky to nearby people. They are also used by some telescopes. But these telescopes use a computer and a clock to figure out where the object The altitude of the celestial pole, whichever one you can see, is equal to the latitude of the observer. Since the star Polaris is nearly at the North Celestial Pole, the altitude of Polaris equals the observer s latitude. This makes it easy to find latitude. Chapter 3 How Earth and Sky Work -The Effect of Latitude 9

40 40 Measure o Pole then place the North Celestial location of Declination o 9 o -14 o =7 o Find the Declination at the which Equals Observer's Horizon North Celestia Pol Observer is perpendicular to a 9 o -76 o =1 o or o -(90 o -altitude of altitude of South Celestial Altitude of Polaris Equals the Observer s Latitude Ex. Polaris altitude is 14 o. Where are you? Ans. Latitude 14 o. Example Polaris is at altitude 83 o. What is your latitude? Orientation Practice Problems Set I (you may look up declinations etc. on the star map) 1) What is the range of declinations that can be seen from latitude 20 o? 2) What is the range of declinations, which is circumpolar from latitude 20 o? 3) What is the furthest north that can be seen from latitude -43 o? 4) What is the furthest south that an observer at latitude at latitude -63 o can see? 5) If you are at latitude 32 o, what is the range of declinations that are circumpolar? 6) When the altitude of the North Celestial Pole is 14 o, where are you? 7) If you are at latitude -30 o, what is the altitude of the SCP? of the NCP? Chapter 3 How Earth and Sky Work -The Effect of Latitude 10

41 41 8) What is the furthest south latitude you can be so that the star Vega will be circumpolar for you? 9) What is the range of declinations that are visible from -60 o? 10) Regulus is circumpolar. It just grazes the horizon at its lowest point, what is your latitude? 11) You are lost at sea. Antares just comes above the horizon at culmination(its highest point), What is your latitude? 12) If you notice that Betelgeuse is circumpolar, but nothing further south is, what is your latitude? 13) If Deneb just rises and nothing further north is visible, what is your latitude? 14) When Antares is circumpolar and nothing further north is, what is your latitude? 15) What latitude allows the observer to see the largest variety of celestial objects? Answers 1) from 90 o to -70 o 2) +70 o to +90 o 3) +47 o 4) -90 o 5) 58 o to 90 o 6) +14 o 7) SCP 30 o altitude, NCP -30 o altitude, below the horizon 8) Vega at 36 o, latitude of observer 54 o 9) +30 o to -90 o 10) Regulus at +12 o, observer +78 o 11) Antares at o, observer at 63.5 o 12) Betelgeuse at 7 o, observer at 83 o 13) Deneb at 45 o you at -45 o 14) Antares at o, observer at o 15) The equator, latitude 0 o Chapter 3 How Earth and Sky Work -The Effect of Latitude 11

42 42 Chapter 4 How Earth and Sky Work -The Effect of Time We have learned what can be seen from various latitudes, provided you wait long enough. How long, is long enough? Half a sidereal day would be long enough, if sunlight were no problem After half a spin, the part of the sky that is seen changes as much as it ever will. There is NO difference in what can be seen over the course of the year (although there is a difference in which objects are up during the day). Solar and Sidereal Time tell the position of the observer compared to the Sun and stars respectively. They allow us to assess what can be seen at any time and date. Solar Time tells the angle of the Observer s meridian with respect to the Sun. Noon is when the Sun is on the observer s meridian (on the side that can be seen) Midnight is when the Sun is on the meridian when it is the highest. The observer points away from the Sun. PM, meaning post meridiem observer s meridian. equals the number of hours since the Sun has been on the AM, meaning ante meridiem means before the Sun is on the meridian. It equals the number of hours since midnight. The pictures we will use are as seen from above the Earth s north pole. Earth spins and orbits counterclockwise in this view. In the picture below, the circle represents the observer s meridian. Find the observers solar times. Draw another observer on the figure above. Make it an observer for whom it is midnight. Chapter 4 How Earth and Sky Work -The Effects of Time 1

43 43 The Effect of Date and the Earth s Orbit The stars are located far far outside the Solar System. So Earth s motion is tiny compared to the distance to the stars. We will identify star positions by their Right Ascensions. The Earth orbits the Sun once per year, returning back to the same position in orbit more or less. The following diagram is your reference for combining the position with the position of the stars. Be sure to fill it in. The circles are positions of the Earth every 21 st of the month (23 rd of September). The lines tell the Right Ascension of the stars in that direction. There are 24 total hours. The date tells the Earth s position in orbit, which in turn determines the right ascension (and sidereal time) at midnight. Conversely, if we knew the sidereal time at midnight, it would be easy to find the date. The solar and sidereal times take every value every day. There are only two motions, so only two different things can be specified. The Earth spins and orbits, and these two motions determine the date, the solar time and the sidereal time. Solar Time tells the position of the observer's meridian compared to the Sun. Date -Tells the position of the Earth in its orbit. Sidereal Time equals the Right Ascension on the observer's meridian (definition) Although all sidereal times and all solar times occur every day, the sidereal time corresponding to a given solar time depends on the date. On September 23, at midnight, Right Ascension 0 hr is on the meridian. Chapter 4 How Earth and Sky Work -The Effects of Time 2

44 44 As time progresses both solar and sidereal time increase at almost the same rate. Every day both solar and sidereal time go through all 24 hours. Sidereal hours are a little smaller than solar hours, so 24 sidereal hours are completed in 23 hr 56min of solar time. Because the Earth orbits the Sun, the midnight direction changes, so the sidereal time at midnight changes. It is easy to find the sidereal time at midnight by remembering how the diagram above works. Memorize that midnight on September 23 is 0 hr sidereal time and that: The Sidereal Time at midnight, increases 2 hours per month 1/2 hour per week 4 minutes per day What is the Solar Time in the figure below for each observer? Orientation Practice Problems Set II 3) Draw a picture with an observer who is at 6 AM 4) Draw a picture with an observer who is at 5 PM 5) Draw a picture with the Earth on Oct 21. Include the Sun, and the Right Ascension markers. 6) Draw a picture with the Earth on Aug 8, Include the Sun, and the Right Ascension markers. Solar Time, Sidereal Time and Date Given any two items from among Solar Time, Sidereal Time and Date, the third can be found. This is because there are only two motions; Earth spinning and Earth orbiting. The date tells where to position the Earth and the time (solar or sidereal, whichever time you have) to determine the observer s position. From the drawing, it is possible to find the other time. Example: What is the sidereal time at 6 AM on May 21? The picture follows. The answer is 22 hr, but why? The observer s meridian points along the same direction as her body. The stars in that same direction are very far away, so it is important NOT to consider the printed numbers on the picture, but to think of the direction parallel to the body line starting from the Sun, as is shown below. One way to find sidereal time for an observer is to To 22 hr, parallel to the observer Chapter 4 How Earth and Sky Work -The Effects of Time 3

45 45 estimate the direction of an arrow at the Sun, but parallel to the observer s body. A better way to find the correct time is to use midnight as a reference and to count the number of hours from midnight to get to the desired time. This method ensures that the result is independent of imperfections in drawing the figure. Since sidereal hours and solar hours are nearly the same length, an accurate answer will result. In the example given, the solar time was 6 AM, six hours after midnight. The sidereal time at midnight was 16 hr, based on the date May 21. So 6 hr LATER than 16 hr is 16+6=22 hr. You get the same answer, but there is less \dependence on the drawing. Example: What is the sidereal time at 9 PM on Aug 21? The sidereal time at midnight is 22 hr and you could subtract three hours to get to 9PM. So 22 hr 3 hr = 19 hr. The drawing shows the same thing. Here it feels natural to subtract 3 hours to go from midnight to 9pm (3 hours earlier). It is equally correct to add 21 hours going forward from midnight to 9PM. Adding the hours gives22hr+21hr=43hr hours. Since there is no sidereal time of 43hr, the remedy is to realize that 24 hr is the same as 0 hours. Subtracting 43hr-24 hr=19hr. We have been counting hours away from midnight to get one kind of time if we know the other. Organize the Computation Using a Table Pretend there are two people involved. One is Midnight Man, for whom it is always midnight. The other is the protagonist, the one the problem is about. ALL of the data is about the protagonist, ALWAYS. The date is the same for the protagonist and the Midnight Man, so there is only one row for the date. The row and column headings tell what to enter. Make two correct addition problems going DOWN. One is in the Solar Time column and the other in the Sidereal Time column. Read down the column to add the first two values and find the third. In each column Midnight Man s time+ Hours to Add = Protagonist s time. Problems are always read the same (going down) when complete, but the order in which they get filled in varies. The arrows indicate that data are related. In the case of the hours to add, the values are identical. In the case of date and midnight sidereal time, one determines the other. The original motivation for making this table was to make it easier to find the DATE when the solar and sidereal times are known. It always works provided that no errors are made. However, it has no checks to indicate whether an error has occurred. Sketching the picture is useful for a check. If the table and picture disagree, there is some error. Chapter 4 How Earth and Sky Work -The Effects of Time 4 0 9/2 Eart 18 6/2 6 12/2 To 19 hr, parallel to the observer 12 3/2

46 46 Example: If it is 4 AM on November 21, what is the sidereal time? Ans. Fill in the block in the Solar Time/Protagonist block with 4AM, the solar time for the Protagonist. Fill in the Date block with the date, 11/21. Midnight Man Hours Add Protagonist to Solar Time Midnight 4AM same Sidereal Time Date 11/21 Use your knowledge of the Sidereal Time at Midnight on November 21 to fill in 4 hr for Midnight Man s Sidereal Time. Use your knowledge of arithmetic to fill in 4hr to add to Midnight Solar Time to get to 4 AM. Midnight Man Hours Add to Solar Time Midnight same Sidereal Time 4hr +4 hr +4 hr Date 11/21 The same amount of time, 4 hr, is added to the Sidereal Time at Midnight. Protagonist 4AM Now add the 4hr to Midnight Man s Sidereal Time at Midnight to get the Protagonist s Sidereal Time. Solar Time Sidereal Time Date Midnight Man Hours Add to Midnight same 4hr Protagonist 4AM 8hr 11/21 So the answer is that the protagonist s sidereal time is 8 hr, but draw the picture to check. Example: Find the solar time at 6hr on April 21? You could draw it, or use the table Solar Time Sidereal Date So enter the protagonist s Time Sidereal Time (6 hr) and the Date. You know that 6hr is a Midnight Man Midnight sidereal time, because it doesn t say AM or Pm or noon or midnight. Hours to same Add 4/21 Protagonist 6 hr Chapter 4 How Earth and Sky Work -The Effects of Time 5

47 47 Use your knowledge of sidereal time to fill in 14 hr for the sidereal time at midnight on 4/21. Midnight Man Hours Add Protagonist to Solar Time Midnight same Sidereal Time 14hr 6 hr Date 4/21 And use your knowledge of arithmetic to to subtract 8 hr from the sidereal time at midnight to get to the protagonist s sidereal time of 6 hr. Midnight Man Hours Add Protagonist to Solar Time Midnight Sidereal Time 14hr same -8 hr -8 hr 6 hr Date 4/21 Subtract the same 8 hr from Midnight to get to the Protagonist s Solar Time, 4 PM. Midnight Man Hours Add to Solar Time Midnight Sidereal Time 14hr -8 hr -8 hr Protagonist 4PM 6 hr Date 4/21 Example: What is the date when Betelgeuse is on the meridian at 7 PM? It is not easy to draw this, because the position of the Earth is not known. On the other hand, the solar time (7 PM) is known and the sidereal time is known because you can look up the Right Ascension of Betelgeuse (6 hr) and since Betelgeuse is on the meridian, the sidereal time is 6 hr. So using the table Solar Time Sidereal Time Date Midnight Man Hours Add to Midnight same same Protagonist 7 PM 6 hr Now complete the arithmetic problem in the Solar Time column. So, reading down Midnight plus what gets you to 7 PM? The number of hours to add is -5. So fill the 5 hours into the solar time column and the sidereal time column. Chapter 4 How Earth and Sky Work -The Effects of Time 6

48 48 Midnight Man Hours Add to Solar Time Midnight same Sidereal Time - 5 hr - 5 hr Protagonist 7 PM 6 hr Date Now complete the arithmetic problem for the Sidereal Time. What minus 5 gives 6? Eleven, of course. It is very common to make an error in this arithmetic. Try writing the number down in the top row. Then read aloud to yourself and see whether it sounds right. 11-6=6. OK Solar Time Sidereal Time Date Midnight Man Hours Add to Midnight 11 hr - 5 hr - 5 hr Protagonist 7 PM 6 hr So what is the date when it is 11 hr Sidereal Time at midnight? Eleven hours is half way between 10 hours and 12 hours, so the position of the Earth along its orbit is half way between Feb 21 and Mar 21. We approximate each month as 30 days. So half way between Feb 21 and Mar 21 is 15 days before the 21 st or the 6 th of March. (Ignore the 28 days or 31 day months. Solar Time Sidereal Time Date Midnight Man Hours Add to Midnight same same 11 hr - 5 hr - 5 hr Protagonist 7 PM 6 hr Mar 6 Now draw Mar 6 and one of the times. See whether the other time is consistent with the picture. If not, there has been some computational error. Orientation Practice Problems Set III 1) On April 7, what is the sidereal time at 11 PM? 2) On Aug. 21, what is the sidereal time at 9 AM? 3) If Orion is on the meridian, what is the sidereal time? 4) What time would you observe Gemini on the meridian on October 21? 5) If it is 13 hours on May 21, what is the solar time? 6) If it is July 4, and it is 10 PM, what is the sidereal time? 7) If you see Taurus, at 4 hours Right Ascension on the meridian and it is Feb. 21, what is the sidereal time? What is the solar time? 8) If it is 4 hr sidereal time and 12 noon, what is the date? 9) When you see Libra on the meridian at 3 AM, what is the date? 10) What is the Right Ascension of the Sun on Nov.7? Answers Set II Get within an hour or so. Be sure to get the AM and PM correct. 1) a 3 AM b 10 PM c 11:30 AM 2) a 7 AM b 10 AM c 2PM Chapter 4 How Earth and Sky Work -The Effects of Time 7

49 49 The direction of the Earth with respect to the Sun doesn t matter for the answer. There is no solar or sidereal time specified, so there is no protagonist to draw 7) About 10 AM Set III 1) 12 hr 2) 7 hr 3) 6 hr approx. 4) 5AM 5) 9 PM 6)17 hr 7) 4 hr, 6 PM 8) May 21 9) Libra is at about 15 hr, you can look this up on a map, so the sidereal time is 15 hr, the date is Mar 21 10) 15 hr Putting Latitude and Time Together As we consider what can be seen at any time, it is necessary to know the sidereal time, and the latitude. We have been computing the sidereal time and the range of declinations visible separately. To combine the two, use the horizon plot provided. This curve is meant to be overlaid on the mercator projection map of the entire sky. The heavy curve is the horizon. The values of marked near the curves distinguish the view from different latitudes. Diablo Valley College is at about +38 o. The rectangular grid on the page is the right ascension and declination grid; the same as on the map. The vertical line is the meridian. To use the curve for the Northern Hemisphere, match the bottom boundaries (not the edge of the paper, but the straight line at the bottom) of the map and the sheet with the curves. Match the meridian with the value of Right Ascension =Sidereal Time. Everything above the curve will be visible. Usually the curve will hang off to either the right or left edge and will leave the other side uncovered. To find the horizon on the uncovered side, remember that the map is supposed to be the surface of a sphere, so the right and left edges (Right Ascension 0 hr) really should be connected. The part of the horizon overlay which is hanging off will be on top of the rest of the map, where it is needed. Using the Visibility Curve We have been considering the effect of latitude separate from the effect of time. If you want to know exactly what can be seen, at any particular time, it is a little more complex. The curves on the next page are designed to be used to block the parts of the sky, on the mercator project, that you cannot. see at a given moment. Each curve is labeled with the latitude for which it applies. It is easiest to copy the page and cut along the line for your latitude with a scissor. This embodies the effect of your latitude. Be careful to follow the curve accurately, they cross. Compute the Sidereal Time for whenever you want to observe. Align the meridian on the visibility curve up on the Right Ascension equal to the Sidereal Time. Line up the edge of the grids on the mercator star map and the bottom of the visibility curve. For observing in the Northern Hemisphere, line up the bottom of the visibility curve grid with the 90 o line on the star map. For observing in the Southern Hemisphere, turn the sheet with the visibility curve upside down and line up the bottom of the curve with the +90 o line on the map. Chapter 4 How Earth and Sky Work -The Effects of Time 8

50 50 Chapter 5 Positions of the Sun and Moon Objects in our Solar System appear to move over the course of weeks to months because they are so close. This motion caused ancient astronomers to use the name planets, which means wanderers for the planets that they could see. Comets show tails and so were named differently. Asteroids, moons and planets past Saturn are too faint to see without telescopes, so they were unknown. Since Solar System objects move, we do not memorize their positions the way that we can for stars.. But we can understand how they move and specify their Right Ascensions and Declinations. The Solar Motion As we look from the Earth toward the Sun, it appears to be in front of the stars on the opposite side of our orbit. As the Earth orbits the Sun, this direction changes and the Sun appears to move in front of each of the constellations of the zodiac. The figure shows the view from above the Earth s North Pole. The Sun s Right Ascension is the Right Ascension BEHIND thesun as we look straight across our orbit. This direction is the same as the direction of the meridian at noon. Another way to look at it is that the Sun s Right Ascension is always 12 hours different from the sidereal time at midnight. The Babylonians started to specify the Sun s position using this concept. Earth s rotation. Each year the Sun appears to move all the way through the constellations, at an average rate of a little less than 1 degree each day. This small motion is not very noticeable as you watch the sky. It is a much smaller effect than the rising and setting of the entire sky due to the The star map that follows shows the Sun s path among the stars, the ecliptic. The Sun s path is called the ecliptic, because eclipses of the Sun and/or Moon occur when the Moon is nearly on the ecliptic. The rest of the planets and the asteroids are usually found near the ecliptic because the solar system is nearly a plane (flat). On the star map, the ecliptic is a wavy line. It goes north and south of the celestial equator due to the tilt of the Earth s axis. It is defined as the path of the Sun, so the Sun is ALWAYS on the ecliptic, NEVER anywhere else. If we know the Right Ascension of the Sun, from the date, we can find the point on the ecliptic with that Right Ascension, and read off the declination, at least approximately. Knowing the date. we can find the Sun's Right Ascension. Chapter 5 Astronomy 110 Motions of the Sun and the Moon 1

51 51 For example, if we know it is Feb 21, then the Right Ascension behind the Sun is approximately 22 hr. Earth has 10 hr at midnight,, so 22 hours is directly across from the Earth, behind the Sun. The declination ON the ecliptic, at 22 hours is about -12 o. This can be found by reading directly off the ecliptic curve. One way to remember the declination of the Sun is to remember the overall shape of the ecliptic curve and that the Sun is at 0h and 0 o on March 21, the traditional starting point of the year. The Sun is at positive declinations (in the northern hemisphere) from March 21 through September 23, the traditional summer months. It is at a southern declination during the rest of the year, the winter months. Check yourself: What is the Right Ascension and Declination of the Sun on Aug 21? To find the declination of the Sun on any day, it is necessary to remember the form of the ecliptic curve. Once the date is known, the Right Ascension of the Sun follows. Once the Right Ascension is known, there is only one point on the ecliptic for the Sun to be. Estimate the declination ON the ecliptic given the Right Ascension Seasons As you have doubtless noticed, it is colder and there are fewer hours of daylight (out of each 24) during the winter. The reason for this lies in the tilt of the Earth s axis. The Earth s rotation axis is tilted about 23.5 o compared to the direction perpendicular to its orbit. The axis keeps the same direction over the year, so sometimes one pole is tipped toward the Sun, and other times the other pole is. The distance to the Sun changes only slightly over the year, but the length of the daylight and the intensity of the light can change dramatically. The following figure shows how the tilted axis changes where the day/night line falls. On December 21, the entire north polar area is in shadow and the south pole area is in sunlight. On June 21, the situation is reversed. The area that the sunlight spreads over is larger on the part of the Earth is tilted away from the Sun, smaller when pointed toward So the hemisphere pointed away from the Sun gets fewer Chapter 5 Astronomy 110 Motions of the Sun and the Moon 2

52 52 hours of daylight and the light it does get is spread out more and is less intense than average. The hemisphere gets colder and colder until the Earth's motion on its orbit changes the situation. What about the effect of distance to the Sun? The earth s orbit is not exactly a circle. The distance varies by ±1.67%, with the closest point on the orbit occurring on Jan 6. This small distance change does not matter very much. It might seem that the southern hemisphere should have hotter summers and colder winters because the distance change accentuates its summer and winter. Actually, the land in the southern hemisphere is near the equator and there is a great deal of water. So the climate in the southern hemisphere is pretty mild. Other planets, notably Mercury, Mars and Pluto, have orbits with substantial eccentricity. So their distances from the Sun vary considerably and the amount of light they get does too. Precession Actually, the direction that our axis points is NOT always the same. It rotates slowly with a period of 25,800 years, The motion of the earth is shown in the figure. The direction of Earth s poles changes, but the stars do not. There is no start date or end date for the precession motion. It just continues. The polar star maps in chapter 2 show the path of the poles. When the Egyptian pyramids were built, the north star was the star Thuban, the brightest star in the constellation Draco (not very bright). The star Vega will be near the North Celestial Pole, the point above the Earth s North Pole in about half a cycle from now (about 13,000 years). There has been a conscious decision to maintain the Declination system with the ±90 o positions lined up with the poles of the Earth. The zero point of Right Ascension is the Sun s position on the Vernal Equinox (when the apparent position of the Sun moves north of the Celestial Equator). As the Earth s axis changes Chapter 5 Astronomy 110 Motions of the Sun and the Moon 3

53 53 direction, the coordinates of every object change. When accurate positions are published, they are given with the word Epoch. That is the Epoch tells what date the positions were for. It may seem that the changes introduced by precession are too small to matter. But the overall motion in declination is up to 47 o and the Right Ascensions change through the entire range of 24 hours. As the coordinates of an object change, whether it is always, sometimes or never visible from a location change. Precession changes correspondence between the position of the Earth in its orbit and the season. In the following picture, the constellation names show where the stars are with respect to the orbit. What should the date be at the position labeled? There may be no one right answer, but the convention that we now are living by is that the date will be MARCH 21. Why? Because it is the Vernal Equinox, the time when spring starts, the time when the Sun goes north of the Celestial Equator. A way to see this is to look at the Earth and the daylight parts. Currently, summer in the Northern Hemisphere occurs when the Earth is on the left, where the North Pole gets 24 hours of daylight. In 12,900 years, the position of the Earth where the North Pole has 24 hours of daylight, will be on the right of the picture. We have chosen to keep the dates in the year aligned with the seasons. So summer in the north will remain in June. This is called the Tropical Year There is no way to keep the dates and the seasons aligned and also keep the position of the earth in its orbit aligned with the dates. The Tropical Year, has leap year days (Feb 29) at the proper interval to keep the seasons and the dates aligned. It has days in a year. (To keep the same part of the orbit aligned with the same date we d use the sidereal year, days.). This combination of precession and the tropical year means that the Gemini and Taurus, which are seen near midnight in December will be seen near midnight in June in the future. You may have noticed that correlation of constellation and date from your horoscope are different from the Chapter 5 Astronomy 110 Motions of the Sun and the Moon 4

54 54 constellation behind the Sun on that same date. This is because the astrologers decided not to update the constellation correlation due to precession. The dates they use are from around the time of the Greeks (~2300 years ago). So what is your real sign? The Lunar Story The Moon orbits the Earth and moves around the Sun together with the Earth. revolves around the Sun (orbits) once per Earth rotates on its axis once per Moon orbits the Earth once per Time between first quarter and full moon Earth Phases of the Moon depend on the angle to the Sun. In the following picture, color the moon to show the bright and dark parts based on illumination from the Sun. Then draw the appearance of the Moon as seen from the Earth and name each phase (each shape/position in orbit combination). Chapter 5 Astronomy 110 Motions of the Sun and the Moon 5

55 55 The Moon s Right Ascension, that is, the Right Ascension of the part of the sky behind the Moon, can be found from the day of the year and the phase of the Moon. The Moon's phase tells the Solar time when the Moon is on the meridian. Pretend the protagonist has that Solar Time. Then use the date and the Solar Time, to find the Sidereal Time when the Moon, with its Right Ascension, is on the Meridian. Then Sidereal Time = Moon's Right Ascension. Use the lunar phase to create a protagonist who has the Moon on the observer s meridian. Then use the table to find the protagonist s sidereal time. This is the same value as the Moon s Right Ascension. Chapter 5 Astronomy 110 Motions of the Sun and the Moon 6

56 56 How often do Eclipses The inclination of the Moon's orbit, approximately 5 degrees, keeps the shadows of both Earth and Moon from causing eclipses unless the three bodies are nearly in a straight line. Most of the time the tilt of the moon's orbit keeps the Moon above or below the Earth-Sun line. Su For an eclipse to occur, the line of nodes of the Moon s orbit must be nearly along the direction toward and away from the Sun. (Nodes are the points where the Moon s orbit and the Earth s orbit cross and the line of nodes joins the two intersections. ) When the nodes are properly aligned, a Lunar and a Solar eclipse always occur, one at new moon, the other at full moon, about two weeks apart. Sometimes the alignment of the line of nodes is just right and three eclipses occur over one lunar month. Chapter 5 Astronomy 110 Motions of the Sun and the Moon 7

57 57 Once the two or three eclipses have occurred, the eclipse season is over. There cannot be any more eclipses until the line of nodes again points toward the Sun, nearly six months later. If the Moon s orbit did not change, the situation would be like the drawing immediately below. Can there be Eclipses Here? Can there be Eclipses Here? But, the tilt of the Moon s orbit changes both direction and angle. The direction of the tilt makes a complete rotation every years due to the gravity from the Sun and the other planets. As the direction changes, the line of nodes regresses, i.e. it goes retrograde and the alignment of the nodes for another eclipse season occurs less that 6 months after the previous one. The diagram below depicts the how the direction changes. The tilt of the orbit varies from about 9 minutes (0.15 degrees) on a 173 day cycle. Orientation Practice Problems Set IV 1) At what time is the first quarter Moon on the meridian? 2) If you can see a crescent moon and it is 5 AM, is it a waxing or a waning moon? 3) You want to fish in the darkness (so the fish won t see your boat, but you want to launch the boat in moonlight (so that you can see what you are doing), but after sunset. You will fish from 3AM until after dawn and you do not want to sit in the boat starting from sunset. 4) If it is full moon on Oct. 15, when is the new moon? 5) If there is a third quarter moon on April 1, when will waning crescent be? 6) If it is March 21, what is the Right Ascension of the third quarter moon? 7) If it is Oct. 7, what is the Right Ascension of the waxing gibbous moon? 8) If you see the waning crescent moon at 15 hr Right Ascension, what is the date? 9) When the waxing crescent moon is in Taurus, at 4 hr, what is the date? 10) What is the Right Ascension of the third quarter moon on May 7? 11) If there is a lunar eclipse on March 12, when can there be a solar eclipse? 12) What is the Right Ascension and declination of the Sun on Jan21? Answers Solar position on Aug 22 the Right Ascension is about 10 hr and the declination is about +12 o Answers Set IV 1) 6 PM 2) Waning 3) You want the moon to set at 3 AM, so it must be Waxing Gibbous. 4) Oct. 29 5) April 5 6) 18 hr 7) 22 hr 8) Treat it as though the protagonist were at 9 AM, so midnight is 9 hr earlier or at 6 hr, which makes it Dec ) April 7 10) 21 hr 11) Either 2 weeks before, two weeks after, or 5 and one half lunar months later (or earlier) 12) 20 hr and -20 O Chapter 5 Astronomy 110 Motions of the Sun and the Moon 8

58 58 Solar Eclipses Eclipse Predictions by Fred Espenak,NASA/GSFC Date Eclipse Saros Eclipse Central Geographic Region of Eclipse Visibility Type Magnitude Duration 2005 Apr 08 Hybrid m42s N. Zealand, N. & S. America [Hybrid: s Pacific, Panama, Colombia, Venezuela] 2005 Oct 03 Annular m32s Europe, Africa, s Asia [Annular: Portugal, Spain, Libya, Sudan, Kenya] 2006 Mar 29 Total m07s Africa, Europe, w Asia [Total: c Africa, Turkey, Russia] 2006 Sep 22 Annular m09s S. America, w Africa, Antarctica [Annular: Guyana, Suriname, F. Guiana, s Atlantic] 2007 Mar 19 Partial Asia, Alaska 2007 Sep 11 Partial S. America, Antarctica 2008 Feb 07 Annular m12s Antarctica, e Australia, N. Zealand [Annular: Antarctica] 2008 Aug 01 Total m27s ne N. America, Europe, Asia [Total: n Canada, Greenland, Siberia, Mongolia, China] 2009 Jan 26 Annular m54s s Africa, Antarctica, se Asia, Australia [Annular: s Indian, Sumatra, Borneo] 2009 Jul 22 Total m39s e Asia, Pacific Ocean, Hawaii [Total: India, Nepal, China, c Pacific] 2010 Jan 15 Annular m08s Africa, Asia [Annular: c Africa, India, Malymar, China] 2010 Jul 11 Total m20s s S. America [Total: s Pacific, Easter Is., Chile, Argentina] 2011 Jan 04 Partial Europe, Africa, c Asia 2011 Jun 01 Partial e Asia, n N. America, Iceland 2011 Jul 01 Partial s Indian Ocean 2011 Nov 25 Partial s Africa, Antarctica, Tasmania, N.Z May 20 Annular m46s Asia, Pacific, N. America [Annular: China, Japan, Pacific, w U.S.] 2012 Nov 13 Total m02s Australia, N.Z., s Pacific, s S. America [Total: n Australia, s Pacific] 2013 May 10 Annular m03s Australia, N.Z., c Pacific [Annular: n Australia, Solomon Is., c Pacific] 2013 Nov 03 Hybrid m40s e Americas, s Europe, Africa [Hybid: Atlantic, c Africa] 2014 Apr 29 Annular s Indian, Australia, Antarctica [Annular: Antarctica] 2014 Oct 23 Partial n Pacific, N. America 2015 Mar 20 Total m47s Iceland, Europe, n Africa, n Asia [Total: n Atlantic, Faeroe Is, Svalbard] 2015 Sep 13 Partial s Africa, s Indian, Antarctica 2016 Mar 09 Total m09s e Asia, Australia, Pacific [Total: Sumatra, Borneo, Sulawesi, Pacific] 2016 Sep 01 Annular m06s Africa, Indian Ocean [Annular: Atlantic, c Africa, Madagascar, Indian] 2017 Feb 26 Annular m44s s S. America, Atlantic, Africa, Antarctica [Annular: Pacific, Chile, Argentina, Atlantic, Africa] 2017 Aug 21 Total m40s N. America, n S. America [Total: n Pacific, U.S., s Atlantic] 2018 Feb 15 Partial Antarctica, s S. America 2018 Jul 13 Partial s Australia 2018 Aug 11 Partial n Europe, ne Asia Chapter 5 Astronomy 110 Motions of the Sun and the Moon 9

59 59 Date Eclipse Saros Eclipse Central Geographic Region of Eclipse Visibility Type Magnitude Duration 2019 Jan 06 Partial ne Asia, n Pacific 2019 Jul 02 Total m33s s Pacific, S. America [Total: s Pacific, Chile, Argentina] 2019 Dec 26 Annular m39s Asia, Australia [Annular: Saudi Arabia, India, Sumatra, Borneo] 2020 Jun 21 Annular m38s Africa, se Europe, Asia [Annular: c Africa, s Asia, China, Pacific] 2020 Dec 14 Total m10s Pacific, s S. America, Antarctica [Total: s Pacific, Chile, Argentina, s Atlantic] 2021 Jun 10 Annular m51s n N. America, Europe, Asia [Annular: n Canada, Greenland, Russia] 2021 Dec 04 Total m54s Antarctica, S. Africa, s Atlantic [Total: Antarctica] 2022 Apr 30 Partial se Pacific, s S. America 2022 Oct 25 Partial Europe, ne Africa, Mid East, w Asia 2023 Apr 20 Hybrid m16s se Asia, E. Indies, Australia, Philippines. N.Z. [Hybrid: Indonesia, Australia, Papua New Guinea] 2023 Oct 14 Annular m17s N. America, C. America, S. America [Annular: w US, C. America, Columbia, Brazil] 2024 Apr 08 Total m28s N. America, C. America [Total: Mexico, c US, e Canada] 2024 Oct 02 Annular m25s Pacific, s S. America [Annular: s Chile, s Argentina] 2025 Mar 29 Partial nw Africa, Europe, n Russia 2025 Sep 21 Partial s Pacific, N.Z., Antarctica 2026 Feb 17 Annular m20s s Argentina & Chile, s Africa, Antarctica [Annular: Antarctica] 2026 Aug 12 Total m18s n N. America, w Africa, Europe [Total: Arctic, Greenland, Iceland, Spain] 2027 Feb 06 Annular m51s S. America, Antarctica, w & s Africa [Annular: Chile, Argentina, Atlantic] 2027 Aug 02 Total m23s Africa, Europe, Mid East, w & s Asia [Total:Morocco, Spain, Algeria, Libya, Egypt, Saudi Arabia, Yemen, Somalia] 2028 Jan 26 Annular m27s e N. America, C. & S. America, w Europe, nw Africa [Annular: Ecuador, Peru, Brazil, Suriname, Spain, Portugal] 2028 Jul 22 Total m10s SE Asia, E. Indies, Australia, N.Z. [Total: Australia, N. Z.] 2029 Jan 14 Partial N. America, C. America 2029 Jun 12 Partial Arctic, Scandanavia, Alaska, n Asia, n Canada 2029 Jul 11 Partial s Chile, s Argentina 2029 Dec 05 Partial s Argentina, s Chile, Antarctica 2030 Jun 01 Annular m21s Europe, n Africa, Mid East, Asia, Arctic, Alaska [Annular: Algeria, Tunesia, Greece, Turkey, Russia, n. China, Japan] 2030 Nov 25 Total m44s s Africa, s Indian Ocean., E. Indies, Australia, Antarctica [Total: Botswana, S. Africa, Australia] [1] Greatest Eclipse is the time at minimum distance between the Moon's shadow axis and Earth's center. [2] Hybrid eclipses are also known as annular/total eclipses. Such an eclipse is both total and annular along different sections of its umbral path. Chapter 5 Astronomy 110 Motions of the Sun and the Moon 10

60 60 [3] Eclipse magnitude is the fraction of the Sun's diameter obscured by the Moon. For annular eclipses, the eclipse magnitude is less than 1; for total eclipses, greater than or equal to 1. The value listed is Moon s apparent diameter divided by the Sun s. [4] Central Duration is the duration of a total or annular eclipse at Greatest Eclipse (see 1). [5] Geographic Region of Eclipse Visibility is the portion of Earth's surface where a partial eclipse can be seen. The central path of a total or annular eclipse is described inside the brackets []. This information and more can be found at Lunar Eclipses Eclipse Predictions by Fred Espenak,NASA/GSFC Date Type Saros Fractional Eclipse Locations where visible coverage Duration (Totality Duration) 2005 Apr 24 Penumbral e Asia, Aus., Pacific, Americas 2005 Oct 17 Partial h58m Asia, Aus., Pacific, North America 2006 Mar 14 Penumbral Americas, Europe, Africa, Asia 2006 Sep 07 Partial h33m Europe, Africa, Asia, Aus Mar 03 Total h42m Americas, Europe, Africa, Asia (01h14m) 2007 Aug 28 Total h33m e Asia, Aus., Pacific, Americas (01h31m) 2008 Feb 21 Total h26m c Pacific, Americas, Europe, Africa (00h51m) 2008 Aug 16 Partial h09m S. America, Europe, Africa, Asia, Aus Feb 09 Penumbral e Europe, Asia, Aus., Pacific, w N.A Jul 07 Penumbral Aus., Pacific, Americas 2009Aug 06 Penumbral Americas, Europe, Africa, w Asia 2009 Dec 31 Partial h02m Europe, Africa, Asia, Aus Jun 26 Partial h44m e Asia, Aus., Pacific, w Americas 2010 Dec 21 Total h29m e Asia, Aus., Pacific, Americas, Europe (01h13m) 2011 Jun 15 Total h40m S.America, Europe, Africa, Asia, Aus. (01h41m) 2011 Dec 10 Total h33m Europe, e Africa, Asia, Aus., Pacific, N.A. (00h52m) 2012 Jun 04 Partial h08m Asia, Aus., Pacific, Americas 2012 Nov 28 Penumbral Europe, e Africa, Asia, Aus., Pacific, N.A Apr 25 Partial h32m Europe, Africa, Asia, Aus May 25 Penumbral Americas, Africa 2013 Oct 18 Penumbral Americas, Europe, Africa, Asia 2014 Apr 15 Total h35m Aus., Pacific, Americas (01h19m) 2014 Oct 08 Total h20m Asia, Aus., Pacific, Americas (01h00m) 2015 Apr 04 Total h30m Asia, Aus., Pacific, Americas (00h12m) 2015 Sep 28 Total h21m e Pacific, Americas, Europe, Africa, w Asia (01h13m) 2016 Mar 23 Penumbral Asia, Aus., Pacific, w Americas 2016 Aug 18 Penumbral Aus., Pacific, Americas 2016nSep 16 Penumbral Europe, Africa, Asia, Aus., w Pacific 2017 Feb 11 Penumbral Americas, Europe, Africa, Asia 2017 Aug 07 Partial h57m Europe, Africa, Asia, Aus Jan 31 Total h23m Asia, Aus., Pacific, w N.America (01h17m) 2018 Jul 27 Total h55m S.America, Europe, Africa, Asia, Aus. (01h44m) 2019 Jan 21 Total h17m (01h03m) c Pacific, Americas, Europe, Africa Chapter 5 Astronomy 110 Motions of the Sun and the Moon 11

61 61 Date Type Saros Fraction al coverag e Eclipse Duration (Totality Duration) Locations where visible 2019 Jul 16 Partial h59m S.America, Europe, Africa, Asia, Aus Jan 10 Penumbral Europe, Africa, Asia, Aus Jun 05 Penumbral Europe, Africa, Asia, Aus Jul 05 Penumbral Americas, sw Europe, Africa 2020 Nov 30 Penumbral Asia, Aus., Pacific, Americas 2021 May 26 Total h08m e Asia, Australia, Pacific, Americas (00h19m) 2021 Nov 19 Partial h29m Americas, n Europe, e Asia, Australia, Pacific 2022 May 16 Total h28m Americas, Europe, Africa (01h26m) 2022 Nov 08 Total h40m Asia, Australia, Pacific, Americas (01h26m) 2023 May 05 Penumbral Africa, Asia, Australia 2023 Oct 28 Partial h19m e Americas, Europe, Africa, Asia, Australia 2024 Mar 25 Penumbral Americas 2024 Sep 18 Partial h05m Americas, Europe, Africa 2025 Mar 14 Total h39m Pacific, Americas, w Europe, w Africa (01h06m) 2025 Sep 07 Total h30m Europe, Africa, Asia, Australia (01h23m) 2026 Mar 03 Total h28m e Asia, Australia, Pacific, Americas (00h59m) 2026 Aug 28 Partial h19m e Pacific, Americas, Europe, Africa 2027 Feb 20 Penumbral Americas, Europe, Africa, Asia 2027 Jul 18 Penumbral e Africa, Asia, Australia, Pacific 2027 Aug 17 Penumbral Pacific, Americas 2028 Jan 12 Partial h59m Americas, Europe, Africa 2028 Jul 06 Partial h23m Europe, Africa, Asia, Australia 2028 Dec 31 Total h30m Europe, Africa, Asia, Australia, Pacific (01h12m) 2029 Jun 26 Total h40m Americas, Europe, Africa, Mid East (01h43m) 2029 Dec 20 Total h34m Americas, Europe, Africa, Asia (00h55m) 2030 Jun 15 Partial h25m Europe, Africa, Asia, Australia 2030 Dec 09 Penumbral Americas, Europe, Africa, Asia Chapter 5 Astronomy 110 Motions of the Sun and the Moon 12

62 Chapter 5 Astronomy 110 Motions of the Sun and the Moon 13 62

63 Calendars and Time One of the earliest and most important functions of astronomy is to provide information for a calendar. Most civilizations want to keep track of the seasons, which depend in turn on the declination of the Sun. But the declination of the Sun changes slowly and it is not always obvious when the Sun gets to one or another extreme of its motion. On the other hand, changes in the Moon s phase are very obvious and easy to keep track of. It would be nice if these changes could both be used to keep track of things. Alas, the moon requires days to go through its cycle of phases, while the seasons (including accounting for precession) repeat every days, every tropical year. The lunar synodic period (as the time for phases is called) will not divide into the tropical year evenly, without a fraction of remainder. The tropical year is between 12 and 13 lunar months. Worse yet, neither the lunar month nor the tropical year is an integer number of days. But no one wants to start the year in the middle of the day (like 11 AM for example) and then try to keep track of the date. Ancient civilizations generally tried to reconcile the lunar and solar cycles. In Egypt, it was most important to keep track of the flooding of the Nile. This occurs on a yearly basis, due to rains flowing into the southern parts of the river. Seed had to be sowed before the flood covered the fields, providing the only water of the year. So it was necessary to know when the Nile would flood, well in advance of the actual event. The Egyptians used a 365-day solar year for the civil calendar. It was constructed by using 12 months of 30 days each plus 5 extra holiday days. This preserved the idea of the 29.5-day lunar month, but does not keep the lunar phases aligned with days of the month. As the ~1/4 day difference between the civil and tropical year accumulated, the Egyptians realized that they had a problem. They decided to use the heliacal rising of Sirius to trigger the year. Heliacal rising is when the body rises just before the glare of sunlight makes it impossible to see. The next day, the same celestial body will normally rise ~3min 56 seconds EARLIER and will be visible during the night for a while. This method of keeping the calendar IS affected by precession, but on a much longer time scale. 63 Q 1) If you used the Egyptian 365 day calendar, about how long would it take for the calendar to get 30 days out of alignment with the Sun? 2) If you used the Egyptian 365 day calendar, about how long would it take for the calendar to get a whole year out of alignment with the Sun? 3) What date would you estimate that Sirius rises just before the Sun these days? (Make a horizon for the Earth and move the earth around until the dawn horizon just touches the Sun. Now estimate the date?) 4) What date would you estimate that Arcturus rises just before the Sun these days? In 238 BCE the Egyptian calendar was reformed by including leap years, with 366 days, every fourth year, bring the average length of the year to days. Lunar calendars were in use in the Middle East at the same time. To keep the seasons aligned with the lunar months, some years need to have 12 lunar months, and others need to include 13. This is done by having another, intercalary month, every 2.8 years on the average. Calendars like the Chinese, Vietnamese, and Jewish ceremonial calendars all work this way. Each of these calendars has its own distinct new year time and scheme for intercalation. These calendars are never allowed to slip far from the seasons. The early Roman calendar also used lunar months, with additional intercalary months in the winter. By the time of Julius Caesar, several intercalary months had been skipped and the traditional March 25 new year had drifted far from the vernal equinox. Caesar reformed the calendar by introducing two intercalary months for that year and by adopting the scheme of 365 Chapter 6 History Calendars and Time 1b

64 days (some 30 and some 31 day months) with one leap year every 4th year. This is called the Julian calendar. 64 The Julian calendar has an average year of days, assuming that the leap year is properly observed. But the tropical year, the year that stays aligned with the seasons, is only days, some days shorter. On the average the Julian calendar runs 1 full day behind the tropical year after 1/. 008 = 125 years. After 1500 years, the Julian Calendar would predict vernal equinox 12 days later than it actually occurred. Perhaps no one would have cared, but the Catholic Church needed to compute when Easter would occur. Traditionally, Easter is on the Sunday, following the Full Moon, which follows the Vernal Equinox. This would make it 2 days after the Passover Seder (when the Last Supper would have occurred). It would be easy to observe the vernal equinox, then the full moon, and then have Easter (assuming that there was a way to correct for bad weather). But people wanted to predict when Easter should be celebrated years in advance. Many numerical schemes were tried, and recorded. But the discrepancy between the Julian calendar and the Jewish lunar calendar, made it obvious that there was a problem. According to the Julian calendar, the vernal equinox got earlier and earlier in the year. Several attempts were made to correct the problem. People were not even certain that the tropical year was constant. Eventually in 1582 Pope Gregory declared a solution based on the findings of a commission he had called. In February 1582, a papal bull was sent instructing people on how to revise the calendar. At that time, January 1 became the start of the year. The decision was that the day following October 4, 1582 would be October 15, At that time the current leap year scheme was adopted Gregorian Calendar Leap Years February 29 occurs in years -divisible by 4 (with no remainder) EXCEPT -century years if they are not also divisible by 400 As you may imagine, it was hard for countries to respond to a calendar change within the same year, even if a country meant to do it. Some Catholic countries adopted the Gregorian calendar immediately. Others adopted it later. The history timeline includes some of the dates. Non-Catholic countries weren t about to do what the Pope said, regardless of whether it was right or wrong. For many years different countries used different dates. So if you read European history, the dates may be in OS, old style (Julian Calendar) or NS (new style) Gregorian dates. Countries switched to NS one by one. Britain and the colonies changed in 1752; Russia changed in When each area switched, the number of days skipped was altered to bring the calendars all together with the same dates. The Gregorian calendar isn t perfect. It is still 26 seconds too short. But the day is getting longer as the Moon spirals away. So the discrepancy is getting smaller. There are several calendars in use that don t use the tropical year as a base or reference. The Islamic calendar uses 12 lunar months and never 13. So the year is complete in less than a solar year and the holidays slip backward through all seasons. The month traditionally begins with the actual sighting of the crescent moon as soon after new moon as is possible. To keep a calendar that approximates this month, the 12 months have 29 and 30 days. The Mayans kept at least three different calendars. One was a 365-day solar calendar, consisting of 18 months with 20 days each. Another was made of 13 cycles of 20 days each for a total of 260 days. These two calendars come into alignment every 52 years, called a calendar round. The Mayans also kept a long count consisting of a cycle of 5130 years. It is composed of shorter 20-day cycles with repeats of 20 s and 13 s. Chapter 6 History Calendars and Time 2b

65 Traditionally, classical period Mayans cosmology states that 3 of these great cycles had been completed before their current cycle (which started in 3114 BCE and ends in 2012). The entire world is supposed to end and be renewed at that time. By this time, you may be wondering how astronomers put up with all this complexity. When we want to find the orbit of a comet, for example, we may have data from previous years. But to know how long ago that really was, we would need to take into account the number of February 29 s etc. that have occurred in between, whether daylight savings time was in place and how many time zones between the observation locations. Astronomers don t mess with this. They use a system called Julian Day. It has not months, weeks or years. It just counts days since noon on Jan 0 at Greenwich England in 4713 BCE. This day was chosen based on the idea that it is unlikely that a historic account will be found (on Earth) which occurs before then. Jan 1, Midnight of 2000 (at Greenwich) was Within each day, astronomers use decimals (like JD ). The second, based on vibrations of a Cesium atom, is the way absolute time is measured. The Earth s orbit and the spin are not exactly constant. The length of the nominal day was set in the 1870 s, so the reference day is not changing due to tides. 65 Chapter 6 History Calendars and Time 3b

66 66 Chapter 6 History of Astronomy-Ancient Times through Galileo In this chapter we will be examining the way people s concept of the Universe has evolved. Some peoples have simply tried to predict what the sky would do and when it would do it. Others have tried to understand the Universe by making a model and comparing what we observe with the model s predictions. Comparing predictions from models with observations and experimental results is the way that science proceeds today. There is a timeline at the back of this chapter. It includes several traditions of astronomy divided by geographic location. Many of these traditions were developed independently. Wherever people looked at the sky, they found a need to explain what they saw. Today s concepts have evolved from Mesopotamia through Greece to Europe. What did they see? They saw everything that we can see today without a telescope. This list includes; stars and planet rising and setting; changing points of sunrise and sunset, phases of the Moon, alignment of the Sun, Moon and planets compared with the stars, comets, eclipses. We will be able to fill in the first part of the table from what was learned in chapters 1 through 5, and the second part by the time that we finish chapter 6. Let us follow the chronological development. They seem to have noticed the different positions Archeoastronomy is the study of astronomy without written records. The date archeoastronomy ended depends strongly on the culture involved. The Babylonians had cuneiform writing as early as 4500 BCE, while Hawaiians did not have writing when they were visited by Captain Cook in 1779 CE. Archaeoastronomers often infer astronomical significance by finding parts of structures aligned with rising, setting, or (more rarely) meridian passage of the Sun, moon, planets or bright stars. In the Great Plains (both the US and Canada), we have found ~50 structures called Medicine Wheels. These are made of piles of stones laid on the ground in patterns with spokes and circles. Typical diameters of the Medicine Wheels are ~50 feet with heights of the rock piles of less than 2 feet. The number of spokes and circles in each varies, but alignments from one circle to another often indicate rising and setting points of bright stars, such as Sirius and Aldebaran. We don t know their purpose. Further south, native Americans living in pueblos in Arizona and New Mexico used the position of sunset compared to distant hills to keep track of planting dates for corn. We have at least one case where these positions were explained to an outsider. Natives of the American southwest Chapter 6 History of Astronomy-Ancient Times through Galileo 1

67 67 Motion 1. Earth Spins Observable Consequences, Remember to Identify all that Apply 2. Earth Orbits 3. Earth Precesses 4. Moon Orbits 5. Moon Spins on its Axis 6. Planet Spins on its Axis 7.Planet Orbits Chapter 6 History of Astronomy-Ancient Times through Galileo 2

68 68 Phenomenon 1a Stars Rise and Set Time for Complete Cycle Explanation Current Model Explanation, Ptolemy s Model 1b Sun Rises and Sets 1c Moon Rises and Sets 1d Planets Rise and Set 2a Sun Moves Along the Ecliptic 2b Sunrise and Sunset Points Change 2c Earth has seasons 3a Planets have day and night 4a Planets move along the ecliptic 4b Planets show retrograde motion Some motions have a range of values, if so, say so. Chapter 6 History of Astronomy-Ancient Times through Galileo 3

69 69 If the explanation won t fit, use a separate sheet. built many buildings with small windows aligned to specific sunrise and sunset dates, typically the solstice and equinox. e observer. On Fahade Butte near Chaco Canyon New Mexico, we have found two spirals carved into rock. This is sometimes called the Sun Daggar because slabs of rock in front of the spirals cause daggers of light to cut down through the larger spiral at noon on the summer solstice, through the smaller spiral at noon on the equinox, and cause daggers to stay out of both spirals at winter spiral. The edge of the slabs of rock cause the shadow of the rising moon to fall in the middle of the spiral at extreme northern moonrise (Moon at o declination) and in the middle of the spiral at minimum extreme northern moonrise (Moon at o declination). Fahade Butte is near Chaco Canyon, the site of Pueblo Bonito a great Kiva with hundreds of rooms. Chaco Canyon was a major trade and cultural center from about 1100 to CE. Today s Mexico, Guatemala and Belize were home to a sequence of related cultures. The Olmec, Toltec, Mayan, and Aztec cultures seem to have evolved from one another. They built stepped temples and ceremonial cities with similar alignments. The Mayans, in particular predicted Venus positions, eclipses and kept a cyclic calendar. They had writing and we are currently interpreting their writings. Some of their writings are carved into stone, others were painted on bark paper. Unfortunately, nearly all of the bark paper writings were burned by the settlers. Today only four Mayan codices written on bark paper survive. They were exported to Europe and not destroyed. Chapter 6 History of Astronomy-Ancient Times through Galileo 4

70 70 The Dresden Codex, so named for the city where it is stored, includes tables of eclipses and of Venus positions. In Britain, Ireland, and Brittany (northwestern France, near the English channel), people constructed passage graves, mounds, stone circles (made of worked stones set into the ground), and large combined constructions like Stonehenge prior to 2000BCE. There is evidence that these replace earlier, similar constructions, made of timbers. Statistical analyses of these constructions show some alignments to the solstice sunrise and sunset, and possibly some to the extreme north and south positions of the full moon rise and set. Over 1000 constructions are known today. Stonehenge, with a diameter of nearly 100 meters is one of the more impressive, though it has neither the largest diameter nor the largest single stone. Stonehenge was constructed in three stages, over a period of more than 1000 years, starting around 3000BCE. Some of its materials were brought from as far away as Wales. The tradition of astronomy leading to our present approach began with the Babylonians. The region they occupied is between the Tigris and Euphrates rivers, where Iran and Iraq are today. The earliest Babylonian writing probably dates to about 4500 BCE. The wrote using cuneiform, a combination of phonetic and ideogram representations was made of lines and triangles impressed into clay. The clay was dried and hundreds of thousands of examples remain today. The Babylonians named many of the constellations of the zodiac, the constellations along the ecliptic. They kept records of the motion of the Sun and the planets going through these constellations and created formulae predicting just where planets would be. We know because tables of the positions of Venus and Jupiter have been found, as have the formulas. How long ago this activity started is less clear. The Babylonians kept dates in terms of number of years into the reign of each king. The problem is that we do not yet know the entire sequence of kings and the lengths of time that they reigned, so we don t know the dates for sure. Documentation of phases of the Moon and stars used to tell the time of day are found in a book called Enum Elish, which dates to around 1600 BCE. By the 700's BCE, regular observations of the planet's positions and of eclipses were made and recorded. Chapter 6 History of Astronomy-Ancient Times through Galileo 5

71 71 Babylonian astronomy stressed computing where things will appear in the sky. They used placeholders, like our 1 s place and 10 s place. But the Babylonians used 360 divisions for a circle and further divisions of 1/60 for each placeholder. This is where our current system of degrees, minutes, and seconds began. This system of numbers is much easier to use for computations than are the Greek (and Roman) number systems. The Babylonians made careful observations and developed formulae predicting planet positions to support their astrological practices. The astrological predictions were considered so useful, that the observations and predictions continued even when the country was conquered. The Babylonian view of the cosmos included a flat earth and roof like heavens called the firmament arching above. This model doesn t lead to mechanisms producing the observed motion of stars or planets. It is, however, very similar to the model underlying the Bible and is similar to some Egyptian and Greek ideas. As the Babylonians continued their observations, civilization grew in the Greek mainland. The earliest indications we have of the state of Greek astronomy are in the Iliad and Odyssey. They include snippets of information such as that one should plant when the Pleiades rise at dawn. The Iliad and Odyssey were developed over hundreds of years, but dates for the completion of the text is usually somewhat after 1000BCE. Hesiod s Works and Days (~ 850BCE) includes a more formal type of star calendar called a parapegma. The parapegma associates the days of the year to plow, plant etc. with heliacal rising (rising right before the Sun, so that the body is just visible before daylight) of specific stars. Because of precession, the times of the year associated with these star risings are not now exactly at the same season. The Greeks got the idea to form theoretical models of the cosmos. Information about their concepts has come down to us, but we have none of the Greeks original writings prior to Plato, Around 600 BCE, a trio of Greek expatriates (folks who left Greece) lived in Miletus, a former seaport in Asia Minor (today 8 miles inland in Turkey). They were the first to formulate theoretical models of the cosmos. Thales( BCE), the earliest of the Miletus astronomers, was reputed to have cornered the market on olives. He thought that water was the most important of the four elements (earth, air, fire, water). His model does not include any specific mechanisms to produce motions of the stars or the Sun or Moon On the other hand there was an eclipse in 585 BCE, and Thales is said to have predicted it and frightened Miletus' enemies in a battle. Chapter 6 History of Astronomy-Ancient Times through Galileo 6

72 72 Anaximander's model is striking because it uses an entire sphere of stars. The star sphere (Primum Mobile) causes the stars to rise and set while Earth stands still. He thought that the surface of the Earth is the horizontal part of a cylinder. He modeled the stars as holes in the Celestial Sphere, illuminated by fire surrounding the sphere. He modeled the motions of the planets, the Sun and the moon as imagining them carried by tilted rings. His tilted rings are similar to the observed paths of the planets, tilted compared to the celestial equator. The source of light for the Sun, Moon, and planets was compressed air, iwithn the tilted ring. The compressed air exits by a hole where it burst into fire, becoming visible. This model is meant to have no beginning or end in time, but to be perfectly regular and repeatable. Perhaps this was a reaction against the unpredictable mythological Greek gods. Ionian School ANAXIMANDER, MILETUS ( aprox BCE) * * * LIGH FROM SUN OR PLANE * * Fire surrounds the sphere light shines through star CYLINDRICAL EARTH, SUPPORTED BY AIR, TOP MAY BE CONVEX TRANSPARENT RING OF AIR, TURNS TO FIRE AT OUTLET WHERE SUN OR PLANET IS SEEN SEPARATE RING FOR EACH CELESTIAL BODY Check Why does Anaximander need several Why can he use rings for the planets, Sun, rather than entire Why are the rings tilted compared to the Is there any evidence of a cylindrical Does this model make the stars rise and COSMOS HAS NO BEGINNING OR END, BUT CONTINUES INFINITELY IN TIME CYLINDRICAL EARTH, HEIGHT = 1/3 BREADTH, PEOPLE LIVE ON TOP SINCE EARTH IS IN THE CENTER, THERE IS NO DIRECTION TO FALL SEPARATE CONCENTRIC SPHERES FOR SUN ( FURTHEST), STARS NEAREST SUN, MOON, STARS ALL ILLUMINATED BY FIRE COMING THROUGH RING SUN RING DIAMETER 27 TIMES EARTH DIAMETER SUN HOLE SAME SIZE AS EARTH MOON RING, DIAMETER 19 TIMES EARTH DIAMETER Anaximenes model, although later in time than Anaximander s is simpler and predicts less. Pythagoras ( BCE) lived nearly contemporaneously. He moved to Croton (~540 BCE), on the instep of Italy and founded a school and religion. It was a religion with secrets, mathematical secrets. Because of the secrecy, we do not know exactly what Pythagoras discovered and what was discovered by others later. Pythagoras is thought to have discovered the relation between the squares of the sides of a right triangle and the square of the hypotenuse (c 2 =a 2 +b 2 ). He also discovered that the value of 2 is an irrational number. That means it cannot be represented exactly by a fraction. At that time the Greeks thought that every number could be represented exactly by the fraction. So they did not welcome the discovery of a value which did not fit in their worldview. The Pythagoreans thought that the planets were small bodies carried on spheres centered on the spherical Earth. They thought that the sizes of the planets spheres were not arbitrary. Rather they were determined by the relations between the notes of musical chords. If one were to listen Chapter 6 History of Astronomy-Ancient Times through Galileo 7

73 73 (and realize that the ever-present background was the music), one would be able to hear the Music of the Spheres. At least one of their models, attributed to Philolaus, hypothesized that the Earth was not exactly at the center of the Universe. Rather the model treats the Earth as moving around a central spindle of fire every day. When we face the Sun, it is daytime. When we face away, it is night. The Sun shines by reflected light from Hestia. We, Earthlings, don t see the spindle of fire because the counter earth, called the Anticthon, stands between Earth and the fire. The system includes 10 bodies total, including the Sun, Moon, Earth, planets, Antichthon, and spindle of fire. Plato ( BCE) is the first of the Greeks whose writings we have today. Plato was primarily a philosopher. He thought it was not worthwhile to make observations, because only external features can be detected. But Plato was interested in the true nature of things, which he thought would never be discovered in this way. On the other hand, Plato was aware of the Pythagoreans and probably knew about Philolaus model. Plato didn t write any astronomy book. On the other hand, he described the natural world in parts of his Dialogues and Timaeus. They were written about 20 years apart, so it is possible that his opinion changed between the times of writing. Timaeus includes a long discussion by a person who is identified as a Pythagorean. Whether Plato actually wrote Timaeus is highly questionable. Plato had the idea that the part of the Earth known to the Greeks (the Mediterranean) was just a small part of the Earth and there might be other civilizations on the Earth, of which the Greeks were unaware. (Was he correct?) Chapter 6 History of Astronomy-Ancient Times through Galileo 8

74 74 In Timaeus, a Pythagorean (NOT Plato) describes the physical universe as rotating around a central spindle of fire which keeps it together. The planets move on concentric spheres or lips or rims with the stars on the most distant rim. The rim where the stars are mounted moved the opposite direction to the motions of the other bodies (Sun, Moon and planets). This is to make the entire sky rise and set (apparent westward motion) while the planets and Sun moves eastward against the star background. Plato seems to have known about Philolaus idea that the Earth was not exactly at the center of the Universe, but rejected the idea. Plato assigns a distance order to the planets, based on the times they take to complete their path through the sky. He assigns two series of numbers to their distances and These sequences do not correspond to either the actual distances or the actual times to move along the ecliptic. The impression of later workers is that Plato and/or Aristotle were convinced that any valid model of the universe must have the Earth at (near) the center (see Aristotle for why). They did not distinguish the Sun or Moon as being very different from among the other bodies, but all the bodies were expected to move in circles at constant speed around the Earth, which stands still at the center. It is not clear that either Plato or Aristotle ever wrote this exactly, but later workers tried to make models with the Earth at the center and only circular motion. Aristotle ( BCE) was Plato s student, but unlike Plato, he did believe that science was important and wrote many books about science. Aristotle generally believed that it was worthwhile to observe the physical world, to find out what it would do naturally. He did not set up controlled experiments (but that would have subjected the situation to an unnatural situation). Aristotle had the idea that the world is made of Earth, Air, Fire, and Water. He distinguished between areas below the Moon, where things can change and the unchanging world of the heavens starting at the Moon and going further out. The Earth is composed of heavy things (earth and air) which sink to their natural places as close as possible to the center of the Earth. The heavens consist of air and fire which both float upward. He did not believe that there is any empty space. Wherever there was no obvious material, he thought that space was filled with ether (not the same as the anesthetic). Aristotle tried to find the nature of things. To do that, he observed them, but did not try to do experiments or control their behavior. Aristotle, and his predecessor Eudoxus, tried to describe all of the motions of the heavenly bodies. Speaking generally, they and all the ancients tried explain the following motions: a) Rising and Setting of Sun, Moon and planets b) Sun, Moon and planets moving eastward among the stars, completing their paths around the sky in times from 27.3 days for the Moon, to years for Saturn (slower than the rise and set) c) Planets moving retrograde when opposite the Sun or when at inferior conjunction (between Sun and Earth) d) Sun, Moon, and planets moving eastward with varying speed at specific repeatable parts of the sky (as measured by the position relative to the constellations of the zodiac) Formulating a model to predict the apparent positions of the heavenly bodies occupied astronomers for nearly the entire next 2000 years. Aristotle thought of physical objects to make the motions occur. He did not believe that there could be empty spaces. Other astronomers were more satisfied with purely mathematical models to predict the positions. Most ancient astronomers, including Aristotle, thought that the heavens were moved by a star sphere called the Primum Mobile (meaning prime mover). The purpose of the Primum Mobile is both to get everything moving and to cause rising and setting. Every day (23 hours 56 minutes) Chapter 6 History of Astronomy-Ancient Times through Galileo 9

75 75 the star sphere moves WESTWARD around the stationary earth dragging all the other objects with it. The Primum Mobile was considered so basic, that most authors do not even mention it. Eudoxus realized that combinations of circular motion with different axes can produce retrograde motion as seen by the Earth at the center. Eudoxus thought of a model using 27 spheres to carry the 5 planets, the Sun, and the Moon around the Earth. Aristotle built on this model, and expanded it to 55 spheres plus the Primum Mobile. The planets, Sun, and Moon were envisioned as small things fixed to the spheres. Aristotle thought that spheres would spin forever, so there would be no problem in keeping the bodies moving. Aristotle envisioned the spheres being made of crystal (rock crystal, like quartz) so that they would be transparent. Primu Mobil outermost carries bodie * * * * Aristotle ( BCE) Model of Tilt of axes of spheres causes varying of motion and varying directions. Can cause motio Cut-away of spheres for Earth at center, neither rotating nor Bod Spheres Eudoxus Mode Spheres Aristotle s Counte rotator Star 1 Not counted Satur Jupite Mar Venu Mercur Su Moo Total Tota Aristotl Mode It may seem awkward to have everything move around the Earth, rather than assuming that the Earth spins. Until telescopes were in use (1600 s CE), there was no reason for people to believe that the planets were anything but little lights. So it was far easier to move them than to move the heavy Earth. In the 200 s BCE. Aristarchus figured out the distances to the Sun and the Moon. The combination of their distances and their appearance indicate that the Sun and Moon are large. This may have been what led Aristarchus to believe that the Earth orbits the Sun. Most people thought that the Earth could not be moving because - we cannot feel it move - we would fall off if the Earth were moving - if the Earth moved, we would notice that we get closer to the stars on one side of the sky for part of the year, but we don t - if the Earth moved, we would see parallax, but we don t Chapter 6 History of Astronomy-Ancient Times through Galileo 10

76 76 -Besides, the Universe is made for mankind, so why would the Earth move? So all of these arguments combined to make most folks (including Aristotle) believe that the Earth did not move. Why didn t the stars look different on the different sides of the orbit? And why didn t they observe parallax as the Earth moves around the Sun? These effects are far smaller than people expected and are very hard to see. It actually took until 1838 CE for anyone to see parallax of any star. Then they picked a nearby star and lined themselves up with a chimney to keep things straight. The very largest parallax angle of any of the stars, is about 1/5000 degree. So it is understandable why ancient people did not observe parallax of the stars. Aristotle believed that the Earth is at the center of the Universe and does not move. He reasoned that if the Earth moved, we would see parallax of the stars and the distances between the stars would appear smaller on the side of the sky that Earth is closer to. Aristotle and other Greeks reasoned that Earth must be spherical due to the following observations. First, different stars are seen at different latitudes on the curved earth. If the Earth were flat, the same stars would be seen. Second, you leave an object it appears to disappear from the bottom up, due to the curvature of the Earth. On a flat Earth, things would just fade into the mist. During lunar eclipse, the Moon goes into the shadow of the Moon and the curvature of the shadow can be seen. Regardless of what part of the Earth faces the Sun and of the declination of the Moon, the curvature of the shadow is the same. If the Earth were any shape other shape, the shadow would have a different curvature at least some of the time. Aristotle wrote many of his ideas in a book called Physics. It was lost to Western Europe during Chapter 6 History of Astronomy-Ancient Times through Galileo 11

77 77 the Dark and Middle Ages, but was retained by Islamic astronomers. When it was later translated to Latin, it became the standard in Europe until after 1600CE. Renaissance professors were required to teach their students how to interpret it. Aristotle s ideas included the following. - Heavy things fall faster than light ones - It is necessary to keep pushing on something (on Earth) to keep it from stopping - When you shoot an arrow, the air keeps pushing the arrow to keep it going - When the arrow is ready to fall, it just drops vertically - Nothing beyond the Earth s atmosphere changes Which of Aristotle s ideas is correct? Aristotle was convinced that the Earth is at the center of the Universe, unmoving. But Aristarchus( BCE) believed that the Earth orbits the Sun. We do not have the book, or books which explain why Aristarchus thought the Earth moves. The idea was not accepted by other astronomers at the time. We do have a book of Aristarchus called On the Distances to the Sun and Moon. In it he finds the sizes of and distances to both bodies using the methods below. How did Aristarchus measure the distance to the Moon and its size? When we look at the Moon (or the Sun) in the sky, we see that each of them is about 1/2 o in diameter. Aristarchus measured the time it takes the moon to move through the Earth s shadow during a lunar eclipse and compared that time to the time for the Moon to complete an orbit.. He formed the ratio Aristarchus knew the times for orbit and eclipse and he knew the 360 o, so he solved for the size of the Earth s shadow. He found that it takes up about 2 o along the Moon s orbit.. Since the Moon takes about 1/2 o, the Moon is about 1/4 as large as the Earth. Not a small thing at all. Using the fact that the circumference of a circle is 2πR and the moon diameter (the 1/2 o ) takes about 1/720 of this distance, we can find that the Earth diameter is about 4/ 720 or 1/ 120 of the distance to the Moon. We could say the Moon s distance is about 60 times the Earth s radius. Aristarchus also measured the distance to the Sun In terms of the distance to the Moon. He got the idea that if he measured the angle between the Sun and Moon at the very moment when the Moon was either first or third quarter, he knew that the triangle with the Sun, the Moon and the Earth at each vertex would have a right angle (90 o ) at the center of the Moon. He measured the. Chapter 6 History of Astronomy-Ancient Times through Galileo 12

78 78 angle between the Sun and Moon as seen from the Earth. Aristarchus measurement, that the Sun is 1200 Earth Radii away, is impressive, but wrong. Interestingly, it was not challenged for at least 1800 years. The measurement was wrong because the angle at the Earth should not be 87 o (leaving 3 o for the angle at the Sun). The angle at the Earth should have been 89 5 / o 6 leaving 1 / o 6 for the angle at the Sun. The corrected measurement puts the sun 400 times as far as the Moon or 400x60=24,000 times the Earth radius. Since the Sun appears to be 1/2 o across, the great distance means that the Sun is far larger than the Earth or Moon. So from Aristarchus point of view, it would have made sense to move the Earth rather than move the Sun and Moon. Aristarchus did not know the size of the Earth. It took Eratosthenes to find it. Eratosthenes had heard that at Syene, upriver on the Nile, the Sun is at the zenith at noon one day of the year. Eratosthenes lived at Alexandria, on the Mediterranean Sea, where he knew that the Sun never reaches the zenith. Eratosthenes believed in the spherical Earth, and he assumed that the sunlight comes in parallel rays. So he expected that the difference in the direction of the sunlight was due to the curve of the Earth. He got the idea to measure the angle between the surface of the Earth at Alexandria and at Syene. Eratosthenes stuck a stick, called a gnomon, into the ground at Alexandria. Sunlight came in at an angle to the stick, causing a shadow. He measured the length of the stick and the length of the shadow. There was a 90 o angle between the stick and the shadow. So he could complete the triangle and measure the angle at the top. He got an angle of 7.1 o. sunlight makes the hypotenuse 90 o gnomon shadow The angle between the stick and the sunlight is the same as the angle at the center of Earth with one end at Alexandria and the other at Syene. Eratosthenes knew that the ratio of the distance between Alexandria and Syene (the 5000 stades) to the Earth s circumference is the same as the ratio of the angle at the center of Earth to 360 o. We do not know the exact location of the gnomon at Alexandria. Neither do we know the exact size of the stade. So we do not know exactly how accurate Eratosthenes measurement was. Estimates are that it is accurate to within ~10%. So by the 200 s BCE, the Greeks had a good idea of the size of the Earth and the Moon. They know that the Earth was not nearly the largest part of the Universe. Aristotle s model for planetary motions did not survive to modern times. The tilted, counter rotating spheres were replaced by a method to produce retrograde motion using epicycles, that is, circular motions on top of other circular motions. Hipparchus (~150BCE) developed this method, first discovered by Apollonius (~225 BCE) to model the Universe. Hipparchus also made the first star catalog to use the magnitude scale of star brightness and he realized that the position of the Sun at the Equinox was changing. This led Hipparchus to the discovery of precession. Chapter 6 History of Astronomy-Ancient Times through Galileo 13

79 79 Hipparchus and Ptolemy s Models Both Hipparchus and Ptolemy used four separate features to explain the motions of the planets (and Sun and Moon) that they had observed. The model is explained, feature by feature below. Hipparchus and Ptolemy (and Aristotle and earlier astronomers) used the Primum Mobile to cause all bodies to rise and set daily. All the celestial bodies were carried by the Primum Mobile. The separate motions of the planets, Sun and Moon were imposed on top of the motion of the Primum Mobile. To envision the way that the Primum Mobile works, imagine a merry-go-round. In Hipparchus and Ptolemy s view the Earth is in the middle not moving. This is like the merry-go-round operator standing in the middle on the ground, unmoving. The floor of the merry-go-round moves quite fast carrying everything on the ride past the operaor. The floor is like the Primum Mobile. As it goes by, the horses and kids pass in and out of view, like rising and setting. To model the motion of each body near the ecliptic, each body was given a separate path around the Earth, RELATIVE to the Primum Mobile. This path, called the deferent, carries the bodies eastward through the sky, near the ecliptic. Continuing to compare the model to a merry-go-round, you are still the operator. Motion of the planets on the deferent is like the motion of people walking on the merry-go-round floor in the direction opposite to the spinning. The people go slowly compared to the floor. Each time the floor passes you (rising and setting), the people are at a little different position compared to the fixed Chapter 6 History of Astronomy-Ancient Times through Galileo 14

80 80 horses and poles. Eventually the people go past every one of the horses and return to the same position. This is like each of the planets (or the Sun or Moon) completing its path along the ecliptic. To make the body move retrograde, each body was modeled moving on an epicycle, on top of the deferent. So for Each body, Hipparchus defined the relative size and timing of the Primum Mobile, a deferent, and an epicycle. Returning to the merry-go-round model, the epicycle is what would happen if the people walked in little circles as they walked along. Some of the time the person is moving backward part of the time, when compared to the horses etc (all the time the floor is causing the person rise and set). The epicycle model, with the Primum Mobile, an epicycle, and a deferent for each body produces rising and setting, motion of the planet eastward through the stars, and in regular retrograde loops. But each planet does not have the exactly the same retrograde motion every time. Hipparchus knew this and modeled the irregular speed and loop size by moving the deferents so the Earth was off-center (called eccentrics). Hipparchus writings have not survived. We know about his work from the work of other astronomers, especially from the work of Ptolemy ( CE). Ptolemy s work has survived. Ptolemy s most famous work is the Almagest, a compendium of models using epicycles, a revised star catalog, revised estimates of the rate of precession, and information on how to use the computations for astrological purposes. Chapter 6 History of Astronomy-Ancient Times through Galileo 15

81 81 Ptolemy used the same kind of model as did Hipparchus for the Primum Mobile, the deferent, and the epicycle. He used equants to cause both the speed of motion through the stars and the size of the retrograde loops to vary. The Earth is to one side of the center and an imaginary point called the equant is at an equal distance on the other side. The motion of the center of the epicycle on the deferent has an angular speed which appears to be constant from the equant. (The actual speed in space would not be constant.) Since the Earth is not at the equant, the speed of the center of the epicycle appears to change, going more slowly when the planet is further from the Earth and more rapidly when the planet is nearer the Earth. Chapter 6 History of Astronomy-Ancient Times through Galileo 16

82 82 Ptolemy understood that Mercury and Venus never appear at midnight. Instead they are roughly in the same direction as the Sun (to within about 27 o for Mercury and to within 46 o for Venus. To ensure this alignment, Ptolemy introduced a linkage between the Sun and each of these inner planets to ensure that they would stay in the same part of the sky. It is not clear whether he believed the linkage to be a physical object, or just a mathematical concept. Ptolemy figured out the sizes, start times, and the speeds for the Primum Mobile, and the deferents, epicycles and equants for each of the planets and the Sun and Moon. He did not have any observational reason to decide the overall size of the orbits, so he made the orbits just large enough that the planets on their epicycles did not hit one another. He used Aristarchus' estimate for the Sun's distance. The relative size of the epicycle compared to the deferent is determined by the apparent size (the angle) of the retrograde motion in the sky. To use Ptolemy's model one has the start time etc for each body, and can figure out the position for any time in the future by adding up the motion of the Primum Mobile, the deferent and the epicycle. The equant is used to find the position of the center of the epicycle. Ptolemy wrote out tables in his books to help astronomers use the model to predict positions with less work. Some of these tables are included in the Almagest and in a book called Handy Tables. After Ptolemy died, Western Europe did not produce much innovation in astronomy. The Romans did not promote new science; in fact, the closest to a scientist we know of are compilers of scientific knowledge. The last Roman emperor was deposed in 476CE and the museum and library at Alexandria were lost its last member near 400CE, leaving the west detached from many o f the writings and works of the Greeks, including Ptolemy, Aristotle and Plato. Chapter 6 History of Astronomy-Ancient Times through Galileo 17

83 83 Astronomy was useful for finding the correct direction to Mecca (for prayer), for computing when the waxing crescent moon should first be visible to start the month, and for computing the time in the patient s horoscope to perform medical procedures. Ptolemy s models were used to make the predictions. In fact most of the star names we use today are Arabic names given by the Islamic astronomers. The Islamic astronomers observed the stars and planets and compared their positions with the predictions. As the observed positions came to differ from the predictions in the Almagest, they made revised tables called zij s. The principals of prediction, the Primum Mobile, deferent, epicycle and equant were the same; the number values were different. As Europe awoke from the Dark Ages, works of the Greeks were translated from Arabic into the Latin of the educated classes. Plato, Aristotle, and Ptolemy were taken as great authorities. Ptolemy s works were studied (and simplified to enhance understanding) and the tables were revised repeatedly. Nicolas Copernicus ( ) was born in Torun, Poland. He was educated at universities in Cracow, Bologna (canon law and astronomy), Padua (medicine), and got a degree in canon laws from the University at Ferrara. His uncle was Bishop of Ermeland. Copernicus was employed as secretary and physician to his uncle while the bishop was alive. He held the post of canon of Frauenberg cathedral for his entire life. After his uncle s death he continued at Frauenberg, acted as a consulting physician, studied astronomy, served in reforming the currency and negotiating in the wars between Poland and Prussia. It is not certain when Copernicus got the idea of letting the stars stand still, and letting the Earth rotate (giving the impression of rising and setting) and having all the planets orbit the Sun. He was aware of Aristarchus beliefs, but did not have Aristarchus writings concerning the motion of the Earth. Copernicus was particularly disenchanted with the equant. Chapter 6 History of Astronomy-Ancient Times through Galileo 18

84 84 Copernicus wrote a brief summary of his theory, the Commentolarius ( ?) and corresponded with other academics discussing his theory. During Copernicus life even the Pope knew about the theory (1536). Copernicus was concerned because his theory conflicts with the Bible. His colleagues in the Church encouraged him to document his theories and predictions. Their approach was that if the theory was correct, it would be reconciled with the Bible properly interpreted. Meanwhile it would be worthwhile to explore the theory and examine its correctness. Copernicus delayed publishing his work. He was visited by Rheticus, a German mathematician, Rheticus. Rheticus was impressed by the theory, and with Copernicus permission, wrote a brief summary of Copernicus work. It was published and went into two printings. There were no negative repercussions. Copernicus was getting old, and he wrote up his life s work in a book called de Revolutionibus Orbium Coelestum (About the Revolutions of the Celestial Spheres)". Copernicus completed the manuscript and sent it to Rheticus to prepare it for printing. Rheticus handed the work to Osiander, a Lutheran theologian. Osiander (and Martin Luther) did not think that the world needed a theory of the universe separate from the information in Genesis. Osiander encouraged Copernicus to portray his model as just another way to compute the positions of the heavenly bodies, not an approach to finding the truth of the construction of the Universe. Copernicus did not take this advice, but Osiander wrote, and included, an unsigned preface to de Revolutionibus, expressing this very sentiment.. De Revolutionibus was published in the spring of Copernicus suffered a stroke in December of 1542, so he probably did not know of the preface. After Copernicus death, his friends realized what had happened, but still the preface was not changed. Copernicus model of the Universe puts the center of the Earth s orbit at the center of the Universe. The Sun is near that point. The Earth spins on its axis and all the planets orbit the center of the Earth's orbit.. The orbits were circular with basically constant rate motion. Retrograde motion occurs as a natural consequence of the fact that the planets complete their orbits in differing lengths of time. As one planet passes another, observers both the inner and the outer planet see retrograde motion. Chapter 6 History of Astronomy-Ancient Times through Galileo 19

85 85 Copernicus knew, however, that the planets appear to change speed even when not in retrograde motion. Uniform speed motion on circular orbit will not make this happen. To model the changing speed, Copernicus introduced many small epicycles. In Copernicus model, the stars are assumed to be fixed on a sphere. Precession and changes in the amount of the tilt of the Earth are caused by changes in the direction of the Earth s axis. Copernicus model made it possible to determine the sizes of the planets orbits in terms of the size of the Earth s orbit. Copernicus included sizes of the orbits in de Revolutionibus. Copernicus made some observations to support his models and developed new computational devices to predict the positions of the planets. After Copernicus death, these computations were used even by those who did not believe that his models were correct. At that time (and before) the astronomer s job was thought to be predicting the positions of celestial bodies. Explaining what lay behind the position computations was thought to be the realm of physics or philosophy. Generally Copernicus models were about as accurate as the Ptolemaic models, assuming that the Ptolemaic models were updated with new data. So most people did not believe that Copernicus was right. They were not anxious to demote the Chapter 6 History of Astronomy-Ancient Times through Galileo 20

86 86 Earth from the center of the Universe to being just one among lots of planets. There was still the problem of conflict with the Bible. There was no good explanation of why parallax was not seen (Copernicus just said that the stars were too distant for parallax to be seen.). So few people accepted Copernicus model. Tycho Brahe ( ) was among the astronomers who did not accept Copernicus model. He tried to measure parallax for stars, but could not find any. So he would not accept that the Earth moves. On the other hand, Brahe did not accept Aristotle's contention that the heavens from the moon on out are unchanging. He found that comets could not be in the atmosphere (as Aristotle had said) because he could not measure any parallax. Since comets come and go, move among the stars etc. the heavens cannot be unchanging. Tycho observed a supernova in Cassiopeia, a star that brightened and faded. Both these phenomena change, but are not within the Earth's atmosphere. Tycho Brahe was born a Dane. He observed the planetary positions at an early age and realized that the planets were not at the places predicted at the time predicted. So he thought he could make better predictions using his own model. His model has the Sun and the Moon orbit the Earth. The other planets orbit the Sun and are carried with the Sun as it moves around the Earth. The stars are on a sphere centered on the Earth. Because he was Danish, and well known as a scientist, the Prince of Denmark lent him the island Hven in This island is near the coast of Sweden (and now is part of Sweden). The Chapter 6 History of Astronomy-Ancient Times through Galileo 21

87 87 agreement was for Tycho to collect rent from the farmers on Hven to support himself, to carry on astronomical research (for the glory of Denmark) and to maintain the lighthouse. Tycho Brahe moved to Hven and set up the first professional observatory in Europe. He built two separate buildings, Uraniborg and Sterneborg to house his instruments and records He built very large instruments allowing very accurate observations. Tycho was able to get observations precise to 1 minute of arc, that is 1/60 of a degree. Tycho hired helpers and they made observations for about 20 years. During that time the Prince of Denmark died and was succeeded by his son. The son was less interested in astronomy and less fond of Tycho Brahe. The farmers were annoyed with the high rents and Tycho is reputed to have taken poor care of the lighthouse. In 1597 Tycho Brahe was forced to leave Hven. He settled briefly at Hamburg, then moved on. Tycho found a new post as the Imperial Mathematician to Prince Rudolph of Prague (1599), so there he went. He brought many of the instruments for measuring the positions of the stars, since they were portable. (Obviously he didn t bring the buildings, and unfortunately they burned down shortly after Tycho left.) Tycho made no more observations once he reached Prague. He tried to use the ones he had to develop tables to predict planet positions using his model. He hired helpers to make the tables. In 1600, he hired Johannes Kepler and set him to work on the planet Mars. Johannes Kepler ( ) was a German Lutheran. He originally wanted to be a clergyman, but was trained in mathematics and astronomy. One of the themes of his life was to find the meaning and structure in the universe. He obtained a job teaching, but his lectures were not attended. Kepler noticed that that if the sizes of the planets orbits in de Revolutionibus are represented by spheres, then the spheres could be fitted between the five known and possible three dimensional perfect solids. This is similar to two-dimensional inscribed and circumscribed polygons. The perfect solids have all of their faces the same and each edge of each face is the same. These solids had been known since the Greeks. The perfect solids have all of their faces the same and each edge of each face is the same. These solids had been known since the Greeks. They consist of the tetrahedron (4 triangular faces), the cube (six square faces), the octahedron (8 equilateral triangles), the icosahedron (twelve pentagons), and the dodecahedron (20 equilateral triangles) There are only five such perfect solids in Euclidean geometry, and Kepler knew it. Kepler reasoned that if the sizes of the planets orbits in de Revolutionibus are represented by spheres, then spheres of the sizes of the orbits for all six planets (Mercury, Venus, Earth, Mars, Jupiter, and Saturn) would fit with the perfect solids between them as spacers. Kepler thought that he had found the divine plan for the Universe; just 6 planets with spacing determined by the five (and only five) perfect solids. Kepler published his theory in a book called Mysterium Cosmographicum (1597). He wasn t 100% happy with the values of the orbital sizes in de Revolutionibus. So Kepler sent a copy of Mysterium Cosmographicum to the man who had the Chapter 6 History of Astronomy-Ancient Times through Galileo 22

88 88 world s best observations, Tycho Brahe. Kepler hoped that these observations would allow him to prove that the sizes of the planets orbits fit with the perfect solids between them as spacers. Fortunately Tycho Brahe, the man with the best observations, was looking for help. He hired Kepler to work on his observations expecting Kepler to prove Brahe s own model. Kepler and Tycho Brahe did not get along. Brahe did not immediately give Kepler all of the observations he needed. Kepler got so frustrated that he went back to Germany once. In 1601 Tycho Brahe died and Kepler got possession of the observations. Kepler was given Brahe s job as Imperial Mathematician, but at a much lower salary than Brahe got. Kepler knew how accurate Brahe s observations were, so he could not simply assume that they were in error. He was forced to abandon the idea of circular motion, or motion carried on spheres and to adopt his three laws. Ellipses are described by a formula involving the squares of the coordinates. You may have seen it in the form, where a is the semimajor axis and b is the semiminor axis. Ellipses have two axes of symmetry. That means they can be folded along either the major or the minor axis and the sides will match (the fact that it would not matter if -x were substituted for x, or if -y were substituted for y, shows this symmetry). The shape of an ellipse is rounded everywhere; there are no straight parts and no points. The foci (the plural of focus) are on the major axis and at positions that depend on the shape of the ellipse. The semimajor axis tells the overall size of an ellipse. In fact the semimajor axis is the average distance of one body from the other. It is like the radius of a circle. Chapter 6 History of Astronomy-Ancient Times through Galileo 23

89 89 Ellipses come in a variety of shapes, ranging from a circle to a very elongated shape nearer a cigar. The eccentricity tells how close to a circle it is, the larger the eccentricity, the more elongated the ellipse.) The orbits of the planets are very nearly circles. In fact, if it were not for the fact that the Sun is not at the center, it would be very hard to tell these ellipses from circles by just looking at the shapes. Kepler did not really know why these laws were correct. The laws do, however give substantially more accurate prediction than did Copernicus model. Today we know that these laws describe the motion of one body around another (laws 1 and 2) under the influence of gravity. The third law is appropriate for the motion of several small bodies around one more massive one, also under the influence of gravity. These laws could be derived from Newton s work. Kepler was not persecuted for these laws, even though they do not have the Earth at the center. Probably this was because few people read or understood his work. Kepler tried to explain why the planets orbit the Sun. The only force known at the time that acts without touching the other body was magnetic force (like when the refrigerator magnet tries to reach the refrigerator door before touching it). So Kepler tried to use magnetic attraction between the Sun and the planets to cause them to move in orbits. Kepler used the models to develop tables, called the Rudolphine Tables, in honor of his (and Brahe s) patron Prince Rudolph of Prague. He went on to develop a new type of telescope (different from Galileo s), He learned that stars appear above further above the horizon than predicted, since their light is bent by Earth s atmosphere. And he computed many horoscopes. He still tried to find the overall plan of the Universe, later using musical harmonies rather than perfect solids. Galileo Galilei ( ) was a contemporary of Kepler s (they did not meet, but they did correspond). Galileo was a northern Italian, born to a musical family. Galileo had one brother and three sisters. His father sent him to university to become a physician so that he would earn money and be able to pay the sisters dowries. The need to pay doweries may be what lead Galileo to put himself forward and seek favor at times when others would have been modest. Galileo quickly decided that mathematics and astronomy were much more interesting than medicine and declined to become a physician. So he switched from the university at Pisa and went to Florence to study mathematics. Galileo obtained a job teaching at Pisa after he finished university. Later he moved to Padua, the leading university of the day. He was supposed to teach Aristotle s physics and Ptolemy s models Chapter 6 History of Astronomy-Ancient Times through Galileo 24

90 90 of the cosmos. Those were the accepted theories. Galileo performed experiments, however, including measuring the time for various bodies to fall. He found that the time to fall did not depend on the mass of the body (but feathers and leaves still fall slowly. Why?). This lead Galileo to conflicts with the scientific establishment. Galileo discovered that a pendulum takes the same length of time to swing, regardless of how high it swings. You have probably experienced this when pushing someone in a swing. You push at the same time interval, regardless of how high they go. The time for the pendulum to swing depends only on the length of the string and the gravity of the Earth. Using this principal, Galileo devised an apparatus to time a patient s pulse. Galileo spent many years studying the motion of falling bodies with their variable speed. Galileo slowed down the fall, to make it easier to measure, by rolling bodies down slopes. He found that bodies could roll to the same height they had come from. This is known as Galileo s law of inertia. He tried to describe the variation of speed that falling bodies undergo. Galileo believed that Copernicus was correct and that the Earth moves. His reasoning was based on his personal theory of tides. Galileo thought that tides were caused by water sloshing around as it turns the corner from going the same direction due to both the Earth spinning and the Earth orbiting to the part of the Earth where it is moving opposite the direction that the Earth is orbiting. This model is NOT correct, but it motivated Galileo. Galileo heard that in Holland, two lenses had been used together and with the result that the image was much magnified. He was living at Venice at the time, where there was (and is) a tradition of glass making. Galileo had many lenses made, and hit upon a telescope made of a weak objective lens and stronger, diverging, eyepiece lens. Galileo s telescope magnified more than had the work others had made (over the years Galileo made other, better telescopes). Galileo immediately made a telescope and gave it to the City of Venice. This allowed them to see whether grain boats or enemy ships were approaching on the Adriatic Sea. This was very advantageous for the city. Knowledge of enemy ships allowed them to raise a chain across the entrance to the Venice lagoon. This would break up the hull of the enemy ship. The City offered Galileo a job for life (which he took, but later got a more lucrative position at Florence). Galileo built several telescopes. They might go for $20 from Toys R Us today. They magnified about 20 times and had diameters about 1.5 inches. Galileo turned his telescope to the heavens and quickly found that - The Moon has mountains and craters, unlike the perfection predicted by Aristotle - The Milky Way is made of lots of stars that had never before been seen - Jupiter is accompanied by four moons. So NOT every body in the Universe circles the Earth (and which one has more moons?) These discoveries were deeply disturbing to people. They differed from the status quo, and they seem to take the Earth from its most central place, by the existence of Jupiter s moons. Galileo published his discoveries in Italian in a small pamphlet called Sidereal Messenger or Starry Messenger in This was rather like publishing scientific data in a supermarket tabloid rather than in a learned journal. Anyone could read it, and anyone could understand what Galileo had to say. He drew pictures of the positions of Jupiter s moons and of shadows cast by lunar craters to explain how he interpreted what had been seen. In Galileo continued his observations. He found - Saturn has three parts. Galileo never knew what they were - The planet Venus has phases as predicted by Copernicus model. - The Sun has spots which come and go over days to weeks. The Sun rotates about once per 25 days at the equator. It is far from perfect and unchanging. Galileo published these results in another book in Italian, Letters on Sunspots, in 1613 Chapter 6 History of Astronomy-Ancient Times through Galileo 25

91 91 In 1611 Galileo took his telescope on a trip to show others what he had seen. He went to Rome, stopping to see astronomers on the way. Some people were convinced that Galileo was correct, others were unable to see through the telescope very well, others refused to even look. One astronomer, Clavius, suggested that the craters on the Moon were not the real surface. The real surface was a smooth crystal with the craters below. Galileo was convinced of the correctness of Copernicus model, but his observations show little direct evidence and no unequivocal proof. He did try to address the issue of discrepancies between the Copernican model and the Bible. He published a letter (1615) called Letter to a Duchess designed for the Duchess Christina who had asked one of Galileo s friends about the Copernican Theory. This letter suggests The Bible tells us how to go to heaven, not how heaven goes. What did he mean by this? Galileo went on to write that the Bible doesn t even mention all the planets. He thought that if there is an apparent disagreement between the Bible and an observation in the physical world, it must be because we do not understand what the Bible is saying. Do you think he was a religious person or not? How do you think that others took this? Eventually the Church decided to do something. It was not clear whether the Ptolemaic or the Copernican theory was true, although many people in the Church were expecting that the Copernican theory would eventually be proved true. However there was still the issue of resolving the theory with the Bible and there still was no firm proof. In March 1616, a general proclamation was made saying that no one (that is no one Catholic who cared what the Church did) should teach the Copernican theory as the truth. It should only be taught as one among competing mathematical theories. If the evidence ever accumulated to the point that the Copernican theory was proven, then the interpretation of the Bible could be dealt with in the Church. At this time, 1616, De Revolutionibus was banned. It was reissued in a corrected version with words inserted softening the assertions that the model with the Sun at the center was true. A corrected version was published in The original was banned until In February Galileo went to Rome and had a conversation with Cardinal Bellarmine. The Cardinal and Galileo knew one from another before Bellarmine was Cardinal. Galileo was asked whether he believed the Copernican theory. Galileo denied that he believed it. At this time, they may have discussed a special edict telling Galileo to refrain from discussing the Copernican theory at all. Galileo went home with a letter signed by Bellarmine refuting the idea that Galileo had been personally forbidden to examine the Copernican theory, but detailing the interaction. Galileo went on with his work; Bellarmine and the Pope died. Pope Urban VIII ascended. He had discussed the Copernican theory with Galileo years before and had held the opinion that the Copernican might be correct. So Galileo thought that the climate might have changed. Galileo put together his work on the new, non-aristotelian physics and the Copernican model in a book called Dialog on Two Chief World Systems. The book is written as a series of four days of questions and answers. There are three characters, Sagredo, the moderator, Salviati, the supporter of the Copernican theory, and Simplicio, a supporter of Aristotle and Ptolemy. All of these names are names of friends of Galileo who were dead at the time the book was written. Galileo tried to get the book approved, by giving the sensor pages as they were written. The sensor decided that the book was too complex and the review should await the complete book. When the book was complete, Galileo was in Florence and got permission for the censor in Florence to do the review. The book was approved, and given the stamp of approval, the Imprimatur. Chapter 6 History of Astronomy-Ancient Times through Galileo 26

92 92 When Dialog on Two Chief World Systems was published in 1632 and copies reached the Pope at Rome, the hit the fan. We don t exactly know why, but Pope Urban VIII was angry. He may have thought that the character Simplicio was a play on the Pope s name, he may have thought that Galileo had been told not to discuss the Copernican theory at all. We do know that Galileo was summoned to Rome to be tried by the Inquisition. Galileo delayed as much as he could and got to Rome in The Inquisition tried to recall all the copies of the book, but they had already been sold. Unlike American courts, where the accused must be told the charge, the Inquisition would ask the accused what they thought the crime was. Galileo didn t know. The Inquisition brought out a document forbidding Galileo personally to discuss the Copernican theory at all. This was supposedly conveyed during Galileo s meeting with Cardinal Bellarmine in Such a document would normally be signed by the two parties and two witnesses who would be priests. The witnesses whose names were on this document were servants. Galileo brought out the letter from Cardinal Bellarmine describing the meeting, and NOT showing that Galileo had been given the edict. The Inquisition was in a tough place. It would look really bad for them to say that they were wrong to accuse Galileo and the Pope wanted something done. On the other hand, Galileo was in a tough place. He didn t want to be tortured, and he really didn t want to be burned at the stake. So he recanted, he swore formally that he did not believe that the Earth moves. He was allowed to go home to his estate Arcetri (near Florence) where he was put under house arrest for the rest of his life. His guards tried to prevent Galileo from communicating with other scientists. Galileo continues his research into the motion of bodies. He died in December Galileo s books on astronomy were on the prohibited list until In 1979 the Church convened a group which, in 1992, concluded that it had been wrong to condemn Galileo. Questions and Problems 1) If the Earth were flat, what would it look like as you sail away from a tree? Would it disappear from the top down? 2) How can we tell whether an alignment is a solar alignment or a lunar alignment? 3) Redraw the picture of solar motion, like the one at the beginning of the chapter, so that it represents the motion of the Sun as seen from Australia. 4) How did Aristotle s model explain the Moon rising and setting? 5) If Eratosthenes had measured that the angle between the Sun and the gnomon was 10 o rather than about 7 o, what would have happened to his value for the size of the Earth. A nswers 1) No, it should just get smaller and smaller. It might get lost in the mist before it gets too small to see. 2) The moon can go to declinations about 5 o further north or further south of where the Sun ever rises or sets. This 5 o of declination turns into 5o azimuth at the equator and more at every other latitude 3) Leave the background, earth, sky, NSEW points all the same. The rise and set points of the Sun could be the same, but tilt the paths toward the north. The June 21 path should go low and in the north, the Dec 21 path should go high 4) Primum Mobile carries the Moon (and everything else) in its basic daily pattern 5) Put the 10 o back into the ratio where 7 o had been before. The distance will come out at 180,000 stades. Chapter 6 History of Astronomy-Ancient Times through Galileo 27

93 93 Date Europe/Egypt/ Modern World Middle East/India China Americas 6000 BCE 5000 Megalithic Tombs Britain and Brittany 4000 Start date for Julian Day count Jan 1, 4713 BCE Earliest Egyptian date found, 4241 BCE 3500 Newgrange, Ireland Burial mound built, Winter Solstice Sunrise alignment Stone Circles in Britain and Brittany Winter Solstice in Aries, start Akkadian Calendar? Earliest writing, Mesopotamia 3000 Stonehenge I Started ~2700BCE, ---Stone Circles in Britain and Brittany ----Egyptian Dynastic History, Hieroglyphic writing Star heliacal rising records started, calendar started 2500 Pyramids Three calendars, lunar phase, 365 day, and Sothis, based on Sirius heliacal rising (Earth s sidereal period) 36 week year, corresponding to 36 star groups 2000 Stonehenge III complete BCE~1900 (trilithons) Empire of Hammurabi ? BCE Venus records kept China 2137 BCE Hi & Ho reputedly executed for failing to predict eclipse 1500 Indian lunar tables kept Chinese eclipse 1000 Trojan War (Troy destroyed 1184 BCE) 1100 BCE Indian Solar Tables records, 1400 BCE Current (not first) Mayan great cycle starts 3114 Earliest known Meso American Temples 800 Homer, Iliad, Odyssey (some date at BCE) Hesiod, Works and Days (incl star rising and activity associations) 700 Babylonians adopt 7 day week 600 Ionian School, Thales( BCE) Earth a disk Anaximander ( BCE) Earth a cylinder Anaximenes ( BCE) Earth a disk with mountains around it 500 Pythagoras ( BCE), Pythagorean school ( music of the spheres, irrational numbers) spherical earth, crystal spheres for motion of planets, Antichton 961 BCE Indian Planetary Motion Tables Babylonian Day and Night divided into 12 parts each, AND 24 equal time divisions made. Chapter 6 History of Astronomy - History Overview 1A

94 94 Date Europe/Egypt/ Modern World Middle East/India China Americas 400 Pythagorean Brotherhood Pythagoras (c 580 -c500bce) - spherical Earth, in center of universe. Explained Moon phases by reflection of sunlight. Planets move on crystal spheres. Also Pythagorean Theorem ( sides of a right triangle), irrational numbers (ones which cannot be represented by fraction or decimal) Parmenides ( BCE) Theorized about spherical Earth with zones (tropics, arctic etc. ) modeled universe with concentric spheres 432 BCE Meton, metonic cycle discovered (19 years=235 lunar synodic months to within 1.5 hrs) 300 Philolaus (~ BCE) Antichton- anti earth which prevents fire from burning us. Universe centered on central fire. Plato ( BCE)Thought the concept, not the observations are important. Proposed that universal motions are combinations of circular, constant rate motions. Motions of bodies around central spindle. Moon shines by reflected sunlight. Aristotle ( BCE) argues spherical earth at center, Used 56 Rotating spheres and counter rotating spheres to make up motion. Spherical Earth explained. Divided world into sub-lunar region where change occurs, and super-lunar regions whereuniform circular motion repeats forever. Babylonia - Venus and Jupiter prediction tables China -Star Catalog constructed Aristarchus BCE Found Distances to Sun and Moon, and relative Sizes of Sun, Moon, Earth Distance to Moon, Thought Earth moves around Sun 200 Eratosthenes ( b ~273 BCE d~ 195 BCE) measured circumference of Earth 100 Hipparchus ( ~ BCE), Star catalog, epicycles adopted for astronomy, precession discovered and 0 BCE - >CE quantified 45 BCE Julius Caesar reforms Calendar, adopt Julian calendar ( leap year every fourth year) Chinese sunspot records 28 CE Medicine Wheels, Great Plains, Alberta 100 Ptolemy ( CE) 140 Ptolemy's Almagest 200 Water Clocks Teotihuacan Empire Mex CE Council of Nicea fixes Easter as Sunday following full moon following vernal equinox Nazca culture Peru Chapter 6 History of Astronomy - History Overview 2A

95 95 Date Europe/Egypt/ Modern World Middle East/India China Americas 400 Fall of Rome 473 CE Start Mayan 500 Church adopts flat Earth, Rectangular heavens above 600 End Teotihuacan 700 Al Mansur at Bagdad gathered astronomers, Almagest translated 800 Arab Astronomy Tabit ben Korra( CE) translated Almagest. Noted difference in precession between Ptolemy and current observations. Introduced "trepidation", for variation in precession rate 900 Spherical earth and sky readopted by Church Toledan Tables (made Toledo, Spain) under direction of Arzachel, 1080 CE, updated comptational basis 1000 Hakemite Tables published at Cairo by Ibn Yunos (d 1008 CE) Chinese record Crab Supernova in Taurus \/ Climax of Maya Earliest date for Anasazi petroglyphs of supernova? End Maya \/ Uxmal and other Yucatan sites Caracol built, Yucatan Chaco Canyon, N.M. habitation 1100 Euclid/Ptolemy rediscovered in Europe Chaco Canyon, center of activity 1200 Albert the Great( CE) & Thomas Aquinas ( CE)- Embrace Aristotle as authority Bighorn Medicine Wheel est. ( ) Roger Bacon ( CE) warns aagainst excessive reliance on Aristotle Spain recaptured by Christians, Corbova1236 CE and Seville1248 CE End of Islamic astronomy in West Pope Alfonso X directed Alfonsine Tables 1252 CE (ellipse for Mercury orbit) 1300 Chaco canyon abandoned by Anasazi 1400 Copernicus ( CE) Aztec Empire, Mexico Chapter 6 History of Astronomy - History Overview 3A

96 96 Date Europe/Egypt/ Modern World Middle East/India China Americas 1500 De Revolutionibus published 1543 CE Tycho Brahe CE Supernova in Casseiopeia 1572 CE Comet 1577 CE Observatory at Hven CE Inca Empire, Peru 1519 Cortez conquers Mexico 1582 Gregorian Calendar adopted in Italy, Spain, Portugal (Oct 15 followed Oct 5), 12/82 adopted France, Belgium, Catholic Netherlands. 1583Bavaria and Austria 1584Protestant Belgium, Catholic Switzerland, Bavaria, Moravia adopted, 1587 Hungary Johannes Kepler ( CE) Elliptic Orbits, Laws 1609, 1626 also Optics 1600 Galileo ( CE)- Telescopic Discoveries , ( sunspots, moons of Jupiter, phases of Venus, mountains of moon, rings of Saturn, Star Messenger 1610 Dialogue on Two Principal World Systems 1633 Tried by Church 1633, recanted Newton ( CE) Optiks,(1704) Newtonian telescope, light split into colors Principia ST ed, Revised by Newton 1713 and Includes Computational basis of motion, 3 laws of motion, Law of Gravity, the Calculus 1675 Greenwich Observatory Founded (goal to make star catalogue good enough to support longitude determination from Moon position) Germany and Denmark adopt Gregorian Calendar 1750 Thomas Wright models galaxy as a lens shape based on number of stars in various directions 1752 Britain and the Colonies adopt Gregorian Calendar Titus - Bode Law, Numerical Relation for semi major axes of planet orbits Herschel discovers Uranus while mapping bright star positions Chapter 6 History of Astronomy - History Overview 4A

97 97 Date Europe/Egypt/ Modern World Middle East/India China Americas Ceres discovered by Giuseppi Piazzi 1838-Parallax of 61 Cygni discovered by William Bessel ( ), first time parallax of a star is found 1846 Neptune discovered by Galle in accord with John Couch Adams and Leverrier's predictions Solar Spectrum observed, Helium discovered Planck determines that light is radiated in discrete amounts called photons Theory of relativity 1917 Russia accepts Gregorian Calendar 1919 Rutherford discovers the proton Robert Goddard launches first liquid fuel rocked 1927 Heisenberg Uncertainty Principle ( we cannot know the position and the velocity of a particle arbitrarily well, no matter what we do) Expansion of the Universe found ~1928 (Hubble const) 1930 Clyde Tombaugh discovers Pluto 1930 Quantum Mechanics 1940 Atom Bomb (fission) Distance to Andromeda Galaxy proves it is outside Milky Way 1948 Hale Observatory at Mt Palomar completed 1949 Gregorian Calendar Adopted, China 1950 Hydrogen Bomb(fusion) 1960 Pulsars and Quasars discovered First Lunar Explorations, landing 1968 Cosmic Background radiation (3 degree) discovered 1970 Viking Landers reach Mars 1976, Pioneer probes to Jupiter and Saturn 1980 Voyager leaves for Jupiter Saturn, Uranus, Neptune COBE satellite measures uniformity of Cosmic background radiation 1990 Hubble Space Telescope Launched End of Mayan Great cycle Chapter 6 History of Astronomy - History Overview 5A

98 98 Chapter 7 The Start of Modern Physics Science was not halted by the Church in The scene moved to northern Europe where the Pope had less influence. Isaac Newton ( CE) was born in Wolstoncroft in England, to a farm-owning family. Newton s father died before Newton was born, and his mother remarried. Newton grew up on their farm, but it became clear that he would not make much of a farmer. He was sent to Cambridge University at ~18 and stayed for 4 years. At the end of that time, in 1665, everyone was sent home from the University because the Bubonic plague was about. The only thing they knew to do to prevent the plague from spreading was to disperse people. (What does spread the plague? Could you get he plague today?) Newton went home to the farm, and in the next 18 months figured out the physics you would study in about 3 semesters at college. He also invented the branch of mathematics, Calculus. He didn t write things down immediately, however. He was concerned that someone would steal his ideas. Only many years later, after urging by Edmund Halley, did Newton document his work in the books Principia and Optics. Newton was always afraid that others would try to steal his ideas and take credit for them. When the plague abated, Newton went back to Cambridge, where his professor resigned to give Newton his job. Newton determined the following three general laws, which definitely break with Aristotle. They are applicable to any sort of body. Newton s Laws of Motion (these are the only ones called Newton s laws) I. In the absence of an outside influence, a body at rest will remain at rest, and a body in motion will remain in uniform, straight line motion. (do nothing, nothing happens) II. Force = Mass x Acceleration III. For every action that a body exerts on another body, it experiences and equal and opposite force (action=reaction). (In this context, action means force. So the law says that the forces of interaction between any two bodies are equal but opposite) These laws are very general. They allow numerical predictions of what will happen during interactions. In a way, all three are restatements of the second law. The first law is the case of the second law when there is NO force. The third law says that when two things interact, ANY two things, they both experience the same force, but in opposite directions. It is sort of an accounting rule. It often bothers people to think that when a bug hits your car, both the car and the bug experience force of the same magnitude. It doesn t mean that the effect on the bug and the car are the same. Which one experiences the greater effect, the bug or the car? Conservation Laws Newton and later physicists also figured out several more fundamental laws, called conservation laws. A conserved quantity in physics is one that is never created or destroyed. This is nearly the opposite of what we think of in everyday life. Because we can predict the amount of a conserved quantity, sometimes we can predict what will happen. One might think of money as a conserved quantity. It does not appear or disappear, it is transferred from one person or account to another. So it can be worthwhile to hire an accountant to figure out what you have and where it is going. It is possible to predict how much money you have left. Chapter 7 The Start of Modern Physics 1

99 99 On the other hand, ideas are not conserved. It if you add up the ideas of all the people in the room, it will not lead to a prediction of the number of ideas in 5 minutes. The conservation laws are often more useful for predicting what will happen, than are Newton s laws of motion. Conservation Laws To use each law, add up the quantity for EVERYTHING involved and get a total before an interaction. Set the total equal to the total for EVERYTHING after the interaction. All of the laws are all true all at one time. Linear Momentum Mass x velocity ( m1 beforev1 before m2beforev2before...) ( m1 afterv1 after m2afterv2 after The arrow above v for velocity indicates that its direction matters. The three dots (called an ellipsis) means that there can be more terms...) Angular Momentum Mass x Velocity in the direction around the Center x Distance to the Center ( m 1before v 1before r 1before m ( m 2before 1after v v 2before 1after r r 2before 1before...) m v 2after 2after r 2after...) Angular Momentum has a magnitude and a direction associated with it. It is always conserved, but the law is most useful when there is something obviously going around something else. Total Energy ( m1 beforev 1before m2 beforev 2before...) ( m1 afterv1 after m2 afterv2 before The total of all the energy in all the forms is conserved Kinetic Energy 1/2 Mass x Velocity 2 Potential Energy takes many forms, All convey the possibility of causing velocity Gravitational Potential Calories Chemical Energy (like in gasoline and cooking gas) Also, not known to Newton,...) Rest Mass Energy = Mass x c 2 Why are there conservation laws? People don t decide that they should exist, the Universe does. They indicate symmetries in the structure of the Universe. There may be more conservation laws. In the laws governing how elementary particles work, there are some conservation laws governing how one (or more) particles transform into others. These laws are sometimes broken, so they have a rather different status from the laws above. What is the use of the conservation laws? They give us some idea of what will happen in physical situations. Sometimes we know enough about a situation that the specific result of an interaction. Sometimes we can only rule out some consequences. HOW TO USE A CONSERVATION LAW To use a conservation law, we find all the bodies involved in an interaction or situation. Then find the amount of a conserved quantity associated with each body and add up the amount of each conserved quantity to find the total BEFORE an interaction. AFTER the interaction, the total will be unchanged. In situations where we know some, but not all, of the quantities, the conservation law(s) allow us to find the remaining quantities. Chapter 7 The Start of Modern Physics 2

100 100 Example: You are driving your 1500kg car at 80 km/hr going East and you run head on into a 3000 kg truck. The truck was going west at 20 km/hr before your collision. After the collision, your car and the truck stick together. No one puts on the brakes. How fast are you (both) going after the collision? Answer: The information given tells the masses of the cars and their velocities. So we know enough to compute the total momentum before the collision. Adding it up TotalMomentum (1500kg)(80km/hr)+ (3000kg)(-20km/hr) 120,000kg km/hr - 60,000kg km/hr 60,000kg km/hr before = m v 1 1 m 2 v 2 before The truck s velocity and your velocity have opposite signs because they go opposite directions. The total momentum has a positive sign, because your car had more than the other car. You made the decision to call eastward positive. It really doesn t matter which direction is positive, but you need to keep track. Now we need to figure out the velocity of each vehicle AFTER the collision. We know that if the two vehicles stuck together, they must be moving with the same velocity. After the collision TotalMomentum = 60,000kgkm/hr (1500kg)(v) + (3000kg)(v) (4500kg)(v) = 60,000kgkm/hr Dividing both sides by 4500kg yields 60,000kgkm/hr = v 4500kg km/hr= v = 60,000kgkm/hr Both vehicles are going the same direction at km/hr. They are both going to the EAST. You can tell because you set up the problem with Eastward velocity as positive. Since your answer is positive, it must be East. What if you had been going the same direction (both eastward) and you rear-ended the truck? Assume that the two vehicles had the same masses and velocities as before, except you are both going East. If they stick together after the collision, how fast would you be going after the collision? (40 km/hr eastward) Example 2 You are parked behind your friend s 2000 kg car. Your car has mass 2500kg. You mess up. You put your foot on the accelerator too hard. Then you realize what you have done. You take your foot off the accelerator, but your car runs into the other car at 4 mph. Your friend s car is sitting, parked, in neutral. If your car is going 1.5 mph after the collision, how fast is your friend s car going? Again, we can use conservation of linear momentum. Before the collision TotalMomentum before = m v 1 (2500kg)(4mi/hr) + (2000kg)(0mi/hr) = 10000kgmi/hr 1 m 2 v 2 before After the collision, the total momentum is the same, and the velocity of your friend s car is unknown, so Chapter 7 The Start of Modern Physics 3

101 101 (2500kg)(1.5mi/hr)+ (2000kg)(v) = 10000kgmi/hr 3750kgmi/hr + (2000kg)(v) = 10000kgmi/hr (2000kg)(v) = 10000kgmi/hr kgmi/hr = 6250kgmi/hr v= 3.125mi/hr We know that your friend s car is going in the same direction that your car was going because the answer has the same positive sign as your original motion had. The law of conservation of linear momentum is generally useful. It is equivalent to Newton s second law, but is easier to use, because we scarcely ever know the exact force between two bodies at every instant. Conservation of linear momentum adds up all the effects of the forces and allows us to know the situation after the interaction. The law of conservation of angular momentum is always true (and it is possible to define the radius to any center you like), but it is most useful when something is obviously going around something else. Conservation of energy is always true as well, but there are many formulae for the potential energy. It is often more useful as a general concept. For example, in the car-truck collision, the kinetic energy of motion of the vehicles is transformed into potential energy by crunching the metal. The amount of energy used in bumper crunching depends on how the cars are built. Gravity Newton also discovered the force of gravity. The story is that he was thinking about why the Moon orbits the Earth and what keeps it from getting away. Then an apple fell. He realized that a force between every object and every other one must exist, and that the form of the force law is F F Gm 1 m 2 r 2 the force G = the Universal Constant of Gravity The negative sign in the force law indicates that the force is in the direction to pull the bodies together, the force acts along the line joining the bodies. According to Newton, there is a m force of gravity between every pair 1,m 2 the two masses involved of bodies. Or better, between r = the distance between the masses every two particles with mass. There is no minimum size of the and there is no maximum distance for gravity to act, so far as we know. So you are pulling on and being pulled on by galaxies you have never seen; ones you didn t know existed. So why don t we feel the gravitational force from each other? The value of G, the Universal Constant of Gravity, is a small number. So the force between you and me is very small. On the other hand, gravity always attracts. So it builds up to a large value between big bodies like planets and satellites. m m m m All parts of Earth pull on the observer M t The distances and amounts of mass average to act like all mass at the center As we consider the force of gravity from some large body, it becomes obvious that the material is not all at the same distance. To find the total force of gravity between two bodies, one would add up the forces between every tiny piece of each. This gets old really fast. Chapter 7 The Start of Modern Physics 4

102 102 So how did Newton compute the force between the Earth and Moon? Newton, used the Calculus (mathematics,not the tooth scum) to add up the force from the different particles in a large body. One of the things he proved was that The force from a body with spherical symmetry produces the same gravitational force as would the same total mass concentrated all at the center. So when we compute the force of gravity on an object on the surface of the Earth, the distance between the body and the Earth is the radius of the Earth. Example:You weigh 150lb on the surface of the Earth. How much would you weigh on a tower 1 Earth radius high? The 150lb is NOT your mass; it is your weight, the force of gravity between you and the Earth. Your bathroom scale is squashed because of this force. The very idea that the weight changes indicates that 150lb is not your mass. Bathroom Scale It is possible to use the force to figure out your mass, but it is not necessary for solving this problem. In stead, we can solve the problem by comparing the situation at the lower and the higher positions. This method simplifies the computation, 2R e Start by writing out the force of gravity on you standing on the Earth. Gm m r 1 2 The general law is F g 2. Substituting the variables for this specific case (just the names, not the numbers). 150lb Gm earth m you R earth 2 Now set up the equation when at the top of the building, at a distance of 2R earth from the center of the Earth. Gm m Gm m Gm earth you earth you earth you Fg R (2) (R earth earth ) 4R earth You still don t know your mass, but the right hand side has all the same terms as the force of gravity on you on the Earth. So, factoring out the parts that equal your weight produces F g 1 4 Gm earth m you 4R earth 2 150lb 37.5lb 1 4 Gm earth m you R earth 2 So doubling the distance from the center of the Earth, divides the force of gravity by 2 2, or 4, and it was not necessary to know your mass, or the Earth s mass or the constant of gravity. Test Yourself: Your dog really wants to be picked up, but at 110lb he is too heavy. You get the idea to take the dog to the top of a tower 1.5 Earth radii high, then lift him. Will this help? How much will he weigh at the top of the tower? Ans 17.6lb What if you want to go to Mars with your dog? What will the dog weigh? In this case BOTH the mass of the planet and the radius of the planet change. The mass of Mars is about x mass m R e Chapter 7 The Start of Modern Physics 5

103 103 of the Earth and the radius is about 0.53 of the Earth s mass. The dog s mass doesn t change. F g Gm dog m mars R mars 2 Gm dog 0.107m earth (0.53R earth ) 2 weigh x as much as on Earth s surface = 41.9 lb Circular and Escape Velocity Newton discovered gravity because he was thinking about why the Moon orbits the Earth. As he worked out the problem, he discovered that an orbit would be a circle, an ellipse, a parabola or a hyperbola. These shapes are shown in the figure. Newton found that for an object, m 1 to go in a circle around another object, m 2, a body must have exactly circular velocity compared to inertial space. The circular velocity formula is V circ Gm r other For one body to escape from another, it must have escape velocity. Escape Velocity V esc HYPERBOLA A 2Gm r other B 2 V You finish the computation. The dog will When one body escapes from another, it has just enough velocity so that gravity slows it down forever and it finally gets to zero velocity at an infinite distance. But it is never pulled back. Again this is the speed of mass 1 compared to inertial space, not to mass 2 Newton didn t know the value of G. On the other hand, the velocity of the Moon is easily found from the distance to the Moon and the time for the Moon to complete its orbit. To orbit the Earth at about 100 miles altitude (but r~ 6400 km, since it is measured from the center of the Earth) requires a speed of about 7.8 km/sec. The Moon, on the other hand is nearly 400, 000 km away and its speed is much less, approximately 1 km/sec. Does this make sense? The gravity force pulls one body toward another. The crosswise motion of the objects (compared to one another) keeps them from just falling into one another. Since gravity is smaller at greater distances, the crosswise velocity needed to prevent impact is smaller. The speed of the Earth as it orbits the Sun is about 30 km/sec. It is nearly constant, since the distance to the Sun is nearly constant. For the Earth to escape from the Sun, we would need to give the Earth only 2 times as large a velocity, or 42.3km/sec. That is just an extra 12.3 km/sec. If an object has speed greater than escape velocity, it moves on a path called a hyperbola. It will be able to escape from the other object. It will slow down until its speed is the difference between its original speed and the escape velocity. circ C PARABOLA D E F G ELLIPSE Starting Point H ELLIPSE CIRCLE Chapter 7 The Start of Modern Physics 6

104 104 Example How fast does an asteroid at 4 AU orbit the Sun (assuming that it is orbiting in a circle)? The formula we use is the formula for the circular velocity, Gm2 Vcirc r In this case, the Sun is m 2 and the distance between the centers of the Sun and the asteroid is 4AU. It is possible to look up G, M sun and then to convert 4 AU into meters. So in this case, it is possible to plug all the values into the equation for circular velocity, convert units and find out the speed. This is fun ONE time, but there is a faster way. Since we already know the velocity of the Earth as it orbits the Sun, and the distance to the Sun, and the fact that the Earth is much less massive than the Sun, the following can be done. First write out the circular velocity law and plug in the definitions for the Earth in orbit around the Sun. Gm sun Vearth orbiting Sun 1AU and substituting the answer is G(m sun ) 30km/sec 1AU Write the equation for the velocity of the asteroid orbiting the Sun at 4AU Gm sun Vcircular, asteroid orbiting Sun 4AU Factoring the equation for the asteroid s velocity to isolate the terms that appear in the formula for the velocity of the Earth produces V asteroid orbiting Sun G(msun ) 4AU 1 G(msun ) 4 1AU The term in the square root sign is something you have seen before. It is just the formula for the circular velocity of the Earth. But we know the answer, that is, the value of the Earth s orbital veloicity. So substituting for the Earth s orbital velocity yields V asteroid orbiting Sun 1 4 G(m sun ) 1AU 1 4 V earth orbiting Sun 1 30 km/sec km/sec = 15 km/sec 2 What was the point? Since one result was known, we didn t have to do any complicated computations. Please notice, the asteroid is 4 times as far from the Sun as is the Earth, but the speed in orbit is half as large. The speed does fulfill our precept of faster when closer, but the speeds are not proportional to the distance. The speed varies less strongly. Test yourself. How fast does Pluto go in its orbit? (The answer is in the book, but be certain that you can compute the answer). How fast would we need to make the asteroid go to get it to escape from the Sun? The asteroid would need to go 2 xv circular, or 2 x 15km/sec = km/sec or faster How fast do we need to escape from the Earth? Remember that you already know how fast a body would need to go to orbit the Earth near its surface. Chapter 7 The Start of Modern Physics 7

105 105 The formula for escape velocity is found based on the idea one body escaping from another with nothing else around. In real life, there are always other objects and the effect of their gravity must be considered as well. Can we always escape? We, you and I, don t personally have the velocity. That is what we build rockets for. But even with the best conceivable rocket, escape is not always possible. We think that the fastest anything can go is c, the speed of light, 300,000km/sec. So what if the escape velocity V esc 2Gm r equals or exceeds the speed of light? Then we think that nothing can escape and we term the situation a black hole. The place where the escape velocity equals the velocity of light. This is called the event horizon. When we are far away from a black hole, we experience normal gravity. We are not sucked in. If you get near the region where the escape velocity reaches the speed of light, eventually an orbiting body will spiral in. If something crosses the event horizon, it cannot escape and no signal from it can come out. You might imagine the black hole like the toilet. It isn t at all dangerous from far away, but once you get too far into the bowl, too bad. Black holes can come in any size. We have already discovered black holes which appear to be the remains of a massive star. The part that is left has perhaps 7 times the mass of the Sun. These black holes are detected by the fact that they are in a system with another star and the other star orbits the black hole (far enough away that it is not sucked in). Another type of black hole we have discovered lives at the centers of galaxies. In this case the black holes have millions to billions of times the mass of our Sun. We are not certain how they got the mass, but probably they have been swallowing stars for billions of years. The center of our own Milky Way includes such a black hole. Larger galaxies have more massive black holes. How can we find a black hole anyway if nothing comes out of it? Basically we need to observe something nearby. If there is something orbiting the hole under the influence of its gravity (but not already sucked in), we can use the circular velocity law to find the Gm 2 mass in the hole. Remembering that Vcirc, we would observe the velocity, V circ, and r the distance between the bodies, r. It is not really necessary to see both bodies, since the size of the orbit can be seen from the motion of just one, The value of G is known. So everything is known except m 2. So we solve for the sum of the mass of the other object. If the mass is large and there is no luminous body visible, it is possible to infer that there is a black hole. This method, measuring V circ and r, and using the circular velocity law to find the mass, is the way we measure the mass of all celestial bodies. If the laws of physics or G are different elsewhere or at other times, we have the wrong values for masses of most celestial objects. Practice Problems 1) How far would you have to go to feel no force from the Earth's gravity? 2) You hit two different golf balls off the tee. You hit both exactly the same, but one has twice the mass of the other. Which leaves the tee faster? What law (s) of physics are useful here? 3) You are throwing a dodge ball against a grocery cart. The dodge ball bounces back to you. What will the cart do? What law (s) of physics are helpful for finding the answer? 4) When you throw a ball in the air, it comes to a halt and returns. What is the kinetic energy at the highest point of the ball's trajectory? Is this the same kinetic energy as when the ball leaves your hand? If not, what happened to the energy? 5) You buy a 5 lb sack of rice at sea level, what does it weigh on top of a tower 3 earth radii high? Chapter 7 The Start of Modern Physics 8

106 106 Answers 1)There is no place you can go 2) The one with twice the mass leaves with half the velocity. Use Newton's second law 3) Grocery cart moves away from you, conservation of momentum or Newton's 1st and 2nd laws 4) 0 at the top of the trajectory, it became potential energy 5) lb Using Equations and Formulae Many students ask, How do you know what equation to use and how do you know what to do with it? While we don t know what to do in every situation, it is often easy to decide which formulae to use. As we look at the laws and formulae in this course so far, they can be organized as follows: Kepler s 3 laws Newton s 3 laws of motion Three conservation laws Three formulae concerning motion with gravity In the future, we will learn another formula concerning the Doppler shift of light Each of these laws concerns a specific subject and involves just a few variables. The first step to knowing what to use is to understand the topic (s) of the formulae and to know what the variables stand for. Once you know the topic, you can be the judge of when to use the information. For example, if your car won t start, you look for a car manual, not for instructions on how to substitute cooking oil for butter in cookies or how to reboot your home computer. Then you look in the instructions or the topics and look for the ones that say car doesn t start, not ones to help change a flat tire. Then you start looking at the symptoms, like key doesn t turn or key turns but doesn t cause the motor to rev etc. When you find whatever looks the closest to what you have, you try what the book suggests. Hopefully, this sounds like basic common sense. It is, just use yours. So the steps are to first 1) Decide the topic of the law or equation 2) Know what all the variables are and what they mean These steps should be done as you learn the equation. They don t depend on the problem at hand. The table on the next few pages has spaces for you to fill in the laws, their topics and variables. Leave the Doppler shift equation until after you have studied it. But do fill in the others. So first of all, let s break out the equations and identify what the topics are. Remember, the laws and definitions are in the chapters. So, check yourself. a) What topic is Kepler s third law about? b) When would you use Newton s third law? c) What is the G in some of the equations? d) Where is r, the distance between bodies measured? e) What can you do with Kepler s first law? What can be computed? So now how would you use the equations or laws? All of them are true at the same time, but they don t always relate to the issue at hand. So look for the one or ones that matter. Which law or laws are relevant for the following situations? f) How much does a 2 lb package of meat weigh when it is on top of a mountain 0.55 Earth radii tall (above sea level)? g) If you notice a comet orbiting at an average distance of 35 AU from the Sun, how long will the comet take to complete an orbit? h) How fast must the comet from the question above go? i) How fast would the comet from the question above need to go to escape from the Sun? Chapter 7 The Start of Modern Physics 9

107 107 j) A comet goes from a distance of 10 AU from the Sun at the closest to a distance of 50 AU at the furthest. Where does it move the fastest? k) A comet goes from a distance of 10 AU from the Sun at the closest to a distance of 50 AU at the furthest. Where does it experience the most force from the Sun? l) You are shooting arrows with a bow. You always draw the bow the same amount and the bow doesn t age etc. If you have some arrows that are more massive and others that are less massive, how can you tell which is which? m) With the bow and arrow above, the arrow should have energy after it leaves the bow. What kind of energy did it get? Where did the energy come from? n) If the bow from the previous question puts a force of 30 lb on the arrow, how much force does it put on the person holding the bow? o) You rear end another car while you are going straight East. Your car has a mass of 1500 kg and the other has mass 1200kg. You were going 10 m/s before the accident and the other car was going 8 m/s to the East before the collision. Can the other car go to the North as a consequence of the collision? p) If you are going 9 m/s after the collision from the question above, how fast is the other car going? q) Is there any body damage in the car accident above? r) How much will you weigh on a planet with half the mass of the Earth and half the radius? Hint: compare your new weight to your weight on Earth. s) You hit a golf ball and give it some spin. You are at a golf practice range which is very noisy and small. So you cannot hear when you hit a ball. You are a good golfer and every ball hits a net at the end of a short practice area. If you hit every golf ball the same, is there any way to tell whether the ball is a hollow practice ball or a ball with a rubber interior? t) Consider the golf ball from the problem above. The cover of the ball opens and the wrapped rubber band inside starts to unravel, will it spin faster or slower than before it started to unravel? Once you have decided which law is relevant, then it MAY be possible to find a numerical answer. There are several issues to remember, however. First, some of the laws don t give a numerical answer. Which ones? Kepler s first law doesn t. Kepler s second law can, but the computation is beyond what we are going to learn. The law of conservation of energy also doesn t give easy numerical values. Second, some of the laws, like the law of gravity, the equations for circular and escape velocity and Kepler s third law (P 2 = a 3 ) have equations with answers that deal with one situation. Others, like conservation laws need values BEFORE and AFTER an interaction. So look for that before and after situation to know if you might used conservation Example: You live on the planet Zonds. You wake up this morning and weigh 200 lb. The planet is having a really bad day. Over the course of the day, Zond swells(due to an excess of underground gas). Before any of the gas escapes, the surface has swollen until it is 15% larger than before. You step onto your bathroom scale before leaving for safer locations. What do you weigh? Work: The equation to use is clearly the formula for the force of gravity F -Gm 1 m 2 r 2, since weight is a measure of the force between the two bodies. But you don t know any of the numbers except, possibly G. To plug in and evaluate the force, would be impossible. On the other hand, we do know the force of gravity, F, to be 200lb to start and we know all the definitions. So it is easy to make a ratio. The masses are the mass of you and the mass of Zonds. Neither is in any textbook. The distance, r, is the distance between you and the center of Zonds. It is r zonds at the start of the day and 1.15 r zonds, 15% larger at the end. So we know: Chapter 7 The Start of Modern Physics 10

108 108 F -Gm 1 m 2 r 2 start of the day 200lb -Gm you m Zonds 2 r zonds -Gm you m Zonds end of the day x (1.15r zonds ) 2 where x will be your weight at the end of the day after the planet has swelled up. The problem tells you that both you and the planet have the same mass as at the start of the day. Expanding the square in the denominator produces -Gm x you m Zonds r zonds 200lb x lb To get to the last step, it we substituted 200lb for all the terms in the formula that produced the 200lb. There was no way to do all the substitutions one by one, because we didn t know the individual values. In the problem above, it was clear that it would be necessary to use the force of gravity equation. What about using a conservation law? For example: You are playing croquet with an odd set of balls. You hit your ball and give it a 1m/s going north. It hits a stationary ball which has twice the mass of yours and stops immediately. How fast does the other ball going after the collision? Answer: Look at the equations and the information you have. You can decide by process of elimination. The information has no data concerning force. So Newton s laws of motion aren t useful. The motion of the croquet balls isn t determined by gravity. Gravity only keeps the balls on the ground. Kepler s laws are related to motion of planets. So that lets out the law of gravity and the formulae for circular and escape velocity. The conservation laws all apply, but the information is only enough for the conservation of linear momentum. So to use a conservation law: Find the conserved quantity, the total linear momemtum, before the interaction. Mass of your ball x velocity of your ball +Mass of other ball x velocity of other ball = (M)(1m/s) + (2M)(0)=1Mm/s Total linear momentum after the interaction Mass of your ball x velocity of your ball +Mass of other ball x velocity of other ball = (M)(0m/s) + (2M)(x)= the total momentum from before the balls hit, that is =1Mm/s 2Mx=1Mm/s x=1/2 m/s There is enough information to solve for the final situation, after computing the total momentum and ignoring the fact that we don t know the mass of our croquet ball. Give the problems a try. First do a e, then look at the rest and see what law to use. Answers follow the table. Chapter 7 The Start of Modern Physics 11

109 109 Name of Law Statement of Law or Formula 1 Kepler s First Law Topics Definitions of the Variables 2 Kepler s Second Law 3 Kepler s Third Law 4 Newton s First Law of Motion 5 Newton s Second Law of Motion 6 Newton s Third Law of Motion 7 Conservation of Linear Momentum Chapter 7 The Start of Modern Physics 12

110 110 8 Conservation of Angular Momentum 9 Conservation of Energy 10 Law of Gravity 11 Circular Velocity Equation 12 Escape Velocity The following is coming Doppler Shift Equation Chapter 7 The Start of Modern Physics 13

111 111 Ans Here you are deciding what law to use. a) The relationship between the period, P, the time to orbit the Sun, and the distance from the Sun as represented by the semimajor axis of the orbit, a b) When you have an interaction between two bodies. It doesn t tell how large the force is, but does say both bodies feel equal force c) The Universal Gravitational Constant, 6.67x10-11 m 3 /(s 2 kg -1 ). But you won t need to know the value. d) r is the distance between the bodies producing force in the formula. It is measured from the position of the actual mass involved. In the case of spherically symmetric bodies, the effective distance of each body is at the center. e) You can decide whether a path is an ellipse and is or isn t a proper path for a planet, or other body, orbiting due to gravity. You can t compute anything with it easily. f) force of gravity g) Keplers third law h)circular Velocity Equation i) Escape Velocity Equation j)kepler s second law k) force of gravity l) Newton s second law m) Conservation of Energy n)newton s Third Law o) Conservation of Linear Momentum p) Conservation of Linear Momentum q) Conservation of Energy, there is less kinetic energy after the collision, so some energy must have gone to potential, in the form or crunching the metal of the cars. r) force of gravity s) Newton s second law t) Conservation of Angular momentum Now try to get numerical answers Ans the numerical values f) 0.832lb g) years h) remember that the Earth orbits at 1 AU and has a speed of 30 km/sec. Then use the circular velocity equation and take the ratio of the velocities for the two distances 1 AU and 35 AU. to get 5.07 km/s. i) ( 2)circular velocity =( 2)5.07km/s=7.17 km/s j) When it is closest to the sun, at 10 AU. You haven t learned any formula for this specific speed and I am not expecting you to. But the essence of the law is conservation of angular momentum, so there are ways to figure out the speed if you feel so inclined. k) When it is closest, because of the law of gravity. Since we don t know the mass of the comet, we cannot compute the force. l) The more massive arrow accelerates less due to the force from the bow which is the same on all different arrows. Since it accelerates less, it goes slower when it leaves the bow entirely m) The arrow gets kinetic energy, 1/2 mv 2, from the bow. The bow has potential energy stored in the stretched string. The bow also must get a little kinetic energy after the arrow leaves, because of conservation of linear momentum. There was zero velocity for the bow and for the arrow before the arrow went free. After the arrow is released, it has momentum in one direction. The bow must have equal and opposite momentum in the other direction to fulfill the conservation law. n) 30lb, but in the opposite direction, as Newton s third law states o) No, momentum must be conserved. Before the collision, all the momentum was eastward, and your car has all the momentum. After the collision, all the momentum must be east. Your car has ONLY eastward momentum and its momentum is less than before the accident. So it cannot cancel any northward momentum from the other car. Thus the other car can have only eastward momentum. [) 9.25m/s, by conservation of momentum q) Yes, but you can t tell how much. You can tell that there is SOME body damage by checking out the kinetic energy of the system before and after the collision. There is slightly less kinetic energy in the two cars after the collision than before. Since the total of kinetic and potential energy is conserved, there must have been a change in the amount of potential energy. It would go into squashing the cars. r) Make the ratio of the force between you and the Earth F and the force between you and the other planet is Gm youm earth r earth 2 your weight F Gm youm planet 2 r planet Gm you 1 2 m earth ( 1 2 r earth )2 your weight on new plane Gm you 1 2 m earth 1 r 2 4 earth your weight on new planet 2 Gm youm earth your weight on new planet 2 r earth 2 weight on earth your weight on new planet s) The less massive ball, the hollow one, goes faster t) As the ball unravels the spinning material goes from being closer to the center of the ball to being further. Conservation of angular momentum says the ball must spin slower because the radius is larger. Chapter 7 The Start of Modern Physics 14

112 Chapter 8 Illuminating Light 112 Humans are largely earthbound. To date we have stood only on the Earth and the Moon. We have landed spacecraft on the Moon, Triton, Venus and Mars and have parachuted a probe into the upper layers of Jupiter. We have flown by all the planets except Pluto and have orbited Mercury, Venus, Jupiter and Saturn. We get some samples from the Solar Wind and from meteorites. So how is it that we have the gall to say that we know anything about what planets and stars are made of? Are astronomers just making it up? Many people think that if an idea is called a "theory" it is one among many equally good notions. In science, many ideas called theories are supported by a large interlocking web of evidence. If a different underlying idea is proposed, it must be consistent with all the known data. Alternate concepts need to address the evidence and be successful in explaining it. It does happen that there is more than one explanation consistent with the observations, as we saw for the geocentric and heliocentric models of the universe. But eventually the data may distinguish between the models (as happened when the phases of Venus and the parallax of stars was finally observed). Astronomers are not just spouting off randomly when they describe conditions at places we have not been. They are using the laws of physics and observations. Light consists of a combination of an electric field and a magnetic field changing strength and direction and moving through space. The structure of light is particularly simple because it always has the layout shown below. Electric Field Wavelength Magnetic Field Light moves at c, speed of light, 300,000 km/sec in a vacuum The electric and magnetic fields are at right angles. They are usually at their maxima at the same place. There is no particular direction for the electric field. Since one field creates the other, there is no such thing as just an oscillating electric field moving through space at c without the magnetic field. The major feature of light is the wavelength. It tells how long between repeats of the wave. The figure shows the wavelength between peaks of the electric field. But there is nothing special about any part of the wave. The wavelength is the distance between the repeats, however they are arranged. Light goes at a fixed speed through a vacuum. The speed is called c, and the numerical value is 300,000 km/sec (This is the same as 186,000 miles/second, but we will be using the metric system). It doesn't matter whether you are moving, light, from whatever source moves at c with respect to you. Because light has a fixed speed, one can characterize it by either the wavelength, or by the frequency, the number of waves passing a point every second. If you know one, you know the other because (length of each wave) x (number of waves passing each second) = speed of wave packet Hopefully this word equation is no surprise. The speed is always the same, c, 300,000 km/sec. So if you know the wavelength, the frequency can be found and conversely. Different wavelengths cause different physiological responses in us. When light has a wavelength between 4x10-7 and 7 x 10-7 meters or 4000 and 7000 Ångstrom units, we can see light and the different wavelengths appear as different colors (a nanometer is 10-9 meters). Other wavelengths Chapter 8 Illuminating Light 1

113 usually cannot be sensed, but do have effects. The figure below shows some of the names for wavelengths of light. 113 All of these names refer to the very same set up, crossed electric and magnetic fields moving through space at the speed c. The names arose because different wavelengths are detected differently. While all these names are given to different wavelengths of light, there are a couple of similarly named things that are NOT light. Sound is a vibration of material, not a form of light. Cosmic rays are particles from outer space. Radiation is a general term that includes light, but also includes particles given off from radioactive elements, Light comes in individual packets called photons. When light is brighter, there are MORE photons, not photons with higher waves. The shorter the wavelength, the more energy carried by each photon. Chapter 8 Illuminating Light 2

114 114 There is a variety of ways to cause light. A changing electric field can generate light. This is the way that radio stations form their over-the-air signal. Their antennas are visible near SF Bay on the mud flats. They are just straight, vertical antennas about 1/4 wavelength. Electrons, negatively charged particles, are sent up and down the antenna. Each charge carries and electric field. The electron s motion causes a varying electric field. The electric field causes the magnetic field. And the combination is a form of light. The resultant radiation is what you pick up on a radio receiver. The sound you hear is the result of the signal being used to vibrate a mechanical piece, often made of paper. In astronomy we are very concerned with light made by atoms and molecules because it allows us to find out about the source. To understand the way it works requires that we learn about atoms and molecules. Atoms all have a nucleus with positively charged particles called protons and neutral (no charge) particles called neutrons. Almost all of the mass of the atom is in the nucleus, although the nucleus takes up about 1/100,000 of the radius of the atom. The number of protons determines the type of atom, that is what element it is. Each element can have a various numbers of neutrons. The number of neutrons determines the isotope (of the element). As you may have heard electric charge comes in both positive and negative and opposites attract, like in love. The closer together, the stronger the attraction or repulsion. The attraction keeps negatively charged particles in orbits as close to the nucleus as physics allows. The reason that protons in the nucleus stay together (in spite of the their electric repulsion) is that there is another, stronger force, called the strong force acting on the protons and neutrons. The strong force is much stronger than the electrical repulsion at small distances. The strong force gets much smaller than the electrical force at large distances. Negatively charged particles, called electrons move around the nucleus in paths or areas orbitals. These orbitals have a variety of sizes and shapes. Each orbital can be occupied by up to a specific number of electrons. "Normally" the number of electrons is the same as the number of protons, so all the charges cancel. If the number of electrons is NOT the same, the situation is called an ion. All of chemistry, all of the processes that usually occur on earth are changes in how the electrons from one or more atoms are shared. The nucleus of the atom is not normally affected. Electric force pulls the electrons toward the nucleus. Electrons have kinetic energy that keeps them from falling into the nucleus. This is rather like the case with planets orbiting the Sun. Gravity pulls the planets, their kinetic energies keep them from falling in. If we want to move electrons to orbits further away from the nucleus, energy needs to be added. Unlike the orbits of the planets, the electrons cannot go to just any path around the nucleus. Each type of atom, molecule and ion has a unique set of orbitals corresponding to the possible energy levels. These orbitals have no physical presence when no electron is in them, but they define the only paths the electrons can take. Chapter 8 Illuminating Light 3

115 115 -e N u c l eus +p Energy Levels get closer together in both energy and space going further from the nucleus Energy Levels Available to electron Electrons have a lowest energy level, typically the orbital allowing the electron to be closest to the nucleus (compatible with the positions of other electrons). When an electron is in any but the lowest energy level, it will eventually return to the lowest level. As it does this, the excess energy is released. Typically a photon with just the right energy is given off to get rid of the energy. When a sample of a material has its electrons excited, different electrons go into different levels. As the electrons come back to lower energy levels, the pattern of wavelengths (colors of light) allows us to distinguish the type of atom or molecule. It is rather like the fingerprint of the material. The pattern of bright light from a diffuse gas is called an emission spectrum. It consists of bright light at the wavelengths (energies) corresponding to the transitions to lower energy levels. Hydrogen light gives a pattern of Red, Teal, and many purple photons when it s electrons jump to lower energy levels. Mercury vapor gives Purple, Green and brownish-yellow. Atoms also give light in many wavelengths we cannot see with our eyes. For us to be able to see these colors, the material must not be too dense and the light from the material must not be overwhelmed by radiation from the background, Electrons can be given energy by collisions, by subjecting them to an electric field to counteract the attraction of the nucleus or by letting them absorb light. The random motions of atoms result in collisions. The hotter a material, the faster its particles move and the more energy transferred in a collision. (Absolute zero is the temperature where particles have as little motion as possible.) If the collision causes an electron to move to a higher level, the electron emits light as it returns to a lower level. If the material is dense enough (like most solids and liquids and some dense gasses), the electrons drop from the higher levels to lower levels, but they do not succeed in giving off exactly the characteristic energy. Collisions from other materials change the Chapter 8 Illuminating Light 4

116 energy slightly. Many molecules have a great number of energy levels, so a small change in these levels smears them together. This makes a continuous spectrum. A continuous spectrum includes all colors including wavelengths not visible to our eyes. The density obscures the information about the type of material, but it does allow us to tell the temperature of the material. The distribution of particle velocities, determined by temperature, determines the amount and the distribution of energy given by a body. Black body spectrum is the name given to the distribution of energy given by a sample of dense material where collisions cause the excitation. The curves below show the amount of radiation a black body gives at each wavelength. The curves are for bodies of the same size and at the same distance from the observer. A formula gives the shape of the curve. Astronomers observe the light from a distant body, and compare the distribution of energy or the peak of the energy distribution to the theoretical curves. Matching the curve and the observations tells the temperature of the body, In many cases, a comparison of the amount of light at only two wavelengths is enough to find the temperature. There is also a formula relating the total amount of energy per second to the temperature for a body of known size. This formula can be used to find the total amount of energy given by a body. 116 Ideally a black body absorbs any incoming light equally well and emits any wavelength with no impediment. Realistically, the overall black body distribution can be used to tell the temperature of most bodies without too much difficulty. When an atom encounters light, it can absorb the light if the light is at just the right energy to raise the electron to a higher energy level. It is not all right for the light to have more energy than is needed to change the energy level. The electron cannot absorb just part of the energy. It can only accept light with exactly correct energy. After an atom absorbs energy and goes to a higher Chapter 8 Illuminating Light 5

117 energy level, it eventually returns to the lower energy level, emitting light. The sequence of events is shown below. 117 Notice that the electron in the figure above has jumped up TWO levels, rather than one. This is perfectly all right, if the light has enough energy (and some other relationships between the levels are met). The electron need not come down to the original lowest level all at once. It could come to the second level, emitted a photon, and then come down to the lowest level, emitting another photon. The direction of the outgoing light is usually independent of the direction of the incoming light. If there is a bright continuous background (a rainbow), with diffuse (not dense) gas in front of it, there is a decrease in the amount of light received at those wavelengths absorbed by the gas. The appearance of the spectrum becomes a rainbow with dark lines where the gas would normally produce bright colors. This is called an absorption spectrum. The dark lines tell the same information that the bright lines would. The continuous background can be used to find the temperature of the background material. Summarizing the types of spectra: A continuous spectrum is produced by dense bodies. The distribution of amount of energy at different wavelengths tells the temperature. The appearance of the spectrum is like a rainbow, all colors with varying amounts of different colors. Diffuse material with nothing bright behind it produces an emission spectrum, that is light at only those wavelengths specific to the material. The type of material can be found from the pattern of lines produced. The temperature of the material can usually be told from the distribution of lines and their intensity, but this requires a simulation of the gas. An absorption spectrum results when diffuse material is viewed with a bright, continuous source of light behind it appears as though it was in silhouette. The continuous spectrum appears and dark lines appear at the wavelengths where the diffuse material is absorbing and reemitting light. The appearance is a rainbow with dark lines on top of it. It is called an absorption spectrum. The continuous background can be used to find the temperature of the material in the background. The absorption lines tell the same information as the emission spectrum would. Chapter 8 Illuminating Light 6

118 118 All the colors of the rainbow, one blends into the next with no breaks All the colors cut by dark lines Colored lines on dark background NOT all colors Among the things we can tell from light, is how fast we and the source are moving toward or away from one another. This motion causes Doppler Effect is a change of the wavelength of light. Doppler effect also occurs for sound, and you have probably heard the change in pitch as a siren or a race car goes by you. The reason that Doppler shift occurs is that the distance between the observer and the light Chapter 8 Illuminating Light 7

119 changes during the time that the light wave is being emitted. When the source approaches, the wavelength you get is smaller than the wavelength originally emitted. This is called blue shift. When the source recedes, the wavelength we get is longer and the effect is called red shift, regardless of the actual color involved. The formula relating the velocity to the Doppler effect is as follows. V is the velocity of the body relative to the observer (+receding, - approaching) c is the speed of light, 300,000 km/sec λ is the symbol for the ORIGINA:L wavelength of the light, the wavelength sent Δλ is the change in the wavelength from when it left the source to when it was received. It is found by subtracting the original wavelength from the wavelength you receive. The combination Δλ does not mean to multiply, it is like a compound word. If we have no idea what the original wavelength of the light was, it is not generally possible to find the velocity of the source. We assume, however, that the spectra of elements and compounds are the same everywhere. When there is a Doppler shift, all the light from the source is affected. The pattern of lines will be shifted in a predictable way. So the pattern will still be recognizable. So if we see the pattern from hydrogen, for example, the red, teal and purple lines would all have their wavelengths changed by Doppler effect, but the pattern still tells that it is from hydrogen. Example: You receive the teal line from Hydrogen. It is normally emitted at 4861Å, but you receive it at 4859 Å. What is the velocity of the source with respect to you? Write the original equation, then substitute for each variable. The original wavelength is 4861Å and the change is -2 Å, since what you receive is 2 Å less than what was sent. The speed of light is always the same, 300,000km/sec. So the Doppler Shift equation is 119 Substituting The Angstrom units cancel. Multiply both sides by 300,000km/sec to get The negative sign indicates that source and recipient are approaching one another. It is not possible to tell whether one or both are moving. An effect like the Doppler shift is the way that we found out the universe is expanding. We talk about the red shift of distant galaxies. Sometimes you will hear the value of the red shift on the news. The way that it would be said is "Distant galaxy with redshift 6 has been found. The value 6 refers to Actually galaxies with redshift nearly 7 have already been found. How can that be? The variable z is the same as the right hand side of the equation for V/c. Does it mean that the speed of the source is greater than c, the speed of light? Actually no. There is a more correct equation for the correspondence between shift and velocity. This other equation is This is the formula to use for z greater than 0.1 or so. You will not need to compute with this equation in this class. Chapter 8 Illuminating Light 8

120 120 Practice Questions 1) Helium normally emits light at 5016.Å, but you receive this light at 5011Å, how fast are you moving compared to the source? 2) You plan to go to the Moon. Your speed might be as large as 1 km/sec both coming and going. If you transmit a signal to NASA at 2 m wavelength, what is the range of wavelengths that will be received? 3) You observe a Nitrogen line at Å. It is normally seen at Å. What can you tell? 4) You are planning to send a probe to Mars. If the probe goes at speeds up to 25 km/sec in either direction, and if it sends 0.5 m radio waves, what is the range of wavelengths you receive? Ans 1) km/sec, be sure to use 5016Å in the denominator. Negative velocity means that you and the source are getting closer together. You cannot tell what or who is moving. 2) Your speed would cause a Doppler shift (Δλ) of ±6.6667x10-6 m. This is NOT the wavelength that is received, this is just the change in the wavelength. It can take either positive or negative sign because the path to and from the Moon is both approaching and receding from the Earth. To get the wavelength actually received, this change is added to the original wavelength. So the range of wavelengths actually received is from to m. In this case, it is necessary to keep enough digits to demonstrate the effect of the Doppler effect 3) You and the source are getting further apart at km/sec 4) From m to m. Chapter 8 Illuminating Light 9

121 Chapter 9 The Solar System-Overview 121 I. What is in the Solar System? The Solar System consists of the Sun and objects that orbit the Sun; eight planets and their moons, comets, asteroids, dwarf planets, small Solar System Bodies, gas and dust. We have visited only the Earth and our Moon in person. We have sent landers to Venus, our Moon, Earth, Mars, Titan and the asteroid Eros. We have sent spacecraft to orbit Mercury, Venus, Mars, Jupiter, and Saturn and have flown by Uranus and Neptune as well as several comets and asteroids. A probe entered Jupiter s upper layers in 1995 and another landed on Titan (Saturn s moon) in The New Horizons mission will reach Pluto in 2015, Charon and proceed into the Kuiper belt. And Mercury Messenger is orbiting Mercury and will begin mapping in Solar system exploration has exploded since the 1960 s. So what can we say about our Solar System and how does it compare with bodies orbiting other stars? Even the definitions of the constituents of the Solar System are changing. Generally our Solar System consists of one star, the Sun, the things that orbit it, and material that is flowing out of it, the solar wind. Until August 2006, there was no agreed upon definition of a planet. Then the International Astronomical Union (IAU) voted to define a planet as a celestial body that (a) is in orbit around the Sun, (b) has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape, and (c) has cleared the neighborhood around its orbit of other objects orbiting the Sun.. Dwarf planets are also spherical and orbit the Sun, but have not cleared their neighborhoods of other material. Even smaller objects that orbit the Sun would be called Small Solar System Bodies. These definitions really apply to planets in our Solar System, rather than objects orbiting other stars. The definitions were studied and debated, but they don t have the force of law and might be changed in the future. In June 2008, the IAU also defined plutoids, as dwarf planets that are further from the Sun than Neptune. Pluto is both a dwarf planet and a plutoid. Speaking generally, planets are not only objects that orbit the Sun. We have discovered planets orbiting other stars. And gravitational interactions among planets, dwarf planets etc can change their orbits, often causing low mass objects to escape from the star. I don t know what the name would be then. Planets are distinguished from stars, because planets are unable to cause nuclear fusion in their interiors. That normally means that they have less than about 13 times as much mass as Jupiter, if there are made of hydrogen and helium Asteroids orbit the Sun, many in the area between Mars and Jupiter. But some come closer to the Sun than the Earth and others go to further out than Saturn. Some asteroids seem to be rocky, others are probably icy, and still others only very loosely consolidated, like rubble or dust bunnies. Asteroid orbits are largely near the same plane as the planets orbits. Kuiper Belt Objects are probably like Asteroids, but their orbits are largely outside of Neptune s orbit and they are more icy than rocky. Comets are distinguished from asteroids because they form tails as they come close to the Sun. When comets are far from the Sun, they are entirely frozen and cannot be distinguished from asteroids. Comets are mixtures of dark, rocky material and ices. The ices are frozen when the comet is far from the Sun. They are partly vaporized by sunlight as they come close to the Sun. The solar wind, particles from the Sun rushing away at hundreds of kilometers per second, pushes the vapor in the direction away from the Sun. The vapor reflects sunlight, resulting in the comet-tail appearance. The comet never regains the material from the tail. So comets lose mass each time they pass near the Sun. Eventually comets break up and disintegrate. Often particles that break loose follow the same orbit as the comet. When the Earth passes through the stream of particles, we experience a meteor shower. Moons orbit planets. Some moons are just a few kilometers across. There are many moons whose sizes we don t know. All we see is that they reflect sunlight, but we don t see their edges Chapter 9 The Solar System 1

122 clearly. They might be large and shiny, so only a single point reflects back to us. Or they might 122 be small and rough surfaced. The largest moon, Ganymede, is larger than the planet Mercury. As of Dec 2007, 163 natural satellites have been discovered orbiting our planets. Surely there are more. As Kepler thought and the figures show, the planets orbits are ellipses, not circles. In OUR solar system, the planets orbits are quite near circles (low eccentricity) and the planets all orbit going the same direction. Venus, Uranus and Pluto spin retrograde. Some moons of the planets orbit retrograde, as do some comets. Pluto s orbit is the more eccentric than those of the planets in our Solar System. That is, Pluto s orbit is the furthest from being a circle. But even Pluto s orbit looks rather like an off-center circle around the Sun. Comets orbits and orbits of planets orbiting stars other than the Sun have even more eccentric orbits. Pluto s orbit carries it inside of Neptune s orbit, but the orbits never intersect. Since Pluto takes 1.5 times as long to orbit the Sun as Neptune does, the two planets never collide. (It is rather like model trains using some of the same track. They are synchronized so there are no collisions.) It isn t chance. Gravitational interactions with Neptune have nudged Pluto into this relationship. Simulations of interactions between Pluto and the planets indicate that changes (perturbations) in Pluto s orbit build up so that in perhaps 50 Million years, Pluto s orbit will change substantially. The overall size of the Solar System is determined by the size of the orbits of the outermost bodies. These are comets (with no tails) orbit in a nearly spherical region surrounding the planets orbits, called the Oört Cloud (after Jan Oört). The Oört Cloud starts outside Pluto s orbit. We think it goes about about 150,000 AU, roughly half way to the next nearest star. In 2004, an object called Sedna was discovered. Its orbit takes it so far away that it is probably part of the Oört cloud. far from the Sun. Current theories suggest that the comet nuclei, small bodies of rock and ice, were formed closer to the Sun than the Oört Cloud, in regions where there was more material. After the comet nuclei formed, gravitational interactions with the early planets threw them We would like to find the sizes, masses, and composition of the planets. But, how is that done? II Finding Planets Distances and Diameters Copernicus found the sizes of the planets orbits in terms of the Earth s orbit. His methods and results were basically correct. Even when Kepler realized that the orbits are ellipses, the overall sizes of planets orbits were little changed. Copernicus did not really know the distance between the Earth and Sun. He knew about Chapter 9 The Solar System 2

123 Aristarchus estimate that the Sun is 1200 Earth radii away and he knew about Eratosthenes (and 123 also later astronomers ) estimates of the size of the Earth. But as we learned, Aristarchus was wrong, the distance to the Sun is really about 24,000 earth radii from Earth. The actual distances of the planets in kilometers were not known until Cassini measured the parallax of Mars in He used a baseline from Paris to Cayenne (France). Mars was at opposition at the time. That is when Mars, Earth and the Sun are all in a straight line with both planets on the same side of the sun. He already knew that this distance was AU. Parallax gave him the equivalent of this distance in kilometers. Once the distance to Mars was known, the distances to the other planets followed. When the distance to a body is known AND the edges of the object are seen, so the angle it takes up is also known, the linear size is easily computed. All of the planets are large enough and close enough that astronomers have now observed the angle they subtend. The distances to them are computed based on the positions of the planets in their orbits. Once we know the angle subtended and the distance, we can solve the equation above for the diameter. The radius and volume follow immediately. This method is not generally used for stars. Stars are usually larger than the planets, but they are so far away that most telescopes cannot tell their size. Telescopes are now being built which operate in groups of two or more, called interferometers. They can distinguish the disks of some of the closer, larger stars. III Finding the Mass Finding the mass of any large body depends on observing its gravity and it assumes that gravity is applicable. Combining the law of gravity and Newton s second law. The acceleration due to gravity force is. Dividing by m 1, The acceleration of a body due to gravity from another depends only on the distance and the mass of the other body. As we track the motion of a moon or a space probe, we can find the mass of the body attracting it. This is why heavy and light things fall with the same acceleration. Another way to measure the mass of a distant body is to use the formula for circular velocity when we know Vcirc and r, the radius of the orbit, we can use the known value of the constant G and solve for m 2. For things orbiting the planets in our solar system, we can normally measure r from the apparent angular size (same method as measuring the planet s diameter). To find V circ, the Doppler effect can be used or we can watch to find the time to complete the orbit, and use r, via Distance = Rate x Time=V circ x Time for orbit = 2πr So, rearranging V circ = 2πr /Time for orbit This method of using the effect of gravity on an orbiting object to infer the total mass is the basis for all of our knowledge of masses of galaxies, groups of galaxies quasars etc. Then the amount of mass computed from V circ is compared to the mass inferred from counting the stars, planets, gas, and dust. Surprisingly the mass of the observed bodies is nowhere near enough. When Chapter 9 The Solar System 3

124 dark matter is discussed, this is the extra material needed to make the observed effect of 124 gravity above and beyond the amount of material attributable to the stars etc. More than 90% of the normal material in the universe is thought to be dark matter. It is called dark matter, because no light or particle radiation is observed coming from it. Only the effect of its gravity is noticeable. In 1998, it was discovered that there is a repulsive effect operating in the Universe that is about 2.3 times as strong as the gravity of the dark matter. This is called dark energy and its effect is mainly seen in the relative motions of clusters of galaxies, not within smaller objects. IV Evidence of Internal Composition The composition of the interior of large bodies cannot be sampled directly. We infer it by modeling the interior. This same modeling procedure is used for stars and for planets. The first indication of the interior construction of a body is the density. Density is defined as the mass divided by the volume (Mass/Volume). We find the density from knowing the mass and the radius of a body,r, and using the formula Volume =(4/3)πR 3 to get the volume, then dividing. How does the density help? Imagine holding a full quart size milk container. It holds a little more than a liter of volume and a liter is 1000 cm 3 (1kg/liter). Water and milk both have a density of 1 gram per cubic centimeter (written gm/cm 3 ) or, equivalently 1000 kg/m 3. On the other hand, the densities of some common materials are Air at sea level gm/cm 3 =1.2 kg/liter =1200 kg/m 3 Water 1 gm/cm 3 =1 kg/liter =1000 kg/m 3 Rocks 3-5 gm/cm 3 =3-5 kg/liter = kg/m 3 Iron 7.8 gm/cm 3 =7.8 kg/liter =7800 kg/m 3 Gold 19.2 gm/cm 3 =19.2 kg/liter =19200 kg/m 3 So, when we find that the Earth has an average density, 5.5 gm/cm 3, can we know what it is made of exactly? Could it be made of all water and air? All rock? There is no way to average air only or rock only to make an average of 5.5 gm/cm 3. We know from the surface that the Earth includes some water and rock, so we must also include some material with density higher than 5.5gm/cm 3 to get the correct average density. The interior of the Earth is compressed by gravity due to the overlying layers. So material in the interior is denser than the same material would be if it were at the surface. To figure out the composition of the planets, we choose common materials that might give the correct density and make a mathematical model of the planet. If the mass, radius, surface temperature and other features of the planet predicted by the model match what we observe, we accept the model as being valid, at least until we find out some new fact that contradicts them. Which are the common elements anyway? When we look at our bodies or the Earth, we get a Chapter 9 The Solar System 4

125 very different picture of the situation than we get from stars and from gas between the stars. The 125 first chart shows numbers of atoms different elements in the Solar System overall. Since the Sun includes about 98% of the material in the Solar System, it dominates the abundances. The vertical scale is the number of atoms compared to the number of Hydrogen atoms. As a reference, the number of hydrogen atoms is set at As you can see, the number of hydrogen atoms is nearly 10 times the number of helium atoms. All other types of atom are far less common. We find these abundances mostly by analyzing the Sun s spectrum. (For some parts of the curve the abundances from meteorites are used.) Abundances of elements in the Universe as a whole are thought to be similar to those for the Sun. This may seem odd. The Earth is NOT mostly hydrogen. We don t have direct information about the interior of the Earth, but the elements in the crust are very different. And the core is dense, not like Hydrogen. The relative abundances of elements in Earth s crust are shown in the chart. So why does the Earth have different elements from the average? Do all the planets have different elements from the average? Do all the planets have the same composition? V Jovian and Terrestrial Planets and the Formation of the Solar System The planets in our solar system generally fall into two categories, the terrestrial planets and the Jovian planets. The terrestrial planets are similar to the Earth, as the word terrestrial indicates. Jovian planets are similar to Jupiter. Jove is another word for Jupiter, the god. Mercury, Venus, Earth and Mars are the terrestrial planets. Jupiter, Saturn, Uranus, and Neptune are the Jovian planets. Little Pluto fits into neither category. It is probably much like other Kuiper Belt objects (asteroid or comet like objects orbiting the Sun at distances AU). The terrestrial planets are closer to the Sun and can be even denser than rocks. So we expect that they are not primarily of hydrogen and helium. The Jovian planets are found further out from the Sun. They are far less dense, with densities from 0.7 gm/cm 3 for Saturn to 1.64 gm/cm 3 for Neptune. This is much denser than hydrogen. The Jovian planets are larger in both mass and radius than are the terrestrial planets. Differences in composition, mass and distance from the Sun are likely related to the way that the Solar System formed. Summarize the features of the different types of planets below. Feature Terrestrial Planets Jovian Planets Number of moons Time to spin Rings Surface features Internal energy sources Density Mass Radius VI Formation of the Solar System We think that the Solar System was once a single cloud of gas, with roughly the same composition as the Sun. That is, 90% of the atoms were (and are) hydrogen, and ~9% helium with less than 1% everything else. As the cloud contracted, the densest part contracted to become the early Sun, and heated up. This was a large part of the mass. Chapter 9 The Solar System 5

126 Gravity tries to pull together small masses of material as well. But as things are compressed, they 126 heat up. The gas pressure grows, fighting gravity. The Equation of State (ch 9 sec VIIi) describes the relationship between temperature, density, volume and pressure. Different materials can have different equations of state. (If you took chemistry, you may have learned the Ideal Gas Law, PV=NRT or PV=ρkT. This is the equation of state for ideal gasses. Other materials have other forms of the equation. For large masses, gravity wins over pressure and the material contracts. For small masses, pressure resists gravity successfully, and the material gets no more compressed. We think that for the Sun, gravity probably was sufficient to overcome the pressure. A shock wave from an exploding star may have given the Sun s material a push As the gas cloud contracted, the part of the material that became the Sun got dense and hot. It heated up the gas remaining around it. How then did the planets form? Solid materials hold together because there are bonds between neighboring molecules or atoms. We think that there was dust in the material that became the Solar System, because dust is seen in distant gas clouds and even in the outer layers of stars. If dust particles happen to hit one another, they may stick together building up to larger and larger bodies. We think that the dust and other solid particles were able to hit and stick together forming larger bodies called planetesimals. Eventually these planetesimals hit and stuck together into large enough bodies that gaseous materials could be attracted and retained. The process of hitting and sticking is called accretion. This is our best current idea of how the planets began to form. What materials would make up the planetesimals? There are some materials, called volatiles, are liquid or vapor at even low temperature compared to room temperature on Earth, like hydrogen and ammonia. Other materials, called refractories, are solid to high temperatures. Examples of refractories include iron and silicates. The terrestrial planets are close to the Sun. It is and was warm there, only the refractories would be available in solid form to hit and stick, and to start planet formation. But referring to the abundance chart, we can see that there is very little of the materials that can make these refractories. The terrestrial planets formed out of this comparatively unusual material. Estimates of the temperature in the gas at the time the planets formed, indicate that starting at 4 AU from the Sun and going further, water (H 2 0), ammonia (NH 4 ) and methane (CH 4 ) all become solid, available to hit and stick. Referring back to the chart of the abundances of elements in the Sun, it is apparent that Hydrogen is the most common element. Hydrogen alone does not solidify except very low temperature (13.8K). The next most common element, Helium, forms no compounds and doesn t solidify until 0.95K. The Solar System was and is too hot for these elements to solidify. The next most common elements are Carbon, Nitrogen, and Oxygen. These are the very things that combine with Hydrogen to make water, methane, and ammonia. So these materials are quite common. Planets that can accrete these materials are able to grow large, because the cloud that formed the solar system contained a large percentage of these materials. The solid material, both refractories and volatiles, hit and stuck, accreting into cores for these distant planets. If the mass of the core is large enough, it can attract the still gaseous (but plentiful) hydrogen and helium, making the large Jovian planets. Jupiter and Saturn seem to have formed at a distance where the Solar Nebula had a lot of mass and where water and ammonia were solid. So they grew very large. At large distances from the Sun, the mass in the nebula probably decreased and the mass of the planets formed decreases with it. Thus the planets get smaller after Jupiter. The very distant Kuiper Belt and Oört Cloud objects were probably formed closer to the Sun and later thrown there by the gravity of the massive Jovian planets. As the early Sun matured, the solar wind began. The solar wind, particles of the Sun streaming outward at hundreds of kilometers per second, pushed the remaining gas out of the Solar System. This stopped the planets from growing any larger. There were still planetesimals around. They were too dense for the solar wind to have much effect. Many of them crashed into the larger planetary bodies during the first billion years of the Solar System. Chapter 9 The Solar System 6

127 So it seems that there is an explanation for the Jovian and terrestrial planets in our Solar System. In fact, it seems that Jovian planets would have to be formed far from the star and terrestrial planets formed near the star. On the other hand, it isn t this way in all systems with planets. Birth of the Solar System 1 Once upon a time, there was a cold cloud 2 Gravity pulled it to contract. Possibly gas from a supernova (star explosion) hit the cloud compressing it and helping it contract As the cloud contracted, the gas collided. Random velocities cancelled, while the common velocity causes the cloud to spin. 4 The center of the cloud contracts fastest, becoming the Sun. A disk of gas and dust called the Solar Nebula is left behind 5 Early Sun was MUCH larger and brighter than Today. Solar Nebula near Sun was hot, further out colder. 6 Solid particles can hit and stick, building up to larger bodies, called planetisimals. Only a few materials are solid near the Sun, more are solid far from the Sun. 7 The largest planetesimals can attract gas, increasing the size of the final planet. The larger planets change the orbits of smaller nearby ones. 8 Solar Wind, gas from the Sun, pushes the remaining solar nebula gas, quenching planet formation VI Extrasolar Planets, planets orbiting stars other than the Sun. In 1995 the first detections of planets orbiting other stars were made. Since that time, more planets are discovered nearly every week. The most current count of planets found and the methods used to find them can be found at information and a cool simulation can be found at There are several methods that have, so far, succeeded in detecting planets. The easiest planets to detect are very massive ones that are close to their planets, and these are the majority of the ones that have been found so far. Unlike our solar system, we often find Jovian planets (gas giants) close to the star. That seems an unlikely place for them to form, since the volatiles cannot be solid there. Simulations of the possible evolution of the orbits of these planets indicate that the planets could have formed far from the stars and their orbits been changed by the effects of other planets (or possibly passing stars) so that they come closer to their stars later. These orbits may well cause the planet to evaporate. Chapter 9 The Solar System 7

128 How can we detect these planets? 128 Light Detection The most obvious way to find a planet is to see its light. In most cases, this is harder than it sounds because the star that is orbits is far brighter than the planet so the planet is lost in the glare. It is a trade off between being able to get the planet out of the glare of star light and having enough light and enough motion to detect. It is not enough to just detect the light from the planet, it is necessary to detect the motion of the planet to know that it is not a distant or very faint star. Spectra of the planet can be used to tell whether it is a star, distant faint galaxy or a planet. As of July 2009, 11 planets have been found by imaging them directly. The stars are typically much less massive than the Sun. B. Detection by Microlensing When an object comes between us and a source of light, gravity from the foreground object warps space and light from the background object follows the bending. The effect of the bending is that the background object appears brighter for a while something is in front of it (not blocking it). If the foreground object is a star, there is one brightening event. If the foreground object is a star plus a planet, the background star brightens for a longer time or two separate times.. The duration of the brightening indicates the size of the foreground object. As of July 2009, 11 planets have be detected that way. C. Detection by Dynamical Effects Most of the planet detections so far are due to observations of the motion of the star they orbit. This occurs because the force of gravity from each body acts on the other. Since both star and planet experience a force, each experiences acceleration and consequent motion. Depending on the direction to us compared to the orbit of the planet, the star may move mainly toward and away from us or basically in a small circle as we see it. x star Planet Gravity of planet and star cause them to orbit the center of mass Motion of star is toward and away from this observer, causing Doppler effect The toward-and-away motion has been noticed, largely by measuring the Doppler Shift of the star. This tells the actual speed of the STAR as it orbits the center of mass. Using the formula for circular velocity, our knowledge of the mass of stars, and Kepler s laws, we can estimate the mass of the unseen companion. In many cases it appears to be the right mass for a planet. xxxxxxx Motion of the star can be a small circle as seen face on xxx This same effect, Doppler shift of the light from the Sun, could be used by a distant observer looking at the Solar System. The distant observer would see mostly the 11.8 year period of the Sun in response to Jupiter. This is because Jupiter is much more massive than the other planets. In fact, it is more massive than all the other planets put together. The other planets would have an effect, so the Sun would move in a complicated motion. An observer would need to measure the motion of a star until it had completed at least half a cycle to be sure that the motion was due to a planet. Having nine planets makes the motion of the Sun more complicated. The small planets, like us, have little effect and are likely to go unnoticed for quite a while. Massive planets close to their stars are the ones that are easiest to find. They produce a strong gravitational force and they change the direction of the force on the star quickly. So the observe can find the pattern of the star s motion quite quickly. If the orbit of the planet is edge-on to the observer, the motion of the star shows up as a Doppler shift. If the orbit of the planet is face on to the observer, the star s motion shows up against the Chapter 9 The Solar System 8

129 background of other stars. As of July 2009,1 plantet had been found that is face on, and 277 that 129 are detected by Doppler shift. C. Detection by Changing Amount of Light-Transits and Eclipses Once in a while, the planet lines up so that it comes directly in between us and the star, as it orbits. The planet is smaller size than the star and colder. So when the planet is in front of the star, the amount of light that we get is decreased. This is called a transit. Halfway around the same orbit, the planet will go behind the star, and again the total amount of light we get will again decrease. This is called an eclipse. When the planet is eclipsed, the total amount of light decreases again, but by a smaller amount, since the planet is cooler than the star. It is not very efficient to look for planets by waiting for transits, but in some cases, planets that we know about from radial velocity curves have also had transits. The great thing about a transit is that the radius of the planet can usually be found. The Doppler shift of the star and models of stars tell us the mass of the planet, So when we combine the mass and the radius of the planet, we can find the density and can tell whether the planet is a gas giant or a terrestrial planet. Sometimes, when the planet is in front of the star, absorption lines from the planet s atmosphere can be seen (because the bright star shines through it). This indicates what the planet s atmosphere is made of. As of July 2009, 59 planets have been found by detecting a transit. D. Detection by Timing - Pulsar Planets In a few cases the planets are found orbiting pulsars, dead stars that spin very fast and sweep beams of optical and radio radiation past the Earth These beams are seen at very regular intervals. The motion of the pulsar in response to the planet causes the time that we receive the radiation to vary. Eleven planets have been detected this way. VII Modeling the Interiors of Planets and Stars To go from a measurement of average density to a model of the interior of a body, astronomers use several simple concepts. For a spherical body, they divide the body into layers and for each layer they have several equations to solve. 1) Mass in Each Layer equals density times volume in the layer (mass=4πr 2 ρ) 2) Hydrostatic Equilibrium force of gravity pushing in is balanced by pressure out 3) Equation of State relates pressure, temperature, density, and volume. Different materials and different states (like solid, liquid, gas) of the same material have different equations of state. 4) Heat transport describes how energy from higher temperature interior layers is transmitted out There are at least three ways that the energy can be transferred, Conduction-Particles collide with one another and transfer kinetic energy Convection Regions of liquid or gas heat, expand, and may be displaced as denser, colder material sinks in the presence of an overall gravitational field. Radiation Photons carry energy between material. This is the only method that can work in a vacuum. The model will calculate the effect of all of these methods, though usually one dominates. 5) Energy generation- describes the amount of energy produced as a function of temperature, pressure, density and composition. Typically planets generate a little energy from radioactive elements. Stars generate energy by nuclear fusion. The composition of the planet or star is guessed, based on the average density and any other features observed. It need not be the same at every layer. Then a computer solves the equations at each layer to find temperature, pressure, density etc. The total mass, the radius, and the temperature at the outside of the body are compared with those observed. If not, the composition is changed and the model computed again. The model must match all the observed properties. Does this prove that the model is an accurate representation of the planets interior? No, of course not. When additional information is obtained, such as a measurement Saturn s flattening from rotation, or detection of a magnetic field the model is revised. Planets models are being Chapter 9 The Solar System 9

130 substantially revised due to the space program. differences from one to the next. Planets in our solar system exhibit many 130 When we use this same procedure on stars, it is a different matter. Modeling the interiors to understand the way stars change over the course of their lives is one of the success stories of astronomy. Stars start their lives as balls of gas, the same composition all the way through. Nuclear reactions and gravity cause them to heat up and convert hydrogen into helium, governing the stars temperatures and luminosities. Computer models of stars at a variety of stages in their lives have been compared to some of the many many stars we observe. The models have been modified to match the life stages of stars quite well. Questions: 1) What are three ways that you can tell a terrestrial planet from a Jovian planet 2) Define the solar nebula 3) The following are steps in the formation of the solar system. Put them in the order they occur a) Planetesimals hit and stick b) Large planetesimals pull in gas with their gravity c)cold gas cloud contracts d ) Solar wind disperses gas e) Early Sun evaporates volatiles f) Sun heats up 4) Which of the following are part of the Solar System a) Milky Way galaxy B) Venus c) comets d) Pluto e) Sirius f) Gas g) Virgo Cluster of Galaxies 5) What is the Oört Cloud? About how large is it? 6) What is the method we use to find the diameter of a planet in our Solar System (not Earth)? 7) How can we detect a planet orbiting a star other than the Sun? 8) Are the orbits of the planets in our solar system exactly circles? Which of the orbits is furthest from being a circle? 9) What are volatiles? 10) What is accretion? 11) What can be told from the density of a planet? 12) What equations are used to model a planet or star? (the content, not the formula) a, semimajor axis of orbit (average distance from Sun) in 10 6 km a, semimajor axis of orbit (average distance from Sun) in AU P, period of time to orbit the Sun in Julian Years e, eccentri city of orbit, (no units) Orbital inclinatio n in degrees Mass in kg Equatorial Radius in km Rotation Period in solar (Earth) Days Inclinati on of Rotatio n Axis in degrees Planet Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune Pluto Data from Allen s Astrophysical Quantities, Fourth Edition, Chapter 9 The Solar System 10

131 10 The Earth, Our Point of Comparison 131 As of July 2009, humans have visited only the Earth and our Moon. Unmanned machines from Earth have landed on Mars, Venus, Titan, the asteroid Eros and our Moon. And we a probe has entered Jupiter s atmosphere. Since our experience with other planets and moons is so limited, we tend to use the Earth as a point of comparison and then compare and contrast the landforms, mountains, rivers, glaciers and oceans floors on the Earth can be compared with the features on other planets and their moons. On the Earth, we see the effects of wind, water, the molten interior, and life. Wind and water are felt by each of us and also produce erosion. Effects of the molten interior can be seen in movements of the continents, mountain building, positions of volcanoes, and the presence of the Earth s magnetic field. The overall theory of how the surface responds to the Earth s heated interior is called plate tectonics. Life on Earth has altered the carbon dioxide in our atmosphere, produced limestone and caused much of the break up of rocks into soil. Plate tectonics can be summarized as follows. The surface of the Earth appears to be divided into major sections, called plates. The plates are moved around on a slippery layer, called the asthenosphere due to convection currents in the next layer down, the mantle. As we go into the interior of the Earth, models, experience, and earthquake evidence lead us to think that the temperature increases with depth. The outer core is interior includes liquid, while the even hotter inner core is solid. Plates under the oceans can be less than kilometers thick. Under land, they can be as thick as 50 kilometers. But the granite that makes up land is less dense than the basaltic ocean floor. Plates move away from one another where magma is oozing up from the interior of the Earth. Since there is no extra space on the surface of the Earth, they collide and the thinner oceanic plate slides under the land. This wrinkles the land, causing folded mountains, Earth s most common kind. The plate boundaries are shown below. Small circles are locations of active volcanoes. Earthquakes occur more often under the boundaries of the plates. Volcanoes occur most often above places where sea plates are sliding under land. Modified from Tilling, Heliker and Wrigley, 1987 and Hamilton1976 Sometimes the plates move past one another, rather than colliding head on. This is what is happening with the famous San Andreas Fault and also with the Hayward Fault. The San Andreas Fault runs along the San Francisco peninsula, west of route 280 and under the San Andreas Lake and the two Crystal Springs Reservoirs. It goes out to sea at Daly City and comes back in at Bolinas. In the other direction it extends to near Los Angeles. Today we can measure the actual change in position from one continent to the next, by direct measurement. The speeds typically average several centimeters per year, but some plates and parts of plates move freely and others are stuck. Typically earthquakes occur near plate boundaries. Earthquakes are especially strong, when the locked parts let loose. During the 1906 San Francisco earthquake, the fault moved about 8 feet on the peninsula. But some of the southern parts of the fault have been locked together, and not moving throughout that time. That is why people are predicting an earthquake near Parkfield, one of the stuck places. Chapter 10 Earth, Our Point of Reference 1

132 132 Alfred Wegener (d 1915) suggested that Africa and South America were once joined. The lump of Brazil would have fit into the notch below Equatorial Africa. The land animals and plants are not the same today on these two continents, but there are fossils, from more than 60 million years ago that are the same. Wegener was not believed during his lifetime. But the evidence accumulated and by the late 1960 s scientists became convinced that the continents were, indeed, moving. How did this come to be? It is a long story. Over the years, people measured the effects of earthquakes. These effects (besides fear, destruction etc.) appear in the form of earth motion. Seismographs at a variety of distant locations record the motion in each direction. As people observe the vibrations from earthquakes, they use mathematical models to see how the vibration has traveled through the earth and where it came from. Whenever we have an earthquake, you will hear the announcement of the epicenter. This is the location on the Earth s surface directly ABOVE the source of the earthquake waves. As people traced back earthquake effects, they follow several types of wave. There are surface waves (along the surface only), P waves and S waves. The P waves are also called primary or pressure waves. They are primary because they travel faster through the Earth and arrive first. The second waves to arrive, S waves or secondary or shear waves have a different pattern as shown. Undisturbed Layers Surprisingly, it was found that P and S waves could not be seen from everywhere on Earth. It was not that the instruments were insensitive. It was found that both P and S waves could be seen near the earthquake epicenter. Then neither could be detected. And then on the side of the Earth opposite the earthquake, the P waves were detected, but not the S waves. P wave, material is compressed along the direction of wave motion T i m e Because of the way that the S wave moves material side-to-side, S waves will not travel through a fluid (liquid or gas). The P wave, however, will go through solid, liquid or gas. (Sound is a P wave and you can easily hear speech as it carries through gaseous air, or though solid walls. Sound travels through water S wave, material moves perpendicular to direction of wave motion as well, but it is pretty hard to talk under water.) T i m e As people modeled the interior of the Earth and tried to match the way that earthquake waves travel, it was found that S waves cannot complete paths that go within about the inner 2/3 of the Earth s radius. This is consistent with the presence of a fluid layer starting about 1/3 of the way in. Chapter 10 Earth, Our Point of Reference 2

133 As scientists modeled the overall structure of the Earth, using the equations in described in chapter 9, they found that radioactive elements decaying and pressure from Earth s gravity do make it hotter inside than outside. The interior temperature is easily hot enough to melt rocks. As time goes by, the amount of the radioactive elements decreases and so does the head they provide. If we wait long enough (and the Sun does not vaporize the Earth first), the interior of the Earth would cool off to the point where it would all be solid. That is probably the situation today with small bodies like our Moon, Mars and various asteroids. Our models of the Earth, supported by earthquake wave transmission data, lead us to an Earth of the Earth pictured below. The Earth includes a solid inner core, a liquid outer core, a fairly rigid mantle, and a thin solid crust. The slippery asthenosphere is between the Mantle and the crust. The inner core is thought to be solid based partly on the high pressure and partly on the observation that waves travel faster going north-south, than going at different speeds depending on what direction they go. This is consistent with a partly crystal inner core, possible with a solid, but not with a liquid. The overall idea of a molten interior, at least starting at the bottom of the mantle, dates from the 1930 s. Evidence for the inner core with crystalline structure has been solidified in the 1990 s. By the early 1960 s special submarines were able to observe the ocean bottoms. They found that lava oozes up near the Mid-Atlantic Ridge and the East Pacific Rise. The lava heats the seawater above the normal boiling temperature. The water cannot become steam because it is under too much pressure. Specially-adapted forms of life found near these hot spots survive from the energy of chemical reactions in the material coming from the interior. Finding these life forms has substantially expanded our concept of where n and how life can exist. Actually observing places where magma is coming up was a powerful demonstration that the plates might have a reason to move. So scientists looked at points at varying distances from the mid-oceanic ridges, they were able to observe a) The seafloor got older and older going away from the ridge b) The seafloor is magnetized in changing directions. How could anyone decide on the age of a rock? Finding the ages As geologists (and you) look at layers in rock or dirt or dirty laundry, there is an initial presumption of age. Where would you say is the oldest part of the heap in the figure? Up Younge Earth Model Mantl e Liquid Outer Core Soli d Inne r Cor e Convectio Crus t Given that the layers of stuff appear horizontal, we would expect that the lowest level is the oldest. We don t know for sure HOW old unless there is something with a definite date, like a newspaper buried or unless we have an accurate idea of how fast material is accumulating. Early geologists estimated the rate that rocks and earth would accumulate and estimated the age of the Earth to be at least a Billion (10 9 ) years. They did not have any way to get an age in years until well into the 20 th century. What would happen if there were several sets of layers, like in this figure? You could reasonably expect that the top layers are the youngest, but there is no way to tell whether the layers in the right hand pile are older or younger than the others, because there is no overlapping relationship. As here, the layers are not generally identical at widely distant points. 133 Chapter 10 Earth, Our Point of Reference 3

134 To get a relationship between these distant layers, we might use fossils found in each area. When a fossil is found in a layer, at least we can be sure that the layer was formed during the time that the particular type of creature was alive. This pins down the age of the layer somewhat. Typical species are around for ~ 5-10 Million years (not the individual plants or animals, the species), but some species change little over much longer times. And some fossils are not readily identified with fossils in other locations. To get an actual age for a rock layer, the best way is to use radioactive dating. This is how we can find absolute ages for the seafloor. To use radioactive dating, it is important to understand how it works. We often think of atoms and their nuclei as permanent, going on forever. But many nuclei are unstable. They fall apart spontaneously, without our doing anything. The falling apart process is called radioactive decay even though it has nothing to do with rot or fungus. Main Remaining Part becomes When a nucleus falls apart, it doesn t just disappear. Usually it becomes one comparatively large nucleus, called the daughter, and a variety of smaller pieces (It s like when you pick off a piece of a muffin. Most is left, and then there are crumbs). Some of the pieces are shown in the figure. Often when people talk of radiation they mean the results of a radioactive decay. In general it is not beneficial to get hit by these smaller pieces. The timing of radioactive decay is what makes it useful for measuring dates. Each nucleus generally falls apart in the same way. They don t get old, wear out, and fall apart (like us). They have a fixed probability of falling apart every second. The probability depends on the type of nucleus, but nothing else. People measure the probability of decay in the laboratory and then apply the knowledge to samples of rocks, bodies etc. A plot of the decay of a hypothetical nucleus is shown below. The plot has two curves. One is the amount of parent, the original nucleus. The other is the amount of daughter, the nucleus that results from decay. The vertical axis shows the amount of each type of nucleus. It is given in relative terms. That is 1, or 100%, is the starting position for the parent. It doesn t mean that something needs to be made of 100% parent; it means that whatever 134 Chapter 10 Earth, Our Point of Reference 4

135 amount of parent you started with is all there. 135 Often people characterize the way a nucleus decays by its half-life. The half-life is the time for half of the existing parent to decay into daughter. After waiting one half-life, there is 50% as much parent as we started with. After two half lives, there is 25%. After 3 half lives, there is 12.5%. Theoretically, the amount of parent is halved each time one half life goes by. As can be seen, the amount of daughter increases as the amount of parent decreases. This is because every time a parent nucleus decays, it becomes a daughter nucleus and some crumbs. At every time, there is a unique combination of amount of parent and amount of daughter. So if we have a body and can measure the amounts of parent and daughter, we can find the age of the body. It is written in scientific notation by a computer. The value 8.0E+05 means 8.0 times x The computer uses E+05 to say, The exponent of the power of 10 is positive 5. It cannot write superscripts, so it uses the E. People normally write 10 and an exponent, NOT E. Considering this particular plot, each large division on the horizontal scale is 2.0E+05 or 0.2x10 6. The next number after 8.0E+05 is not 10.0E+05 because it must be in scientific notation (only one digit before the decimal). So instead, it must be 1.0E+06. The small divisions are 1/5 as large as 2.0x10 5 or 4.0x10 4 years, just the result of dividing the number 2x10 5 (=200,000) by 5. Other types of nucleus will have different decay rates and different horizontal scales, but the principle will be the same. How old is the material above when there is 70% daughter and 30% parent? 7.0x10 5 years When there is 30% daughter and 70% parent? It may seem odd to bother with the daughter. If we were running a simple experiment, we would know the amount of parent we started with and it would be unnecessary to assess the amount of daughter. In the real world, especially with rocks, we rarely know how much parent was present to start. So when we measure the amount of parent in a rock, we don t know what fraction of the original is left. IF both the remaining parent and daughter are still in the rock, one can add up the amounts and find the original amount of parent. THEN it is possible to find the age. If the daughter has been washed away or if it is a gas that has escaped, then the original total amount is not known, and there is no accurate way to find the age. (Minerals are rather like lemonade. You make lemonade with water, sugar and lemon juice. There is no exact fixed amount of these different components, although there are limits to how much sugar you can get to dissolve. Because you wouldn t know the amount of lemon juice that you started with, it wouldn t be possible to know what fraction of it was left at some later time.) Not every rock has any radioactive elements in it, and not every radioactive element allows us to find the age of a rock. The amounts of parent and daughter give a good age determination when there are substantial amounts of both present. When a sample has 99.99% daughter, for example, it is hard to tell the age accurately. The amount of parent is so tiny it is hard to measure and the amount of daughter is not sensitive to the age. The properties of some radioactive elements are shown in the table. The number before the element name tells the atomic weight, the number of protons plus the number of neutrons in the nucleus. As you can see, in some cases the decay causes a substantial change in the atomic number. In others, one neutron changes to a proton and the atomic number stays the same. Parent Daughter Half-Life (years) 238 Uranium 206 Lead 4.508x Uranium 207 Lead 0.713x Iodine 129 Xenon 1.7x Potassium 40 Argon 1.3 x Carbon 14 Nitrogen 5870 For rocks, elements like Uranium and Potassium are useful. The half-lives for these elements are so long that there will surely be some of the parent left in a rock. The Argon produced when Potassium decays is a noble gas. It does not form compounds. So argon will be Chapter 10 Earth, Our Point of Reference 5

136 bubble out of a rock if it melts after the argon is formed. The age from potassium-argon dating 136 tells the time since the rock solidified. You may have heard about Carbon 14 ( 14 C ) dating. It is important, but never used for rocks. It is only useful for things that were once alive and that have died within the last 30,000 years or so. This is because the short half-life of 14 C means that it will be all decayed by the time a rock has formed. Carbon 14 is continuously created in our atmosphere by the effect of cosmic rays on the nitrogen. As we all eat and breath, some of the 14 C is incorporated in our bodies. It is always decaying, but we renew the 14 C by eating and breathing more. When we die, the carbon changes to nitrogen. Anthropologists often dig up sites where people used to live. They find bones and baskets (made of reeds) and are able to find the time since these things were alive from the 14 C dating. Carbon 14 dating has been compared with tree ring ages for the last several thousand years, thus verifying its time scale. Trees form rings every year and the size of the ring depends on growing conditions. So the rings and 14 C both tell an age, and the ages can be corrected to be the same. How old is a sample with 90% 14 C and 10% 14 N? (as shown in the plot) So to summarize, we find ages by a) Stratigraphic Dating, the younger thing is on top, if the layers are horizontal b) Fossils tell that a layer was first formed when the species was living c) Radioactive dating tells the actual age since the rock was formed Back to Plate Tectonics So as scientists looked at the rocks in the sea floor on either side of the mid oceanic ridge, they found that the further away from the ridge, the older the rocks. They also found that the rocks at the bottom of the ocean are igneous rocks, that is rocks which formed from solidification of lava or magma. When these rocks solidified, they were magnetized by the Earth s magnetic field. A magnetic field is due to the orbits of the electrons in the atoms aligning to one another, so that the electrons have a predominant direction of motion. The electrons can align when the atoms move around as a melted material cools and solidifies. Once it is solid, the atoms do not move around very much and the magnetic field remains fixed. If the material is heated too much, even if it is not melted again, the electron orbits realign. The magnetic field can be lost. When scientists examined the material in the seafloor, they found that there were regions of reversing magnetic field, symmetrically placed on the sides of the mid oceanic ridge. This is just what we expect for a seafloor formed in the presence of the Earth s magnetic field. For many years, geologists have noticed that as they dig down into rock layers, the rocks have reversing magnetic fields. At least 92 magnetic field Chapter 10 Earth, Our Point of Reference 6

137 reversals have been detected in just the last 118 million years. But there may have been more. If 137 the magnetic field reversed for just a short time, there would be few rocks magnetized by the reversed field and it would be hard to detect. The plot shows the history of the direction of Earth s magnetic field over the last 10 million years. The magnetic field has been in the same direction for about 780,000 years, an unusually long time. The Earth s magnetic field has a consistent shape over the entire surface of the Earth, called a dipole, as shown in the diagram. It is a little like the surface of an apple, with the North and South magnetic poles at the stem and flower ends of the apple. Magnets, like the magnet in a compass or like the magnetic field of a rock, line up just opposite the magnetic field lines. Because of this consistent shape, we can relate the direction of the field at any two positions near the Earth. the geographic poles. Many maps show the correction to apply to the magnetic north direction (what a compass shows). The magnetic poles wander around on a scale of years, as can be seen in the figure. But why a magnetic field? And why does it change? We think that the rotati on of the liqui d oute r core, an elect ricall You may notice that the directions of the North and South MAGNETIC Poles are not the same as the North and South GEOGRAPHIC poles. Maps, latitude and longitude are all referred to Magnetic Field to North Celestial Pole Rotation Axis Magnetic Field Lines compass needle lines up along these to South Celestial Pole y conducting material, will generate electric currents. These currents, in turn, result in magnetic fields. As time goes by the direction of the flow changes. Since approximately 1995, computer simulations that model the motion of the interior of the Earth have resulted in magnetic field reversals. Regardless of exactly how the magnetic field Chapter 10 Earth, Our Point of Reference 7