DEPARTMENT OF ASTROPHYSICAL AND PLANETARY SCIENCES

Transcription

1 DEPARTMENT OF ASTROPHYSICAL AND PLANETARY SCIENCES APS 1010 Laboratory Introduction to Astronomy Fall 1999 University of Colorado at Boulder

2 Acknowledgements The content of this laboratory manual is based to a large extent upon experiments compiled and developed over the course of many years by Dr. Roy Garstang for the APAS 121/122 labs. In 1987 Dr. Garstang published the Sommers-Bausch Observatory Manual of General Astronomy Projects; a number of his 88 exercises were adapted for use in the new APAS 101 (now APS 1010) course that was initiated in Since that time the manual has undergone considerable evolution and expansion under the guidance of faculty lab coordinators Drs. Raul Stern, Scott Roberston, Larry Esposito, and Fran Bagenal. Many other faculty members have contributed new exercises or major suggestions for improvements, including in particular Drs. John Stocke, Larry Esposito, J. McKim Malville, Carl Hansen, and the late Ned Benton. Virtually every graduate teaching assistant who has conducted a lab in the APAS/APS 121/122/101/1010/1030 series has contributed to this manual by identifying areas of difficulty, made suggestions for improvements, or provided ideas that germinated into new experiments. Although the contributors from this quarter are too numerous to list, special mention should be made of those who developed a new lab exercise or assisted in the coordination and production of earlier editions: Alexis Hayden, Marsha Allen, Josh Colwell, Ron Wurtz, Joel Parker, and Eric Perlman - and most recently and significantly to the current version of the manual, Marc DeRosa, KaChun Yu, Mary Urquhart, and Travis Rector. Finally, unfailing educational support and promotion for these laboratories has been provided by the past and present Directors of Sommers-Bausch Observatory and Fiske Planetarium: Drs. Bruce Bohannan and Katy Garmany. Keith Gleason, Editor SBO Manager/Lab Coordinator Summer, 1999 Front Cover: Comet Hale-Bopp over the Flatirons courtesy Niescja Turner and Carter Emmart Back Cover: CCD Mosaic of the Full Moon contributed by Keith Gleason

3 APS 1010 Astronomy Lab 3 Table of Contents TABLE OF CONTENTS Celestial Calendar - Fall General Information... 6 Units and Conversions Scientific Notation Math Review Using Your Calculator Celestial Coordinates Telescopes & Observing DAYTIME EXPERIMENTS Colorado Model Solar System The Seasons Motions of the Sun Motions of the Moon Gravity and the Mass of the Earth Kepler's Laws Temperature of the Sun Spectroscopy Telescope Optics Planetary Temperatures Encounter with the Galilean Moons OBSERVING PROJECTS Constellation and Bright Star Identification Telescope Observing Observing Lunar Features The Messier Catalog (CCD Imaging) Clear skies are required for the exercise - Clear skies are needed for a portion of the exercise

4 APS 1010 Astronomy Lab 4 Celestial Calendar Fall, 1999 CELESTIAL CALENDAR - Fall 1999 THE SUN The Sun reached its highest declination (+23.5 ) on June 21 st, marking the Summer Solstice. On September 23 rd, it will be directly over the Earth s equator at 5:31 a.m. Mountain Daylight Time; the arrangement marks the Autumnal Equinox, the moment when fall officially begins. Finally, on December 22 nd, the Sun will reach its lowest declination (-23.5 ), marking the Winter Solstice and the smallest number of daylight hours of the year. Our time-keeping method, by which we keep track (roughly) of the Sun s location in the sky, makes a one-hour jump backward at 2:00:00 a.m. Mountain Daylight Time on Sunday, October 31 st - the next second of time will be referred to as 1:00:01 a.m. Mountain Standard Time. The last total solar eclipse of the millenium happens on August 11 th ; unfortunately for us, the eclipse will only be visible from Europe and Asia, not from North America. THE MOON MERCURY Month Last New First Full Last August September October November December The innermost planet won't be visible as an "evening star" this fall until early December. However, a rare grazing transit of the Sun by Mercury will occur on the late afternoon of November 15 th, when the tiny black disk of the planet will skim along the edge of the Sun for about a half-hour. Transits of Mercury occur only 13 times each century, while a grazing transit is far more rare. If skies are clear, Sommers-Bausch Observatory will be holding a special observing session for viewing this once-in-a-lifetime opportunity - watch the website lyra.colorado.edu/sbo/ for further details.

5 APS 1010 Astronomy Lab 5 Celestial Calendar Fall, 1999 VENUS Venus appears as a brilliant "morning star" by mid-september, and will remain in the pre-dawn eastern sky throughout the remainder of the semester. EARTH The third planet from the Sun is visible throughout the year, any day or night. Look down. MARS Mars will remain very low in the southwest throughout the fall - its prograde motion through the skies just keeping it always above the horizon just after sunset. However, the planet will be a disappointing telescope sight, shrinking from 10 arc-seconds in diameter in August to only 5 arcseconds by December, while becoming a full magnitude dimmer. JUPITER The King of the Planets will become a prominent evening object after September, when it rises as twilight fades. October through December, the giant planet's disk will exceed 45 arc-seconds across, permitting spectacular views of its cloud bands and subtle atmospheric features. The four Galilean moons (Io, Europa, Ganymede, and Callisto) change their positions around Jupiter nightly, and are easily seen with a small telescope. SATURN Saturn can be observed late at night early in the semester, or shortly after sunset in November and December. This fall and winter offers the best viewing of the ringed planet since 1978! It is higher in the northern sky (+13 degrees declination), closer to Earth (disk 20 arc-seconds across and rings 46 arc-seconds across), with rings highly-tipped (over 20 degrees). The Ringed Planet is guaranteed to be a glorious jewel for telescope observation! URANUS, NEPTUNE The two outermost gas giants are only several degrees apart in the constellation of Capricornus, where they may be found by telescope low in the southern skies late evening throughout the semester. Mars passes only 1.7 degrees from Neptune on November 28 th, and 0.7 degrees from Uranus on December 14 th. PLUTO Always difficult to see at best, Pluto might be glimpsed in Ophiuchus (with good finder charts) early evening early in the fall semester. METEOR SHOWERS Fall is prime time for good meteor showers, and this fall they should be better than ever. Watch for the Perseids on the evening of August 12 th, the Leonids on the night of November 17 th /18 th, and the Geminids the night of December 14 th. The Leonids in particular may be especially spectacular this year, perhaps increasing to "storm" levels visible in some locales of the Earth. Moonlight will not be a problem for midnight observers of any of these showers.

6 APS 1010 Astronomy Lab 6 General Information GENERAL INFORMATION You must enroll for both the lecture section and a laboratory section. Your lecture section will generally be held in the classroom in Duane Physics Building (just south of Folsom Stadium). An occasional lecture may be held instead at the Fiske Planetarium (at the intersection of Regent Drive and Kittridge Loop). Your laboratory section will meet once per week in the daytime in Room S175 at Sommers- Bausch Observatory (just east of the Fiske Planetarium); follow the walkway around the south side of Fiske and up the hill to the Observatory. You will also have nighttime observing sessions using the Observatory telescopes to view and study the constellations, the moon, planets, stars, and other celestial objects. Folsom Street Engineering Center Folsom Stadium Colorado Avenue Events Center DUANE PHYSICS (CLASSROOMS) Business Colorado Scale Model Solar System Regent Drive JILA Tower GAMOW TOWER (APAS OFFICE) Hallet SOMMERS-BAUSCH OBSERVATORY CDSS 18th Street Willard FISKE PLANETARIUM Kittridge Regent MATERIALS The following materials are needed: APS 1010 Astronomy Lab Manual, Fall 1999 (this document). Available from the CU Bookstore. Replacement copies are available in Acrobat PDF format downloadable from the SBO website ( Calculator. All students should have access to a scientific calculator which can perform scientific notation, exponentials, and trig functions (sines, cosines, etc.). A 3-ring binder to hold this lab manual, your lab notes, and lab write-ups. Highly recommended: a planisphere, or rotating star map (available at Fiske Planetarium, the CU bookstore, other bookshops, etc.).

7 APS 1010 Astronomy Lab 7 General Information THE LABORATORY SECTIONS Your laboratory session will meet for one hour and fifty minutes in the daytime once each week in the Sommers-Bausch Observatory (SBO) Classroom S175. Each lab section will be run by a lab instructor who will also grade your lab exercises and assign you a score for the work you hand in. Your lab instructor will give you organizational details and information about grading at the first lab session. The lab exercises do not exactly follow the lectures or the textbook. Rather, we concentrate on how we know what we know, and thus spend more time making and interpreting observations. Modern astronomers, in practice, spend almost no time at the eyepiece of a telescope. They work with photographs, with satellite data, or with computer images. In our laboratory we will explore both traditional and more modern techniques. You are expected to attend all lab sessions. The lab exercises can only be done using the equipment and facilities in the SBO classroom; thus, if you do not attend the daytime lab sessions, you cannot complete those experiments and cannot get credit. The observational exercises can only be done at night using the Observatory telescopes; if you do not attend the nighttime sessions, you cannot complete these either. NIGHTTIME OBSERVING You are expected to attend nighttime observing labs. These are held approximately every third week at the Sommers-Bausch Observatory. Your lab instructor will tell you the dates and times. Write the dates and times of the nighttime sessions on your calendar so you do not miss them. If you have a job that conflicts with the nighttime sessions, it is your responsibility to make arrangements with your instructor to attend at different times. Nighttime sessions are not necessarily cancelled if it is cloudy; an indoor exercise may be done rather than observing - check with your instructor. The telescopes are not in a heated area, so dress warmly for the night observing sessions! THE LABORATORY WRITE-UPS You are expected to turn in lab assignments of collegiate quality: neat and easy to read, wellorganized, and demonstrating a mastery of the English language (e.g. grammar, spelling) as well as mastery of the subject matter. Your presentation of neat, well-organised, readable work will help you prepare for other courses and jobs where appearance certainly counts (it also makes your work much easier to grade!). By requiring you to explain your work clearly, we can ensure that you fully understand it. If you find writing clear explanations to be difficult, it may mean that you aren't understanding the concepts well. Some of the labs are designed to be written up as full reports. A few are of the "fill in the blank" type. In either case, the following guidelines should be followed.

8 APS 1010 Astronomy Lab 8 General Information 1. Write the title and date at the top of the first page of the exercise. 2. Write an introductory sentence or two describing what you are doing. For instance: "Today we used the heliostat to observe and draw sunspots." 3. Number the parts of your lab the same as the numbers in the lab manual: I.1, I.2, II.1, II.2, etc.; this is particularly useful to help the instructor find your responses to the questions. 4. Put titles on your figures and label the columns in your tables. 5. Put units after your numerical answers. One hundred millimeters is a bit different from one hundred kilometers! 6. Use complete sentences to answer questions. For example: "The largest planet is Jupiter" is much better than just "Jupiter". 7. Be sure to write your results in your own words and not the words of your lab partner. 8. It is better to neatly cross though long mistakes than to erase them. Use a ruler and a pencil to make neat lines through mistakes. ACADEMIC DISHONESTY We expect students in our classes to hold to a high ethical standard. In general we expect you, as college students, to be able to differentiate on your own between what is honest and dishonest. Nevertheless, we point out the following guideline regarding laboratory assignments: All work turned in must be your own. You should understand all work that you write on your paper. While we encourage you to work in groups if it is helpful, you must not copy the work of someone else. We have no objection to your consulting friends for help in understanding problems. If you copy answers without understanding, however, it will be considered academic dishonesty. HELPING YOU HELP YOURSELF Astronomy uses the laws of nature that govern the universe: i.e., physics. We will cover the physics that is needed as we go along. To move beyond just the "ooooh and aaaah" of stargazing, we also need to use mathematics. We are also aware that most of you may not be particularly fond of math. You are expected, however, to be able to apply certain aspects of high school algebra and trigonometry. This manual includes a summary of the mathematics you will need; we recommend that you review it as necessary. The "rule of thumb" for the amount of time you should be spending on any college class is 2-3 hours per week outside lectures and labs for each unit of credit. Thus, for a 4-unit class, you should expect to spend an additional 8 to 12 hours per week studying. In general, if you are spending less time than this on a class, then it is either too easy for you, or you are not learning as much as you could. If you are spending more time than this, you may be studying inefficiently.

9 APS 1010 Astronomy Lab 9 General Information We recommend the following strategies for efficient use of your lab time: Review the accompanying material on units and conversions, scientific notation, math, and calculator usage. Discuss with your lab instructor any problems you have with these concepts before you need to use them. Use these sections as a reference in case you are having difficulties. Read the appropriate lab manual exercise before you come to lab. Read any background material in the textbook before you come to lab. Complete the whole of the lab exercise before the end of the lab period; avoid the temptation to "wrap it up later". If you have difficulty with a specific lab exercise, get help before the assignment is due! We will attempt to give you as much help as needed to overcome your difficulties, provided you make the effort to seek assistance. Do not procrastinate on assignments until the night before they are due - it will be too late to get help! If you find that you are having difficulties of any kind, talk to your lab instructor, your lecture professor, or your lecture teaching assistant. We can help you only if we are aware that there is a problem. SOMMERS-BAUSCH OBSERVATORY Sommers-Bausch Observatory (SBO), on the University of Colorado campus, is operated by the Department of Astrophysical and Planetary Sciences to provide hands-on observational experience for CU undergraduate students, and research opportunities for University of Colorado astronomy graduate students and faculty. Telescopes include 16, 18, and 24-inch Cassegrain reflectors and a 10.5-inch aperture heliostat. In its teaching role, the Observatory is used by approximately 1500 undergraduate students each year to view celestial objects that would otherwise only be seen on the pages of a textbook or discussed in classroom lectures. The 16- and 18-inch telescopes on the observing deck are both under computer control, with objects selected from a library that includes double stars, star clusters, nebulae, and galaxies. In addition to the standard laboratory room, the Observatory recently added a computer lab consisting of one instructor and twelve student computers, each capable of running either Macintosh or PC software. We re currently developing new computer-based lab exercises, and have added planetarium-style and image-processing software to further enhance the student s hands-on astronomy experience. The 18-inch telescope has an additional computer interface for planetarium-style "click-and-go" pointing, plus a charge-coupled device (CCD) electronic camera so that students can image celestial objects through an 8-inch piggyback telescope. The 10.5-inch aperture heliostat is equipped for viewing sunspots, measuring the solar rotation, solar photography, and for studies of the solar spectrum. A unique optical system called SCRIBES permits simultaneous observations of the photosphere (using white light) and the solar chromosphere (using red light from hydrogen and ultraviolet light from calcium in the sun).

10 APS 1010 Astronomy Lab 10 General Information The 24-inch telescope is primarily used for graduate student training and for research projects not feasible with larger telescopes because of time constraints or scheduling limitations. A Texas Instruments 3-phase, 800x800-pixel CCD camera is used for both spectroscopic and direct imaging applications. CU is the only facility in the nation with a telescope of under 90-inches aperture to be awarded this advanced technology detector by the National Science Foundation. The ultra-high efficiency CCD gives the 24-inch telescope at SBO a light-detecting capacity comparable to the Palomar 200-inch telescope with conventional photographic plates. Images are analyzed and processed using IDL and the National Optical Astronomical Observatory's IRAF software running on a Sun Sparcstation 10 microcomputer. An easy-to-operate, large-format SBIG ST-8 CCD camera with focal reducer assembly is also now available for graduate and advanced undergraduate use on the 24-inch telescope. In addition, this fall the 24-inch is being upgraded to include computerized control and automatic pointing capabilities. These and other recent improvements and additions have all been made possible by the funding provided by the student laboratory fees. Free Open Houses for public viewing through the 16-and 18-inch telescopes are held every Friday evening that school is in session. Students are welcome to attend. Call for starting times and reservations. Call for general astronomical information. For additional information about the Observatory, including schedules, information on how to contact your lab instructor, and examples of images taken by other students in the introductory astronomy classes, see our website located at FISKE PLANETARIUM The Fiske Planetarium and Science Center is used as a teaching facility for classes in astronomy, planetary science and other courses that can take advantage of this unique audiovisual environment. The star theater seats 210 under a 62-foot dome that serves as a projection screen, making it the largest planetarium between Chicago and California. The Zeiss Mark VI star projector is one of only five in the United States. Two hundred additional slide and special effect projectors are controlled by a SPICE (Specialized Projector Interface Electronics) automation system. Astronomy programs designed to entertain and to inform are presented to the public on Fridays and Saturdays and to schoolchildren on weekdays. Laser-light shows rock the theater late Friday nights as well. Following the Friday evening starshow presentations, visitors are invited next door to view the stars at Sommers-Bausch Observatory, weather permitting. The Planetarium provides students with employment opportunities to work on show production, presentation, and in the daily operation of the facility. Fiske is located west of the Events Center on Regent Drive on the Boulder campus of the University of Colorado. For recorded program information call and to reach our business office call Alternatively, you can check out the upcoming schedules and events on the Fiske website at

11 APS 1010 Astronomy Lab 11 Units & Conversions UNITS AND CONVERSIONS You are probably familiar with the fundamental units of length, mass and time in the American system: the yard, the pound, and the second. The other common units of the American system are often strange multiples of these fundamental units such as the ton (2000 lbs), the mile (1760 yds), the inch (1/36 yd) and the ounce (1/16 lb). Most of these units arose from accidental conventions, and so have few logical relationships. Most of the world uses a much more rational system known as the metric system (the SI, Systeme International d'unites, internationally agreed upon system of units) with the following fundamental units: The meter for length. Abbreviated "m". The kilogram for mass. Abbreviated "kg". (Note: kilogram, not gram, is the standard.) The second for time. Abbreviated "s". Since the primary units are meters, kilograms and seconds, this is sometimes called the ' mks system'. Some people also use another metric system based on centimeters, grams and seconds, called the 'cgs system'. All of the unit relationships in the metric system are based on multiples of 10, so it is very easy to multiply and divide. The SI system uses prefixes to make multiples of the units. All of the prefixes represent powers of 10. The table below gives prefixes used in the metric system, along with their abbreviations and values. Metric Prefixes Prefix Abbreviatioviation Value Prefix Abbre- Value deci d 10-1 decka da 10 1 centi c 10-2 hecto h 10 2 milli m 10-3 kilo k 10 3 micro m 10-6 mega M 10 6 nano n 10-9 giga G 10 9 pico p tera T femto f atto a The United States, unfortunately, is one the few countries in the world which has not yet made a complete conversion to the metric system. (Even Great Britain has adopted the SI system; so what we used to call "English" units are no more - they are strictly "American"!) As a result, you are forced to learn conversions between American and SI units, since all science and international commerce is transacted in SI units. Fortunately, converting units is not difficult. Although you can find tables listing seemingly endless conversions, you can do most of the lab exercises (as well as most conversions you will ever need in science, business, etc.) by using just the four conversions between American and SI units listed below (along with your own recollection of the relationships between various American units).

12 APS 1010 Astronomy Lab 12 Units & Conversions American to SI Units Conversion Table SI to American 1 inch = 2.54 cm 1 m = inches 1 mile = km 1 km = mile 1 lb = kg 1 kg = pound 1 gal = liters 1 liter = gal Strictly speaking, the conversion between kilograms and pounds is valid only on the Earth since kilograms measure mass while pounds measure weight. However, since most of you will be remaining on the Earth for the foreseeable future, we will not yet worry about such details. (If you're interested, the unit of weight in the SI system is the newton, and the unit of mass in the American system is the slug.) Using the "Well-Chosen 1" Many people have trouble converting between units because, even with the conversion factor at hand, they aren't sure whether they should multiply or divide by that number. The problem becomes even more confusing if there are multiple units to be converted, or if you need to use intermediate conversions to bridge between two sets of units. We offer a simple and foolproof method for handling the problem, which will always work if you don't take shortcuts! We all know that any number multiplied by 1 equals itself, and also that the reciprocal of 1 equals 1. We can exploit these rather trivial properties by choosing our 1's carefully so that they will perform a unit conversion for us. Suppose we wish to know how many kilograms a 170 pound person weighs. We know that 1 kg = pounds, and can express this fact in the form of 1's: 1 = 1 kg pounds or its reciprocal 1 = pounds 1 kg. Note that the 1's are dimensionless; the quantity (number with units) in the numerator is exactly equal to the quantity (number with units) in the denominator. If we took a shortcut and omitted the units, we would be writing nonsense: neither 1 divided by 2.205, nor divided by 1, equals "1"! Now we can multiply any other quantity by these 1's, and the quantity will remain unchanged (even though it will look considerably different). In particular, we want to multiply the quantity "170 pounds" by 1 so that it will still be equivalent to 170 pounds, but will be expressed in kg units. But which "1" do we choose? Very simply, if the unit we want to "get rid of" is in the numerator, we choose the "1" that has that same unit appearing in the denominator (and vice versa) so that the undesired units will cancel. Hence we have 170 lbs x 1 = 170 lbs x 1 kg lbs = 170 x x lbs x kg lbs = 77.1 kg. Note that you do not omit the units, but multiply and divide them just like ordinary numbers. If you have selected a "well-chosen" 1 for your conversion your units will nicely cancel, which will assure you that the numbers themselves will also have been multiplied or divided properly. That's what makes this method foolproof: if you used a "poorly-chosen" 1, the expression itself will immediately let you know about it:

13 APS 1010 Astronomy Lab 13 Units & Conversions 170 lbs x 1 = 170 lbs x lbs 1 kg = 170 x x lbs x lbs kg = 375 x lbs2 kg! Strictly speaking, this is not really incorrect: 375 lbs 2 /kg is the same as 170 lbs, but it's not a very useful way of expressing it, and it's certainly not what you were trying to do! Example: As a passenger on the Space Shuttle, you note that the inertial navigation system shows your orbital velocity at 7,000 meters per second. You remember from your astronomy course that a speed of 17,500 miles per hour is the minimum needed to maintain an orbit around the Earth. Should you be worried? 7000 m s = m s x 1 km 1000 m x 1 mile km x 60 s 1 min x 60 min 1 hr = 7000 x 1 x 1 x 60 x 60 1 x 1000 x x 1 x 1 = 15,662 miles hour. x m x km x mile x s x min s x m x km x min x hr Because of your careful analysis using "well-chosen 1's", you can conclude that you will probably not survive long enough to have to do any more unit conversions. Temperature Scales Scales of temperature measurement are tagged by the freezing point and boiling point of water. In the U.S., the Fahrenheit (F) system is the one commonly used; water freezes at 32 F and boils at 212 F (180 hotter). In Europe, the Celsius system is usually used: water freezes at 0 C and boils at 100 C. In scientific work, it is common to use the Kelvin temperature scale. The Kelvin degree is exactly the same "size" as the Celsius degree, but is based on the idea of absolute zero, the temperature at which all random molecular motions cease. 0 K is absolute zero, water freezes at 273 K and boils at 373 K. Note that the degree mark is not used with Kelvin temperatures, and the word "degree" is often not even mentioned: we say that "water boils at 373 kelvins". To convert between these three systems, recognize that 0 K = -273 C = -459 F and that the Celsius and Kelvin degree is larger than the Fahrenheit degree by a factor of 180/100 = 9/5. The relationships between the systems are: K = C C = 5/9 ( F - 32) F = 9/5 K Energy and Power: Joules and Watts The SI unit of energy is called the joule. Although you may not have heard of joules before, they are simply related to other units of energy with which you probably are familiar. For example, 1 food Calorie (which actually is 1000 normal'' calories) is 4,186 joules. House furnaces are rated in btus (British thermal units), indicating how much heat energy they can produce: 1 btu = 1,054 joules. Thus, a single potato chip (having an energy content of about 9 Calories) could also be said to possess 37,674 joules or 35.7 btu's of energy. The SI unit of power is called the watt. Power is defined to be the rate at which energy is used or produced, and is measured as energy per unit time. The relationship between joules and watts is:

14 APS 1010 Astronomy Lab 14 Units & Conversions 1 watt = 1 joule second. For example, a 100-watt light bulb uses 100 joules of energy (about 1/42 of a Calorie or 1/10 of a btu) each second it is turned on. Weight-watchers might be more motivated to stick to their diet if they realized that one potato chip contains enough energy to operate a 100-watt light bulb for over 6 minutes! Another common unit of power is the horsepower; one hp equals 746 watts, which means that energy is consumed or produced at the rate of 746 joules per second. (In case you're curious, you can calculate (using unit conversions) that if your car has fifty "horses" under the hood, they need to be fed 37,300 joules, or the equivalent energy of one potato chip, every second in order to pull you down the road.) To give you a better sense of the joule as a unit of energy (and of the convenience of scientific notation, our next topic), here are some comparative energy outputs: Energy Source Energy (joules) Big Bang Radio galaxy Supernova Sun s radiation for 1 year Volcanic explosion H-bomb Thunderstorm Lightening flash Baseball pitch 10 2 Hitting keyboard key 10-2 Hop of a flea 10-7

15 APS 1010 Astronomy Lab 15 Scientific Notation SCIENTIFIC NOTATION Scientific Notation: What is it? Astronomers deal with quantities ranging from the truly microcosmic to the macrocosmic. It is very inconvenient to always have to write out the age of the universe as 15,000,000,000 years or the distance to the Sun as 149,600,000,000 meters. To save effort, powers-of-ten notation is used. For example, 10 = 10 1 ; the exponent tells you how many times to multiply by 10. As another example, 10-2 = 1/100; in this case the exponent is negative, so it tells you how many times to divide by 10. The only trick is to remember that 10 0 = 1. Using powers-of-ten notation, the age of the universe is 1.5 x years and the distance to the Sun is x meters. The general form of a number in scientific notation is a x 10 n, where a must be between 1 and 10, and n must be an integer. (Thus, for example, these are not in scientific notation: 34 x 10 5 ; 4.8 x ) If the number is between 1 and 10, so that it would be multiplied by 10 0 (=1), then it is not necessary to write the power of 10. For example, the number 4.56 already is in scientific notation (it is not necessary to write it as 4.56 x 10 0, but you may write it this way if you wish). If the number is a power of 10, then it is not necessary to write that it is multiplied by 1. For example, the number 100 can be written in scientific notation either as 10 2 or as 1 x (Note, however, that the latter form should be used when entering numbers on a calculator.) The use of scientific notation has several advantages, even for use outside of the sciences: Scientific notation makes the expression of very large or very small numbers much simpler. For example, it is easier to express the U.S. federal debt as $3 x rather than as $3,000,000,000,000. Because it is so easy to multiply powers of ten in your head (by adding the exponents), scientific notation makes it easy to do "in your head" estimates of answers. Use of scientific notation makes it easier to keep track of significant figures; that is, does your answer really need all of those digits that pop up on your calculator? Converting from "Normal" to Scientific Notation: Place the decimal point after the first non-zero digit, and count the number of places the decimal point has moved. If the decimal place has moved to the left then multiply by a positive power of 10; to the right will result in a negative power of 10. Example: To write 3040 in scientific notation we must move the decimal point 3 places to the left, so it becomes 3.04 x Example: To write in scientific notation we must move the decimal point 4 places to the right: 1.2 x 10-4.

16 APS 1010 Astronomy Lab 16 Scientific Notation Converting from Scientific to "Normal'" Notation: If the power of 10 is positive, then move the decimal point to the right; if it is negative, then move it to the left. Example: Convert 4.01 x We move the decimal point two places to the right making 401. Example: Convert 5.7 x We move the decimal point three places to the left making Addition and Subtraction with Scientific Notation: When adding or subtracting numbers in scientific notation, their powers of 10 must be equal. If the powers are not equal, then you must first convert the numbers so that they all have the same power of 10. Example: (6.7 x 10 9 ) + (4.2 x 10 9 ) = ( ) x 10 9 = 10.9 x 10 9 = 1.09 x (Note that the last step is necessary in order to put the answer in scientific notation.) Example: (4 x 10 8 ) - (3 x 10 6 ) = (4 x 10 8 ) - (0.03 x 10 8 ) = (4-0.03) x 10 8 = 3.97 x Multiplication and Division with Scientific Notation: It is very easy to multiply or divide just by rearranging so that the powers of 10 are multiplied together. Example: (6 x 10 2 ) x (4 x 10-5 ) = (6 x 4) x (10 2 x 10-5 ) = 24 x = 24 x 10-3 = 2.4 x (Note that the last step is necessary in order to put the answer in scientific notation.) Example: (9 x 10 8 ) (3 x 10 6 ) = 9 x x 10 6 = (9/3) x (10 8 /10 6 ) = 3 x = 3 x Approximation with Scientific Notation: Because working with powers of 10 is so simple, use of scientific notation makes it easy to estimate approximate answers. This is especially important when using a calculator since, by doing mental calculations, you can verify whether your answers are reasonable. To make approximations, simply round the numbers in scientific notation to the nearest integer, then do the operations in your head. Example: Estimate 5,795 x 326. In scientific notation the problem becomes (5.795 x 10 3 ) x (3.26 x 10 2 ). Rounding each to the nearest integer makes the approximation (6 x 10 3 ) x (3 x 10 2 ), which is 18 x 10 5, or 1.8 x 10 6 (the exact answer is x 10 6 ). Example: Estimate (5 x ) + (2.1 x 10 9 ). Rounding to the nearest integer this becomes (5 x ) + (2 x 10 9 ). We see immediately that the second number is nearly /10 9, or one million, times smaller than the first. Thus, it can be ignored in the addition problem and our approximate answer is 5 x (The exact answer is x ).

17 APS 1010 Astronomy Lab 17 Scientific Notation Significant Figures: Numbers should be given only to the accuracy that they are known with certainty, or to the extent that they are important to the topic at hand. For example, your doctor may say that you weigh 130 pounds, when in fact at that instant you might weigh pounds. The discrepancy is unimportant and will change anyway as soon as a blood sample has been drawn. If numbers are given to the greatest accuracy that they are known, then the result of a multiplication or division with those numbers can't be determined any better than to the number of digits in the least accurate number. Example: Find the circumference of a circle measured to have a radius of 5.23 cm using the formula: C = (2 x π x R). Since the value of pi stored in your calculator is probably , the numerical solution will be (2 x x 5.23 cm) = = x 10 1 cm. If you simply write down all 10 digits as your answer, you are implying that you know, with absolute certainty, the circle s circumference to an accuracy of one part in 10 billion! That would mean that your measurement of the radius was in error by no more than cm; that is, its true value was at least cm, but no more than cm (otherwise, your calculator would have shown a different number for the circumference). In reality, since your measurement of the radius was known to only three decimal places, the circle s circumference is also known to only (at best) three decimal places as well: you round the fourth digit and give the result as 32.9 cm or 3.29 x 10 1 cm. It may not look as impressive, but it s an honest representation of what you know about the figure. Since the value of "2" was used in the formula, you may wonder why we're allowed to give the answer to three decimal places rather than just one: 3 x 10 1 cm. The reason is because the number "2" is exact - it expresses the fact that a diameter is exactly twice the radius of a circle - no uncertainty about it at all. Without any exaggeration, we could have represented the number as , but merely used the shorthand "2" for simplicity - so we really didn't violate the rule of using the least accurately-known number.

18 APS 1010 Astronomy Lab 18 Math Review MATH REVIEW Dimensions of Circles and Spheres The circumference of a circle of radius R is 2πR. The area of a circle of radius R equals πr 2. The surface area of a sphere of radius R is given by 4πR 2. The volume of a sphere of radius R is 4/3 πr 3. Measuring Angles - Degrees and Radians There are 360 in a full circle. There are 60 minutes of arc in one degree. (The shorthand for arcminute is the single prime ( ): we can write 3 arcminutes as 3.) Therefore there are 360 x 60 = 21,600 arcminutes in a full circle. There are 60 seconds of arc in one arcminute. (The shorthand for arcsecond is the double prime ( ): we can write 3 arcseconds as 3.) Therefore there are 21,600 x 60 = 1,296,000 arcseconds in a full circle. We sometimes express angles in units of radians instead of degrees. If we were to take the radius (length R) of a circle and bend it so that it conformed to a portion of the circumference of the same circle, the angle subtended by that radius is defined to be an angle of one radian. Since the circumference of a circle has a total length of 2πR, we can fit exactly 2π radii (6 full lengths plus a little over 1/4 of an additional) along the circumference; thus, a full 360 circle is equal to an angle of 2π radians. In other words, an angle in radians equals the subtended arclength of a circle divided by the radius of that circle. If we imagine a unit circle (where the radius = 1 unit in length), then an angle in radians numerically equals the actual curved distance along the portion of its circumference cut by the angle. The conversion between radians and degrees is 1 radian = π Trigonometric Functions degrees = = 2 π 360 radians = radians In this course we will make occasional use of the basic trigonometric functions: sine, cosine, and tangent. Here is a quick review of the basic concepts:

19 APS 1010 Astronomy Lab 19 Math Review In any right triangle (one angle is 90 ), the longest side is called the hypotenuse and is the side that is opposite the right angle. The trigonometric functions relate the lengths of the sides of the triangle to the other (i.e. not 90 ) enclosed angles. In the right triangle figure below, the side adjacent to the angle α is labeled adj, the side opposite the angle α is labeled opp. The hypotenuse is labeled hyp. The Pythagorean theorem relates the lengths of the sides to each other: (opp) 2 + (adj) 2 = (hyp) 2. The trig functions are just ratios of the lengths of the different sides: sin α = (opp) (hyp) (adj) cos α = (hyp) (opp) tan α = (adj). Angular Size, Physical Size and Distance The angular size of an object (the angle it subtends, or appears to occupy, from our vantage point) depends on both its true physical size and its distance from us. For example, if you stand with your nose up against a building, it will occupy your entire field of view; as you back away from the building it will occupy a smaller and smaller angular size, even though the building s physical size is unchanged. Because of the relations between the three quantities (angular size, physical size, and distance), we need know only two in order to calculate the third. Suppose a tall building has an angular size of 1 (that is, from our location its height appears to span one degree of angle), and we know from a map that the building is located 10 km away. How can we determine the actual physical size (height) of the building? We imagine we are standing with our eye at the apex of a triangle, from which point the building subtends an angle α = 1 (greatly exaggerated in the drawing). The building itself forms the opposite side of the triangle, which has an unknown height that we will call h. The distance d to the building is 10 km, corresponding to the adjacent side of the triangle.

20 APS 1010 Astronomy Lab 20 Math Review Since we want to know the opposite side, and already know the adjacent side of the triangle, we need only concern ourselves with the trigonometric tangent relationship: which we can reorganize to give tan α = (opp) (adj) or tan 1 = h d h = d x tan 1 or h = 10 km x = km = meters. Small Angle Approximation We used the adjacent side of the triangle for the distance instead of the hypotenuse because it represented the smallest separation between us and the building. It should be apparent, however, that since we are 10 km away, the distance to the top of the building will only be very slightly farther than the distance to the base of the building; a little trigonometry shows that the hypotenuse in this case equals km, or less than 2 meters longer than the adjacent side of the triangle. In fact, the hypotenuse and adjacent sides of a triangle are always of similar lengths whenever we are dealing with angles that are not very large. Thus, we can substitute one for the other whenever the angle between the two sides is small. Now imagine that the apex of a small angle α is located at the center of a circle whose radius is equal to the hypotenuse of the triangle, as shown above. The arclength of the circumference subtended by that small angle is only very slightly longer than the length of the corresponding straight ( opposite ) side. In general, then, the opposite side of a triangle and its corresponding arclength are always of nearly equal lengths whenever we are dealing with angles that are not very large. We can substitute one for the other whenever the subtending angle is small. Now let s go back to our equation for the physical height of our building: h = d x tan α = d x (opp) (adj). Since the angle α is small, the opposite side is approximately equal to the arclength subtended by the building. Likewise, the adjacent side is approximately equal to the hypotenuse, which is in turn equivalent to the radius of the inscribed circle. Making these substitutions, the above (exact) equation can be replaced by the following (approximate) equation: h = d x (arclength) (radius). But remember that the ratio (arclength)/(radius) is the definition of an angle expressed in radian units rather than degrees - so we have the very useful small angle approximation: For small angles, the physical size h of an object can be determined directly from its distance d and angular size in radians by

21 APS 1010 Astronomy Lab 21 Math Review h = d x (angular size in radians). Or, for small angles the physical size h of an object can be determined from its distance d and its angular size α in degrees by h = d x 2 π 360 x α. Using the small angle approximation, the height of our building 10 km away is calculated to be meters high, an error of only about 2 cm (less than 1 inch)!... and best of all, the calculation didn t require trigonometry, just multiplication and division! When can the approximation be used? Surprisingly, the angles don t really have to be very small. For an angle of 1, the small angle approximation leads to an error of only 0.01%. Even for an angle as great as 10, the error in your answer will only be about 1%, and you avoided using trig! Powers and Roots We can express any power or root of a number in exponential notation: We say that b n is the nth power of b, or b to the n (power). The number represented here as b is called the base, and n is called the power or exponent. The basic definition of a number written in exponential notation states, as you know, that the base should be multiplied by itself the number of times indicated by the exponent. That is, b n means b multiplied by itself n times. For example: 5 2 = 5 x 5; b 4 = b x b x b x b. From the basic definition, certain properties automatically follow: Zero Exponent: Any nonzero number raised to the zero power is 1. That is, b 0 = 1. Examples: 2 0 = 10 0 = -3 0 = (1/2) 0 = 1. Negative Exponent: A negative exponent indicates that a reciprocal is to be taken. That is, b -n = 1 1 b n b -n = b n a b -n = a x b n. Examples: 4-2 = 1/4 2 = 1/16; 10-3 = 1/10 3 = 1/1000; 3/2-2 = 3 x 2 2 = 12. Fractional Exponent: A fractional exponent indicates that a root is to be taken. b 1/n = n b ; b m/n = n b m = n m b. Examples: 8 1/3 = 3 8 = 2 8 2/3 = /2 = 2 4 = 16 = 4 x 1/4 = ( x 1/2 ) = 2 2 = 4 1/2 = x

22 APS 1010 Astronomy Lab 22 Using Your Calculator USING YOUR CALCULATOR Calculator Rule #1: Don't switch off your brain when you switch your calculator on! Your calculator is intended to eliminate tedious arithmetic chores, not to do your thinking for you. It's very easy to accidentally press the wrong buttons. Before you write down any answer, ask yourself if the answer seems reasonable. Intelligent use of your calculator will make your success in this course far more likely! Example: Suppose you punch in the following: (3.28 x 10 4 ) x (2.4 x 10-7 ). Since 3 x 2 = 6, and (10 4 ) (10-7 ) = 10-3, you know that your answer should be near 6 x If your calculator gives you the answer 2.3 x 10 15, then you would know you have done something wrong and should try again. Example: Suppose you punch in: 47. Since 47 is between 36 and 49, and you know that 36 = 6 and 49 = 7, you know that your answer should be between 6 and 7. If your calculator gives you the answer 8.3, then you would know you have made an entry error and should try again. Variations among Calculators: Most scientific calculators have keys to perform all of the operations described below. However, the labeling of the keys on your calculator, and the sequence in which they must be pushed, may differ slightly from the examples given here. If you cannot get your calculator to do all the operations in these examples, ask your instructor for assistance. Scientific Notation: Your calculator should have a key for entering scientific notation. It probably is labeled either EXP or EE (for "exponent" or "enter exponent"). This key is used to enter the power of 10 multiplying the number you have entered previously. For example, to enter the number 3.5 x 10 6 you would use the key sequence: 3.5 EE 6 Note that the EE key can be thought of as meaning "times 10 to the power that I enter next". Thus, you must be especially careful in entering powers of 10, since there must be a preceding number for you to multiply "times 10 to the power of..." with. For example, to enter the number 10 8 you would press: 1 EE 8. A common mistake is to enter: 10 EE 8. Note that this means 10 x 10 8 or 10 9.

23 APS 1010 Astronomy Lab 23 Using Your Calculator Most calculators are a bit tricky in the way you must enter a negative exponent. If you want to enter 5 x 10-3, for example, you do not press 5 EE -3 = ; the calculator will probably perform the operation (5 x 10 0) - 3 = 2. Instead, you must use the "change sign" key, +/- or CHS, which toggles the sign between positive and negative values (check the display to see if the exponent is correct): 5 EE +/- 3 = or 5 EE 3 +/- = Switching Between "Normal" and Scientific Notation: Most calculators have a single key which switches between scientific and "normal" notation. The labeling of this key varies significantly among calculators, but often includes the letters "F" and "E" (which stand for "floating point notation" and "exponential notation", respectively). A common label for this key is F-E. On some calculators a sequence of keys must be used instead of a single key. On Sharp brand calculators, for example, the key is labeled FSE ; you may have to press this key more than once. On the Casio fx-250, notation is changed by using the MODE key: MODE 82 gives you scientific notation with 2 significant figures. MODE 84 gives you scientific notation with 4 significant figures. To convert to normal notation, press MODE 9. Angles and Trigonometry Your calculator should have keys for all of the standard trigonometric functions including sin, cos, tan, and their inverse operations: arcsin, arccos, and arctan. Using the keys for the trigonometric functions is straightforward, except for one complication: the trig functions are derived from work with angles, and there is more than one system for measuring angles. Besides degrees, angles can also be measured in radians (common in math and science) and in grads (common in engineering). Unless you tell your calculator in advance which type of angle measurement you are using, your answer may come out incorrect. Most calculators have a key labeled DRG which switches the calculator between degrees, radians, and grads; usually, the numerical display has a label showing which mode is in effect. Before using any trigonometric function, always put your calculator into the correct mode! In this lab course, if you see the symbol, you will know to work with degrees, otherwise you should assume we are working with radians. For example, to calculate the sine of 45, first make sure your calculator is in degree mode, and then enter: 45 sin =. You will get the answer (to 3 decimal places). Now switch your calculator to radian mode, and find the sine of 45 radians with the same sequence of keys. You should find that sin 45 = 0.851, demonstrating the importance of setting the mode before starting

24 APS 1010 Astronomy Lab 24 Using Your Calculator a problem! (Note: it is not necessary to distinguish between these types of angle measure if you are not using any trigonometric functions.) If you know that the tangent of an unknown angle equals 0.235, for example, and you want to know what the angle itself must be, you should press the inverse function key (usually labeled arc or INV ) before selecting the trigonometric function:.235 arc tan = to get the answer or radians (depending upon the angular mode the calculator was in). Some calculators combine the inverse trigonometric function into a single key, such as tan -1 ; you may have to press a "shift key" on your calculator to access it. Powers and Roots: Your calculator should have keys for raising numbers to powers or for taking roots. To raise a number to a power, use the key which is usually labeled as y x or 5 3 you would use the following sequence of keys: and get the answer y x 3 = x y. For example, to do Many people are reluctant to use the "to the power of" key because they don't remember whether the base number or the exponent should be entered first. If you find yourself in this situation, here s a simple test you can do to figure it out: enter the sequence 2 y x 1 =, and note the result. If the answer is "2", then the base number comes first, because the calculator performed the operation 2 1 = 2. If the answer is "1", then the exponent comes first, since 1 2 = 1. To take roots, you use the key usually labeled x y or y x or x 1/y. For example, to take the 4th root of 16 ( 4 16 or 16 1/4 ) you would use the keys: 16 x y 4 = and get the answer 2. If your calculator doesn't have a "root" key, you can get the same answer by using the "power" key sequence: 16 y x.25 = since = 16 1/4 = 4 16.

25 APS 1010 Astronomy Lab 25 Using Your Calculator Reciprocals, Squares, Square Roots: Reciprocals, squares, and square roots, can all be done using the "power" and "root" keys described above. For example, to get the reciprocal of 25 you could enter the calculator equivalent of 25-1 : 25 y x +/- 1 = and get the answer 0.04 (which is 1/25). To square a number, you can use the "power" key and an exponent of "2"; To get the square root, you can use the power key with an exponent of "0.5", or the "root" key and a root of "2". To make your life simpler, however, most calculators have special keys for taking squares (key labeled x 2 ), square roots (key labeled ), and reciprocals (key labeled 1/x or x -1 ). Some calculators also have special keys for cubes x 3 and cube roots 3. For example, to calculate 38 2 you would enter: 38 x 2 = and get the answer 1,444. To calculate the decimal equivalent of 1/25, you would enter 25 1/x = and get the answer You can even use the square root key twice to find the fourth root of a number, since the square root of a square root is the fourth root: for example, you could find that 3 is the fourth root of 81: by keying in the sequence 4 81 = ( 81 ) 1/4 = ( 81 1/2 ) 1/2 = = Pi (π): The key labeled π can be used to automatically enter the numerical value of π. Simply press the π key to see that π = (to 9 decimal places). Logarithms You probably won't be doing any logarithms in this course, but since scientific calculators come equipped with this capability, we will mention them very briefly. To take the common logarithm of a number (to find out what power that 10 must be raised to in order to equal that number), use the log key; for example, 50 log will produce an answer of 1.699, showing that = 50. To perform the inverse operation (to find out what number you would get if you raised 10 to a particular power), you use the INV log or 10 x keys.

26 APS 1010 Astronomy Lab 26 Using Your Calculator Finally, there is the mysterious ln or ln x key, which performs what is known as a "natural" logarithm. It works like a "common" logarithm, except that the base is the number e = instead of 10. Believe it or not, the number e is as important to science and mathematics as the number π. However, if you aren't overly fond of these subjects, you won't have to worry about this key or its inverse e x either. The Parentheses Keys: All calculators have a priority system for performing operations. For example, multiplication has a higher priority than addition, so that if you enter the key sequence: x 2 = the calculator will first multiply 3 x 2 = 6 and then add the 5 to get 11 (as opposed to first adding to get 8 and then multiplying by 2, which would give 16.) When performing calculations involving multiple steps, you can get incorrect answers if you are not careful to understand your calculator's priority system. You often can avoid problems, however, by making judicious use of the keys ( and ) (if your calculator has them) to group your operations. For example, if you wished to alter the priority of the above calculation, you could enter: which will give you the answer 16. ( ) x 2 = Of course, if you are uncomfortable with long numerical calculations and want to make sure that your calculator doesn't do something that you didn't intend for it to do, you can simply perform the mathematical operations one at a time in the correct sequence, write down the intermediate answers, and re-enter the needed numbers when appropriate. It may not be the most elegant use of your calculator, but who cares, as long as you get what you wanted!

27 APS 1010 Astronomy Lab 27 Celestial Coordinates CELESTIAL COORDINATES GEOGRAPHIC COORDINATES The Earth's geographic coodinate system is familiar to everyone - the north and south poles are defined by the Earth's axis of rotation; equidistant between them is the equator. North-south latitude is measured in degrees from the equator, ranging from -90 at the south pole, 0 at the equator, to +90 at the north pole. East-west distances are also measured in degrees, but there is no "naturally-defined" starting point - all longitudes are equivalent to all others. Humanity has arbitrarily defined the prime meridian (0 longitude) to be that of the Royal Observatory at Greenwich, England (alternately called the Greenwich meridian). Each degree ( ) of a 360 circle can be further subdivided into 60 equal minutes of arc ('), and each arc-minute may be divided into 60 seconds of arc ("). The 24-inch telescope at Sommers-Bausch Observatory is located at a latitude of 40 0'13" North of the equator and at a longitude '45" West of the Greenwich meridian. Boulder +40 0' 13" Latitude ' 45" Longitude North Pole +90 Latitude Greenwich 0 Longitude Equator 0 Latitude The Earth's Latitude - Longitude Coordinate System Parallels or Small Circles Meridians ALT-AZIMUTH COORDINATES The alt-azimuth (altitude - azimuth) coordinate system, also called the horizon system, is a useful and convenient system for pointing out a celestial object. One first specifies the azimuth angle, which is the compass heading towards the horizon point lying directly below the object. Azimuth angles are measured eastwardly from North (0 azimuth) to East (90 ), South (180 ), West (270 ), and back to North again (360 = 0 ). The four principle directions are called the cardinal points.

28 APS 1010 Astronomy Lab 28 Celestial Coordinates Next, the altitude is measured in degrees upward from the horizon to the object. The point directly overhead at 90 altitude is called the zenith. The nadir is "down", or opposite the zenith. We sometimes use zenith distance instead of altitude, which is 90 - altitude. Every observer on Earth has his own separate alt-azimuth system; thus, the coordinates of the same object will differ for two different observers. Furthermore, because the Earth rotates, the altitude and azimuth of an object are constantly changing with time as seen from a given location. Hence, this system can identify celestial objects at a given time and location, but is not useful for specifying their permanent (more or less) direction in space. In order to specify a direction by angular measure, you need to know just how big angles are. Here s a convenient yardstick to use that you carry with you at all times: the hand, held at arm's length, is a convenient tool for estimating angles subtended at the eye: Index Finger Hand Fist 10 EQUATORIAL COORDINATES Standing outside on a clear night, it appears that the sky is a giant celestial sphere of indefinite radius with us at its center, and upon which stars are affixed to its inner surface. It is extremely useful for us to treat this imaginary sphere as an actual, tangible surface, and to attach a coordinate system to it.

29 APS 1010 Astronomy Lab 29 Celestial Coordinates The system used is based on an extension of the Earth's axis of rotation, hence the name equatorial coordinate system. If we extend the Earth's axis outward into space, its intersection with the celestial sphere defines the north and south celestial poles; equidistant between them, and lying directly over the Earth's equator, is the celestial equator. Measurement of "celestial latitude" is given the name declination (DEC), but is otherwise identical to the measurement of latitude on the Earth: the declination at the celestial equator is 0 and extends to ±90 at the celestial poles. The east-west measure is called right ascension (RA) rather than "celestial longitude", and differs from geographic longitude in two respects. First, the longitude lines, or hour circles, remain fixed with respect to the sky and do not rotate with the Earth. Second, the right ascension circle is divided into time units of 24 hours rather than in degrees; each hour of angle is equivalent to 15 of arc. The following conversions are useful: 24 h = m = 15' 1 h = 15 4 s = 1' 4 m = 1 1 s = 15" The Earth orbits the Sun in a plane called the ecliptic. From our vantage point, however, it appears that the Sun circles us once a year in that same plane; hence, the ecliptic may be alternately defined as "the apparent path of the Sun on the celestial sphere". The Earth's equator is tilted 23.5 from the plane of its orbital motion, or in terms of the celestial sphere, the ecliptic is inclined 23.5 from the celestial equator. The ecliptic crosses the equator at two points; the first, called the vernal (spring) equinox, is crossed by the Sun moving from south to north on about March 21st, and sets the moment when spring begins. The second crossing is from north to south, and marks the autumnal equinox six months later. Halfway between these two points, the ecliptic rises to its maximum declination of (summer solstice), or drops to a minimum declination of (winter solstice). As with longitude, there is no obvious starting point for right ascension, so astronomers have assigned one: the point of the vernal equinox. Starting from the vernal equinox, right ascension increases in an eastwardly direction until it returns to the vernal equinox again at 24 h = 0 h. North Celestial Pole +90 DEC Hour Circles Celestial Equator 0 DEC 16h 18h 20h RA 22h 24h = 0h 2h 4h Earth Ecliptic 23.5 Sun (March 21) Vernal Equinox 0h RA, 0 DEC Winter Solstice 18h RA, DEC

30 APS 1010 Astronomy Lab 30 Celestial Coordinates The Earth precesses, or wobbles on its axis, once every 26,000 years. Unfortunately, this means that the Sun crosses the celestial equator at a slightly different point every year, so that our "fixed" starting point changes slowly - about 40 arc-seconds per year. Although small, the shift is cumulative, so that it is important when referring to the right ascension and declination of an object to also specify the epoch, or year in which the coordinates are valid. TIME AND HOUR ANGLE The fundamental purpose of all timekeeping is, very simply, to enable us to keep track of certain objects in the sky. Our foremost interest, of course, is with the location of the Sun, which is the basis for the various types of solar time by which we schedule our lives. Time is determined by the hour angle of the celestial object of interest, which is the angular distance from the observer's meridian (north-south line passing overhead) to the object, measured in time units east or west along the equatorial grid. The hour angle is negative if we measure from the meridian eastward to the object, and positive if the object is west of the meridian. For example, our local apparent solar time is is determined by the hour angle of the Sun, which tells us how long it has been since the Sun was last on the meridian (positive hour angle), or how long we must wait until noon occurs again (negative hour angle). If solar time gives us the hour angle of the Sun, then sideral time (literally, "star time") must be related to the hour angles of the stars: the general expression for sidereal time is Sidereal Time = Right Ascension + Hour Angle which holds true for any object or point on the celestial sphere. It s important to realize that if the hour angle is negative, we add this negative number, which is equivalent to subtracting the positive number. For example, the vernal equinox is defined to have a right ascension of 0 hours; thus the equation becomes Sidereal time = Hour angle of the vernal equinox Another special case is that for an object on the meridian, for which the hour angle is zero by definition. Hence the equation states that Sidereal time = Right ascension crossing the meridian Your current sidereal time, coupled with a knowledge of your latitude, uniquely defines the appearance of the celestial sphere; furthermore, if you know any two of the variables in the expression ST = RA + HA, you can determine the third. The following illustration shows the appearance of the southern sky as seen from Boulder at a particular instant in time. Note how the sky serves as a clock - except that the clockface (celestial sphere) moves while the clock "hand" (meridian) stays fixed. The clockface numbering increases towards the east, while the sky rotates towards the west; hence, sidereal time always increases, just as we would expect. Since the left side of the ST equation increases with time, then so must the right side; thus, if we follow an object at a given right ascension (such Saturn or Uranus), its hour angle must constantly increase (or become less negative).

31 APS 1010 Astronomy Lab 31 Celestial Coordinates Sidereal Time = Right Ascension on Meridian = 21 hrs 43 min Vernal Equinox 0 h 0m 23h 20m Ecliptic 22h 40m 22h 0m 21h 20m 20h 40m 20h 0m 19h 20m Sidereal Time = Right Ascension + Hour Angle Saturn RA = 21h 59m Hour Angle of Vernal Equinox = - 2h 17m = 21h 43m = Sidereal Time Hour Angle - 0h 16m Hour Angle + 2h 21m Uranus RA = 19h 22m Saturn: 21h 59m RA + (- 0h 16m) HA = 21h 43m ST Uranus: 19h 22m RA + 2h 21m HA = 21h 43m ST 1:50 am MDT 20 August 1993 SOLAR VERSUS SIDEREAL TIME Every year the Earth actually makes 366 1/4 complete rotations with respect to the stars (sidereal days). Each day the Earth also revolves about 1 about the Sun, so that after one year, it has "unwound" one of those rotations with respect to the Sun; on the average, we observe 365 1/4 solar passages across the meridian (solar days) in a year. Since both sidereal and solar time use 24-hour days, the two clocks must run at different rates. The following compares (approximate) time measures in each system: SOLAR SIDEREAL SOLAR SIDEREAL days days 24 hours 24h 3m 56s 1 day d 23h 56m 4s 24 hours d 1 day 6 minutes 6m 1s The difference between solar and sidereal time is one way of expressing the fact that we observe different stars in the evening sky during the course of a year. The easiest way to predict what the sky will look like (i.e., determine the sidereal time) at a given date and time is to use a planisphere, or star wheel. However, it is possible to estimate the sidereal time to within a halfhour or so with just a little mental arithmetic. At noontime on the date of the vernal equinox, the solar time is 12h (since we begin our solar day at midnight) while the sidereal time is 0h (since the Sun is at 0h RA, and is on our meridian). Hence, the two clocks are exactly 12 hours out of syncronization (for the moment, we will ignore the complication of "daylight savings"). Six months later, on the date of the autumnal equinox (about September 22) the two clocks will agree exactly for a brief instant before beginning to drift apart, with sidereal time gaining about 1 second every six minutes.

32 APS 1010 Astronomy Lab 32 Celestial Coordinates For every month since the last fall equinox, sidereal time gains 2 hours over solar time. We simply count the number of elapsed months, multiply by 2, and add the time to our watch (converting to a 24-hour system as needed). If daylight savings is in effect, we subtract 1 hour from the result to get the sidereal time. For example, suppose we wish to estimate the sidereal time at 10:50 p.m. Mountain Daylight Time on August the 19th. About 11 months have elapsed since fall began, so sidereal time is ahead of standard solar time by 22 hours - or 21 hours ahead of daylight savings time. Equivalently, we can say that sidereal time lags behind daylight time by 3 hours. 10:50 p.m. on our watch is 22h 50 m on a 24-hour clock, so the sidereal time is 3 hours less: ST = 19h 50m (approximately). ENVISIONING THE CELESTIAL SPHERE With time and practice, you will begin to "see" the imaginary grid lines of the alt-azimuth and equatorial coordinate systems in the sky. Such an ability is very useful in planning observing sessions and in understanding the apparent motions of the sky. To help you in this quest, we ve included four scenes of the celestial sphere showing both alt-azimuth and equatorial coordinates. Each view is from the same location (Boulder) and at the same time and date used above (10:50 pm MDT on August 19th, 1993). As we comment on each, we'll mention some important relationships between the coordinate systems and the observer's latitude. Looking North From Boulder, the altitude of the north celestial pole directly above the North cardinal point is 40, exactly equal to Boulder's latitude. This is true for all observing locations: Altitude of the pole = Latitude of observer The +50 declination circle just touches our northern horizon. Any star more northerly than this will be circumpolar - that is, it will never set below the horizon. Declination of northern circumpolar stars > 90 - Latitude Most of the Big Dipper is circumpolar. The two pointer stars of the dipper are useful in finding Polaris, which lies only about 1/2 from the north celestial pole. Because these two stars always point towards the pole, they must both lie approximately on the same hour circle, or equivalently, both must have approximately the same right ascension (11 hours RA).

33 APS 1010 Astronomy Lab 33 Celestial Coordinates Looking South If you were standing at the north pole, the celestial equator would coincide with your local horizon. As you travel the 50 southward to Boulder, the celestial equator will appear to tilt up by an identical angle; that is, the altitude of the celestial equator above the South cardinal point is 50 from the latitude of Boulder. Your local meridian is the line passing directly overhead from the north to south celestial poles, and hence coincides with 180 azimuth. Generally speaking, then, Altitude of the intersection of the celestial equator with the meridian = 90 - Latitude Since the celestial equator is 50 above our southern horizon, any star with a declination less than -50 is circumpolar around the south pole, and will never be seen from Boulder. Declination of southern circumpolar stars < Latitude - 90 The sidereal time (right ascension on the meridian) is 19h 43m - only 7 minutes different from our estimate. Looking East The celestial equator meets the observer's local horizon exactly at an azimuth of 90 ; this is always true, regardless of the observer's latitude: The celestial equator always intersects the east and west cardinal points

34 APS 1010 Astronomy Lab 34 Celestial Coordinates At the intersection point, the celestial equator makes an angle of 50 with the local horizon; in general, The intersection angle between celestial equator and horizon = 90 - Latitude Our view of the eastern horizon at this particular time includes the Great Square of Pegasus, which is useful for locating the point of the vernal equinox. The two easternmost stars of the Great Square both lie on approximately 0 hours of right ascension. The vernal equinox lies in the constellation of Pisces about 15 south of the Square. Looking Up From a latitude of 40, an object with a declination of +40 will, at some point in time during the day or night, pass directly overhead through the zenith. In general Declination at zenith = Latitude of observer The 24 Ephemeris Stars in the SBO Catalog of Astronomical Objects have Object Numbers ranging from #401 to #424. Each of these moderately-bright stars passes near the zenith (within 10 or so) over the course of 24 hours. At any time, the ephemeris star nearest the zenith will usually be the star whose last two digits equals the sidereal time (rounded to the nearest hour). For example, at the current sidereal time (19h 43m), the zenith ephemeris star is #420 (δ Cygni). At this time of the year (late summer) and at this time of night (mid-evening), the three prominent stars of the Summer Triangle are high in the sky: Vega (in Lyra the lyre), Deneb (at the tail of Cygnus the swan), and Altair (in Aquila the eagle). However, the Summer Triangle is not only high in the sky in summer, but at any period during the year when the sidereal time equals roughly 20 hours: just after sunset in October, just before sunrise in May, and even around noontime in January (though it won't be visible because of the Sun).

35 APS 1010 Astronomy Lab 35 Telescopes & Observing TELESCOPES & OBSERVING Telescope Types Telescopes come in two basic types - the refractor, which uses a lens as its primary or objective optical element, and the reflector, which uses a mirror. In either case, light originating from an object (usually at infinity) is brought to a focus within the telescope to form an image of the object. The size of a telescope refers to the diameter its primary lens or mirror, rather than its length. By placing photographic film at the focal plane, the objective lens or mirror forms a camera system. If instead we position an eyepiece lens at an appropriate distance behind the focal plane, we form an optical telescope. The optical arrangement of a refracting telescope is shown below. The image is formed by the refraction of light through the lens. The refractor has an advantage over reflectors in that there is no central obscuration to produce diffraction patterns, and therefore yields crisper images. However, refraction introduces chromatic abberation, which is corrected by using two-element (doublet or achromat) or three-element (apocromat) lenses. The lens complexity makes the refractor very expensive; hence, refractors are much smaller in diameter than comparably-priced reflectors. All of the Sommers-Bausch Observatory (SBO) finder telescopes are of the refractor type. Objective Lens Eyepiece Lens Light from Object at Infinity Focal Plane Eye A reflecting telescope focusses and re-directs light back towards the incident direction, and therefore requires additional optics to get the image "out of the way". This central obscuration reduces the amount of light reaching the primary, and adds diffraction patterns which degrade the resolution. However, the telescope does not suffer from chromatic abberation, since only mirrors are used. Reflectors can be built much larger since the mirror is supported from behind (while a lens is mounted only at its edges). Furthermore, only one objective surface must be ground and polished, making the reflector much less expensive. As a result, virtually all large telescopes are of the reflector type. The Newtonian (invented by Sir Isaac Newton) is the simplest form of reflector. It uses a diagonal mirror (a plane mirror tilted at a 45 angle) to re-direct the light out the side of the telescope to the eyepiece. The placement of the eyepiece at the "wrong" end of the telescope limits it practical size, and its asymmetric design precludes the use of heavy instrumentation. The newtonian is used principly by amateur astronomers since it is the "cleanest" as well as least expensive reflector.

36 APS 1010 Astronomy Lab 36 Telescopes & Observing Light from Object at Infinity Diagonal Mirror Prime Focal Plane Eyepiece Primary Mirror Eye In the Cassegrain reflector, a convex secondary mirror intercepts the light from the primary and reflects it back again, reducing the convergence angle in the process. The light passes through a central hole in the primary and comes to a focus at the back of the telescope. The location of the Cassegrain focus makes it easy to mount instrumentation, and the folded optical design permits larger diameter telescopes to be houses within smaller domes; hence this design is most widelyused at professional observatories. All three of the permanently-mounted SBO telescopes (16", 18", 24") are Cassegrain reflectors. Light from Object at Infinity Eyepiece Eye Prime Focus (not used) Secondary Mirror Primary Mirror Telescopes that use a combination of lenses and mirrors to form images are called catadioptric. One form is the Schmidt camera, which uses a weak lens-like corrector plate at the entrance to the telescope to correct for off-axis image abberations; this specialized telescope can't be used for viewing but does produce panoramic sky photographs. SBO has an 8" Schmidt for astrophotography. Corrector Lens Light from Object at Infinity Focal Plane Film Concave Mirror One of the most popular, albeit expensive, telescope designs is the Schmidt-Cassegrain. As the name suggests, it looks like the Cassegrain telescope but with the addition of a Schmidt corrector plate. SBO has six of these smaller, portable telescopes: an 8" Meade, two 5" Celestrons, and three 3.5" Questars.

37 APS 1010 Astronomy Lab 37 Telescopes & Observing The fundamental optical properties of any telescope are described by three parameters: the focal length, the aperture, and the focal ratio (f/ratio). The focal length (f) is the distance from the objective where the image of an infinitely-distant object is formed. The aperture (A) of a telescope is simply the diameter of its light-collecting lens (or mirror). The f/ratio is defined to be the ratio of the focal length of the lens or mirror to its aperture: f/ratio = f A. (1) Obviously, if you know any two of the three fundamental parameters, you can calculate the third. Focal Length As shown in the diagram below, an object that subtends an angular size θ in the sky will form an image of linear size h given by θ tan(θ) = h/f. Therefore h = θ radians f = θ 57.3 f. (2) Object at Infinity Parallel Incident Rays θ f θ Image at Focal Plane h The image scale is the ratio of linear image size to its actual angular size: Image Scale = h θ = f (3) Thus, the scale of the image of any object depends only upon the focal length of the telescope, not on any other property: two telescopes with identical focal lengths will produce identically-sized images of the same object, regardless of any other physical differences. Furthermore, the image scale is directly proportional to f: doubling the focal length will produce an image twice the linear size (and four times the areal size). The plate scale (used in photography) is usually expressed as the inverse of the above - the angular size of the object (usually in arc-seconds) corresponding to a linear size (usually in millimeters) in the focal plane. For a compound telescope (with more than one active optical element), we refer to the effective focal length (EFL) of the entire optical system, and treat it as a simple telescope with single lens or mirror of focal length f = EFL. Aperture The aperture A of a telescope is the diameter of the principle light-gathering optical element. The light-gathering ability, or light grasp, of the telescope is proportional to the area of the objective element, or A 2. For point sources such as stars, all of the collected light will (to a first

38 APS 1010 Astronomy Lab 38 Telescopes & Observing approximation) converge to form a point-like image; hence, stars appear brighter, and fainter stars can be detected, with telescopes of larger aperture. Telescope aperture is the principle criteria for determining the limiting visible stellar magnitude. The resolving power (ability to resolve adjacent features in an image) of an optical telescope is also chiefly a function of aperture; the larger the aperture, the smaller the diffraction pattern formed by each point source, and therefore the better the resolution. The theoretical diffraction-limited resolution of a telescope is given by θ diff 1.2 λ A 5 arc-sec Inches of Aperture (4) where λ is the wavelength of the light used, assumed to be 5500 Å. Focal Ratio Although the amount of light gathered by a telescope is proportional to A 2, the collected light is spread out over an area at the focal plane that is proportional to h 2, and therefore propertional to f 2 ; hence, the image brightness of an extended (non-pointlike) object will scale linearly with the ratio (A/f) 2, or inversely with the square of the f/ratio = f/a of the telescope: Brightness 1 f/ratio 2. (5) The f/ratio of a telescope is therefore the only factor that determines the image brightness of an extended object. For example, if one telescope has twice the aperture and twice the focal length of another, both telescopes are geometrically similar and would use exactly the same photographic exposure to produce identically-bright images of, say, the Moon. Of course, the first telescope would produce an image twice the linear size (and four times the area) as the latter, but both would have the same photographic "speed". Note that the smaller the f/ratio, the brighter the image and the faster the speed: a 35mm camera using an f/ratio of f/2 will photograph the Milky Way in less than 5 minutes, while the same film on an f/15 telescope will require an hour or more to capture the diffuse glow! On the other hand, individual stars will record much better using the telescope. The optical speed of a compound telescope is simply the ratio of its effective focal length to its aperture. Both effective or actual f/ratios are a measure of the final angle of convergence angle of the cone of light before it forms the image; the smaller the f/ratio, the greater the convergence, and the more critical the focus; this is why "slow" optics, with a slowly-converging beam, exhibit a larger "depth-of-field". Seeing and Clarity Equation (4) gives the theoretical limit to the angular size that can be resolved by a telescope. This limit is almost never achieved in practice, since atmospheric turbulence is always present to blur our image of the object. The quality of the seeing is measured by the angular separation needed between two stars for their images to just be resolved. Average seeing in the Boulder area is about 2 arc-seconds, making it a marginal task to "split" the 2 arc-sec pairs of the "double-double" star Epsilon Lyrae. Good seeing in Boulder is when the atmosphere is stable enough to resolve 1" separations. Poor seeing conditions can be as bad as 5" or even worse. By comparison, half-arcsecond seeing occurs routinely at several optimally-located major observatories, but it is rare for any ground-based telescope to experience 0.1" conditions. One can estimate the seeing of a night simply by glancing up. If the stars glow solidly, the seeing is probably "good"; if they twinkle, the seeing is "average"; if bright stars dance and planets flash with color, the seeing is "poor". Another measure is to look towards Denver - if there are lots of

39 APS 1010 Astronomy Lab 39 Telescopes & Observing particulates in the air, and Denver is on smog alert, you will see a bright horizon glow; in this situation, you can usually count on good seeing! These conditions are created by an inversion layer of stagnant air, which permits rock-solid astronomical viewing. The best conditions for good seeing are the worst for sky clarity. Good clarity implies dark skies due to a lack of light-scattering dust particles, and an absence of water-vapor haze. Clarity usually improves in Boulder after the passage of a thunderstorm, which clears out the dust. Of course, the conditions that improve clarity usually destroy seeing. Since ideal nights of good clarity and seeing are rare, an observer must be prepared to take advantage of the best properties of the night, if any. Lunar and planetary observing requires good seeing conditions, since planetary disks are small, only 2-40 arc-seconds in diameter. Poor clarity is not a major problem for bright solar system objects, although low-contrast features may be washed out. On the other hand, good clarity (and the absence of strong moonlight) is essential to observe galaxies and diffuse nebulae, since the light from these objects is faint and dark skies are needed for contrast. Seeing is not critical, since these objects are fuzzy patches to begin with. When both seeing and clarity are poor, it's best to focus your attention on bright star clusters and widely-spaced double stars. Eyepieces and Magnification An eyepiece or ocular is simply a magnifier that allows you to inspect the image formed by the objective from a very short distance away. The eyepiece is placed so that its focal plane coincides with the focal plane of the objective, so that the rays from the image emerge parallel from the eyepiece. As a result, the telescope never forms a final image - the lens of your eye does that. By selecting appropriate rays for both the objective lens (obj) and the eyepiece lens (eye), we can see that rays incident at the telescope at an angle θ obj will emerge from the eyepiece at a larger angle θ eye ; the observer perceives that the object subtends a much larger angle than is actually the case. A little geometry gives the angular magnification M θ produced by the arrangement: M θ θ eye θ obj f obj f eye. (6) That is, magnification is the ratio of the objective focal length divided by the eyepiece focal length. For example, the 16-inch f/12 telescope has a focal length of 192 inches, or 4877 mm. If we use an eyepiece with a focal length of 45 mm (engraved on its barrel), the "power" of the telescope will be about 108 X; by switching to an 18 mm eyepiece, we will have 271 X. The answer to the question "what is the power of this telescope?" is "whatever you want - within the range of the available eyepiece assortment".

40 APS 1010 Astronomy Lab 40 Telescopes & Observing Eyepieces come in a variety of designs, each representing a different trade-off between performance and cost, ranging from the inexpensive short-focal-length two-element Ramsden (R) to the 6-element triple-doublet Erfle (Er). Other types include: the Kellner (K), an improved Ramsden; orthoscopic (Or), good at moderate focal lengths at reasonable cost; and the expensive low-power wide-field designs - the Plossl (including Clave), the Konig, and the Televue. Besides focal length (and image quality), the other important characteristic of an eyepiece is its field-of-view - the size of the solid angle viewable through the ocular, or when used on a particular telescope, the actual angular size of the observable sky field. The field available with a given telescope-eyepiece combination can be measured directly by positioning a bright star just at the northern edge of the field; after noting the declination, you move the telescope northward until the star is at the southern boundary of the field, note the declination again, and calculate the difference in angle. The field can also be calculated from the image scale of the telescope (equation (3)): measure the diameter of the field stop (the ring installed within the open end of the eyepiece), equate that to the linear image size h, and calculate the corresponding angle θ. The Barlow is a telecompressor (concave or negative) lens that can be installed in front of the eyepiece. It reduces the angle of convergence of the objective light cone and hence increases the f/ratio and the EFL of the telescope, thus increasing the magnification (by a factor of 2 to 3) from a given eyepiece. It helps achieve high magnification without sacrificing eye relief (see below). Selecting an Eyepiece The choice of eyepiece is one of the few factors that an observer may control to enhance the visibility of astronomical objects. The Observatory's eyepieces range from focal lengths of 70 mm down to 4 mm. The longer focal lengths are in the 2"-diameter format, which fit directly into the large telescope tubes; the shorter (higher magnification) eyepieces have 1-1/4" diameter barrels, but can be used in the 2" tube using an eyepiece adapter plug. Although equation (6) implies that it's possible to have any magnification one desires, there are practical limits. The entrance pupil of the human eye (the diameter of the iris opening) is about 7 mm for a fully dark-adapted eye (5 mm for older individuals). The exit pupil of an telescope (diameter of the bundle of light rays exiting the eyepiece) can be shown to be Exit Pupil = A M θ = f eye f/ratio (7) If the exit pupil is larger than the entrance pupil of the eye, the eye can't intercept it all and some of the light is wasted. This occurs if the magnification is too low. If the exit pupil just matches the eye pupil, all of the light is utilized and we have the brightest-possible, or "richest-field" arrangement. This is why 7x50 (7 power, 50 mm aperture) and 11x80 (11 power, 80 mm aperture) binoculars are excellent for night observing - their exit pupils optimally match the darkadapted human eye. At higher magnifications, all of the light enters the eye but is spread over a larger solid angle which dims the field. The average human eye can just barely resolve two objects separated by about 1 arc-minute, although a separation of about 4' (240") is much more comfortably perceived (about 50 such 4 arcminute "pixels" comprise the face of "the man in the Moon"). Hence, one criterion for a telescope's maximum useful power M max is "that magnification that matches a 250 arc-second visual separation to the diffraction limit of the telescope"; from equation (4) this equates to M max 50 x Aperture of Telescope in Inches (8)

41 APS 1010 Astronomy Lab 41 Telescopes & Observing By this "rule of thumb", the 16-inch telescope has a maximum useful magnification of 800 X on a night of perfect seeing, which would be achieved with a 6 mm eyepiece. Any greater magnification will be "empty" - that is, the image will become larger, but the enlargement will contain only "blur", not additional detail. (Note: poor-quality 2.4"-refractors are provided with 4 mm eyepieces plus a cheap 2.5X barlow lens so that the manufacturer can advertise "600 power" - 5 times beyond any useful application!) The above magnification limit is somewhat optimistic for telescopes of moderate-to-large aperture, since detail is almost invariably limited by atmospheric seeing rather than by telescope resolution. For example, if the seeing is about 1", a 250" perceived separation implies a useful maximum magnification of about 250 X - or an eyepiece in the mm range for the 16-inch telescope. For 2" seeing, a reasonable choice is about 125 power, or eyepieces in the mm range. There are several additional considerations related to high magnification. On the negative side, short-focal-length eyepieces require critical focussing and eye placement, making them difficult for inexperienced observers to use. In addition, they exhibit short eye relief - the distance behind the lens where the eye is positioned to see the entire field-of-view. In particular, eyepieces shorter than about 12 mm focal length are problematic for eye-glass wearers, since glasses prevent the eye from being placed close enough to avoid "tunnel vision". On the positive side, high magnification reveals fainter stars. Remember that stars are unresolved point sources whose light is concentrated (to a first approximation) at a single point in the image regardless of magnification. The glow of the background sky is a diffuse source, which will be spread out by higher magnification, reducing its brightness. Although high magnification doesn't increase the brightness of faint stars, it improves their contrast against the sky, making them more visible! By this same token, high magnification helps diminish the intense glare from bright solar system objects, making the Moon less painful to look at, and the bands of Jupiter easier to see. Finally, there is the consideration of the type and angular extent of the object being viewed. High magnification certainly helps resolve fine planetary detail and separates close double stars, provided that seeing conditions permit. Open clusters usually extend over a large patch of the sky, and hence need low power (a wide field-of-view) to encompass them - in fact, the small finder scopes may present a more pleasing view than the main telescope. High power won't help the contrast between sky background and diffuse nebulae (since both are extended sources), and in fact may keep the observer from seeing the glow since all aspects of the image are dimmer. Low power is essential for extremely large nebulae, since these objects can fill the field-of-view - creating a situation where "you can't see the forest for the trees". Globular clusters can be appreciated at a variety of magnifications: low power creates an impression of a "cotton-ball" floating in space, while high magnification shows a magnificent sparkling array of bright points reminiscent of distant city lights. In the end, your personal experience and judgement should be your guide. Observing Technique Observing through an eyepiece is an unnatural experience; good observing techniques come with time and experience. Here are some hints to help you get the most out of your telescope time: Let your eyes become fully dark-adapted before doing "serious" observing. This can take minutes. Keep both eyes open; this will help you relax your eyes to infinity focus. "Gaze", don't "glimpse". It takes a a few moments to mentally and optically adjust to the scene in an eyepiece. Continued observation also improves the chances for brief periods of atmospheric stability when new details may appear.

42 APS 1010 Astronomy Lab 42 Telescopes & Observing Don't stare fixedly through the eyepiece; let your eye wander. The human eye is much more sensitive to changes in brightness than to constant light levels. By looking around, you'll see fainter detail. Use averted vision to help bring out dim features. The color-sensitive cone cells concentrated near the center of the eye's retina don't respond to low light levels. If you look out of the "corner of your eye", you'll utilize the much more sensitive black-andwhite rod cell receptors that are used for peripheral vision. Finally, don't expect to see the colors that appear in photographs; for the reason just mentioned, most faint objects appear greenish to whitish because they are too faint to stimulate the color receptors in your eye.

43 APS 1010 Astronomy Lab 43 Daytime Experiments DAYTIME EXPERIMENTS

44 APS 1010 Astronomy Lab 44 Daytime Experiments The SBO Heliostat and a television image of a solar flare observed with it

45 APS 1010 Astronomy Lab 45 Colorado Model Solar System THE COLORADO MODEL SOLAR SYSTEM SYNOPSIS: A walk through a model of our own solar system will give you an appreciation of the immense size of our own local neighborhood and a feel for astronomical distances. EQUIPMENT: This lab write-up, a pencil, perhaps a calculator, and walking shoes. Astronomy students and faculty have worked with CU to lay out a scale model solar system along the walkway from Fiske Planetarium northward to the Engineering complex (see figure below). The model is a memorial to astronaut Ellison Onizuka, a CU graduate who died in the explosion of the space shuttle Challenger in January Colorado Ave Regent Dr. Folsom St. Pluto Neptune Uranus Saturn Jupiter Mars Earth Venus Mercury Sun The Colorado Scale Model Solar System is on a scale of 1 to 10 billion (10 10 )!!! That is, for every meter (or foot) in the scale model, there are 10 billion meters (or feet) in the real solar system. Note: A review of scientific notation can be found on page 15 of this manual. All of the sizes of the objects within the solar system (where possible), as well as the distances between them, have been reduced by this same scale factor. As a result, the apparent angular sizes and separations of objects in the model are accurate representations of how things truly appear in the real solar system. The model is unrealistic in one respect, however. All of the planets have been arranged roughly in a straight line on the same side of the Sun, and hence the separation from one planet to the next is as small as it can possibly be. The last time all nine planets were lined up this well in the real solar system, the year was 1596 BC! In a more accurate representation, the planets would be scattered in all different directions (but still at their properly-scaled distances) from the Sun. For example, rather than along the sidewalk to our north, Jupiter could be placed in Kittridge Commons to the south; Uranus might be found on the steps of Regent Hall, Neptune in the Police Building, and Pluto in Folsom Stadium. Of course, the inner planets (Mercury, Venus, Earth, and Mars) will still be in the vicinity of Fiske Planetarium, but could be in any direction from the model of the Sun.

46 APS 1010 Astronomy Lab 46 Colorado Model Solar System I. The Inner Solar System Read the information on the pyramid holding the model Sun in front of Fiske Planetarium. Note that the actual Sun is 1.4 million km (840,000 miles) in diameter - but on a one-ten-billionth scale, it s only 14 cm (5.5 inches) across. I.1 Step off the size of the orbit of each of the four inner planets. Using your normal walking stride, count the number of paces from the model Sun to (a) Mercury: paces (b) Venus: (c) Earth: (d) Mars: paces paces paces Contemplate the vast amount of empty space that lies between these planets and the Sun. As the saying goes, you ain t seen nothin yet (There's a whole lot more of "nothingness" to come)! I.2 Since the Sun is the size of a grapefruit, what appropriately-sized objects might you choose to represent the scaled size of each of the four inner planets? Read the information at each of the four innermost planets, and answer the following: 1.3 (a) Which planet is most like the Earth in temperature? (b) Which has the greatest range of temperature extremes? (c) Which planet is most similar to the Earth in size? (d) Which is the smallest? (e) Which planet has a period of rotation (a day) very much like the Earth s? (f) Which planet has an extremely long period of rotation? The real Earth orbits about 150 million km (93 million miles) from the Sun - a distance known as an astronomical unit, or AU for short. The AU is very convenient for comparing relative distances in the solar system by using the Earth-Sun separation as a yardstick. I.4 What fraction of an AU does one of your paces correspond to in the model? I.5 (a) Using your pace measurements from I.1, what is the distance in AU between the Sun and Mercury? (b) Between the Sun and Mars? (c) Between the Sun and Venus? (d) Which of these planets comes closest to the Earth? Another way to describe distance is to use light-time - the time it takes light, travelling at 300,000 km/second (186,000 miles/sec, or 670 million mph!) to get from one object to another. Since light

47 APS 1010 Astronomy Lab 47 Colorado Model Solar System travels at the fastest speed possible in the universe, light-time represents the shortest time-interval in which information can be sent from one location to another. Sunlight takes 500 seconds, or 8 1/3 minutes, to reach the Earth; we say that the Earth is 8.33 light-minutes from the Sun. Remember, the light-minute is a measure of distance! I.6 (a) Again, walk at a normal pace from the Sun to the Earth, and time how many seconds it takes for you to travel that distance: (b) Since light takes 500 seconds to travel that same distance in the real solar system, how many times faster than light do you walk through the model? I.7 (a) Mars is depicted in the model at its closest approach to Earth (that is, both the Earth and Mars are on the same side of the Sun). In this configuration, what is the distance, in astronomical units, between Earth and Mars? (b) What is this distance expressed in light-minutes? On July 4th, 1997, the Pathfinder spacecraft landed a rover named Sojourner on the surface of Mars. The vehicle was equipped with a camera and an on-board computer that enables it to recognize obstacles and to drive around them. I.8 Explain why Sojourner was not steered remotely by an operator back on the Earth. Finally, take a closer look at Earth's own satellite, the Moon - the furthest object to which mankind has traveled "in person". It took three days for Apollo astronauts to cross this "vast" gulf of empty space between the Earth and the Moon. I.9 (a) How many years has it been since mankind first walked there? (b) At the scale of this model, estimate how far (in cm or inches) mankind has ventured into space. I.10 Assuming that we could make the trip in a straight line over the smallest possible separation (neither of which are feasible), roughly how many times farther would astronauts have to travel to reach even the nearest planet to the Earth? II. The View From Earth Stand next to the model Earth and take a look at how the rest of the solar system appears from our vantage point (remember, since everything is scaled identically, the apparent sizes of things in the model are the same as they appear in the real solar system). II.1 (a) Stretch out your hand at arm s length, close one eye, and see if you can cover the model Sun with your index finger. Are you able to completely block it from your view? (b) Estimate the angle, in degrees, of the diameter of the model Sun as seen from Earth. Note: see page 28 of this manual for a handy way to estimate angles.

48 APS 1010 Astronomy Lab 48 Colorado Model Solar System II.2 If it s not cloudy, use the same technique to cover the real Sun with your outstretched index finger. Verify that the apparent size of the real Sun as seen from the real Earth is the same as the apparent size of the model Sun as seen from the model Earth. Caution! Staring at the Sun can injure your eyes - be sure the disk of the Sun is covered! Now look towards Mars. This Sun-Earth-Mars arrangement is called opposition, since Mars lies in the opposite direction from the Sun as seen from Earth. II.3 II.4 (a) When is a good time of day (or night) for humans to observe a planet in opposition? (Hint: if you can see Mars, is the Sun up in the sky at the same time, or not?) (b) When Mars is in opposition, will it appear larger or smaller to Earthlings than at some other point in its orbit? Now turn to face Venus. What time of day are you simulating now? (Once again, consider the direction of the Sun!) This configuration is called a conjunction, meaning that a planet appears lined up with (i.e., in conjunction with) the Sun as seen from Earth. II.5 Although Venus is as close to Earth as possible in this configuration, it would not be a good time to observe the planet. Why not? II.6 Neither Mercury nor Venus can ever be viewed (from Earth) in a direction opposite the Sun. Explain why not. (Hint: If you re having trouble answering this question, have a classmate orbit at Mercury s distance of 6 meters (20 feet) from the Sun while you observe from Earth - and note which directions you look to follow Mercury s motion.) II.7 Mars can appear in conjunction with the Sun as well as in the opposite direction. Explain or sketch how this is possible. (Hint: have a classmate orbit the Sun at the distance of Mars). Off in the distance to the north, along the walkway leading to the Engineering Building, you can just see the pedestals for the next two planets, Jupiter and Saturn. II.8 Before launching off on your journey to these planets, use your hand to measure the angle between Jupiter and Saturn, as seen from the model Earth. (Remember, if this were the real solar system, 10 billion times bigger in all directions, the angle between them would still be the same!) III. Journey to the Outer Planets As you cross Regent Drive heading for Jupiter, you ll also be crossing the region of the asteroid belt, where thousands of planetoids or minor planets can be found crossing your path. The very largest of these is Ceres, which is 760 km (450 miles) in diameter. III.1 If the asteroids are scaled like the rest of the solar system model, would you be able to see Ceres as you passed by it?

49 APS 1010 Astronomy Lab 49 Colorado Model Solar System Jupiter contains over 70% of all the mass in the solar system outside of the Sun - but still weighs less that one-tenth of one percent of the Sun itself. III.2 (a) What object would you choose to represent this, the solar system s largest planet? (b) How many times more massive is it than the Earth? (c) What moon orbits Jupiter at about the same distance as our Moon orbits the Earth? Besides Io, there are three additional large moons of Jupiter that are easily seen with a telescope from Earth: Europa, Ganymede, and Callisto. These moons orbit Jupiter at a distance of roughly 2.5, 4, and 7.5 inches, respectively at our scale. Ganymede is slightly larger than the planet Mercury - making it the 8 th largest object in the solar system after the Sun! III.3 (a) Use your hand measurement to compare the apparent size of the Sun as seen from Jupiter with your earlier measurement (in II.1) from the Earth. (You ll have to walk a few paces to the west to avoid the intervening evergreen, which plays no useful role in our model.) (b) How does the surface temperature of Jupiter compare with the temperatures of the inner planets? (The answer shouldn t surprise you, considering what you just noted about the apparent size of the Sun.) Next stop, the beautiful Ringed Planet - the most distant object in the solar system that you can see from Earth without a telescope. III.4 III.5 III.6 On your way, count the number of steps between Jupiter and Saturn: paces. (a) Earlier (in II.8) you found that Jupiter and Saturn appeared to be very close to each other as seen from Earth. How far apart are they really, expressed in astronomical units? (b) Compare the size of the entire inner solar system (from the Sun out to Mars) with the empty space between the orbits of Jupiter and Saturn. Compare the diameter of the rings of Saturn to the diameter of planet Jupiter. Which do you think would appear wider (through a telescope) from Earth: the ball of Jupiter, or the rings of Saturn? (Hint - consider distance from Earth as well as actual size). Now continue the journey onward to Uranus. On your way: III.7 (a) Time how long it takes for you to walk from the orbit of Saturn out to the orbit of Uranus: seconds. (b) Since you already have figured how many times faster-than-light that you walk (in I.6), calculate how long would it take a beam of light to cover this same distance. As you walk to Neptune, ponder the vast amount of nothingness through which you are passing. When you arrive, answer the following: III.8 (a) Which of the planets you ve just explored most resembles Neptune? (b) How many complete orbits has Neptune made around the Sun since its discovery? (c) What is the name of the only spacecraft to visit this planet, and when did it pass?

50 APS 1010 Astronomy Lab 50 Colorado Model Solar System Now begin the final walk to Pluto. When you get there, you ll be standing three-tenths of a mile, or one-half of a kilometer, from where you started your journey. You ll also be standing about 33 times further away from the Sun than when you left the Earth. III.9 You may have been surprised by how soon you arrived at Pluto after leaving Neptune. Read the plaque, and then explain why the walk was so short. III.10 (a) Although you can t actually see the model Sun from this location, describe how you imagine it would appear from Pluto. (b) How does the temperature compare out here in the depths of space with that in the inner solar system? IV. Beyond Pluto Although we ve reached the edge of the solar system visible through a telescope, that doesn t mean that the solar system actually ends here - nor does it mean that mankind s exploration of the solar system ends here, either. Down by Boulder Creek to your north, at 58 AU from the Sun, Voyager II is still travelling outwards towards the stars, and still sending back data to Earth. IV.1 Voyager II uses a nuclear power cell instead of solar panels to provide electricity for its instruments. Why do you think this is necessary? In 2000 years, Comet Hale-Bopp will reach its furthest distance from the Sun (aphelion), just north of the city of Boulder at our scale. Comet Hyakutake, the Great Comet of 1996, will require 23,000 years more to reach its aphelion distance - 15 miles to the north near the town of Lyons. Beyond Hyakutake s orbit is a great repository of comets-yet-to-be: the Oort cloud, a collection of a billion or more microscopic (at our scale) dirty snowballs scattered over the space between Wyoming and the Canadian border. Each of these is slowly orbiting our grapefruit-sized model of the Sun, waiting for a passing star to jog it into a million-year plunge into the inner solar system. And there is where our solar system really ends. Beyond that, you ll find nothing but empty space until you encounter Proxima Centauri, a tiny star the size of a cherry, 4,000 km (2,400 miles) from our model Sun! At this scale, Proxima orbits 160 kilometers (100 miles) around two other stars collectively called Alpha Centauri - one the size and brightness as the Sun, the other only half as big (the size of an orange) and one-fourth as bright. The two scale model stars of Alpha Centauri orbit each other at a distance of only 1000 feet (0.3 km). IV.2 Suppose there's an Earth-like planet orbiting the Sun-like star of Alpha Centauri, at the same distance as the Earth is from the Sun. Use your imagination to describe what the nighttime and/or daytime sky might look like to a resident of than planet.

51 APS 1010 Astronomy Lab 51 Seasons THE SEASONS SYNOPSIS This exercise involves making measurements of the Sun every week throughout the semester, and then analysing your results at semester s end. You ll learn first-hand what factors are important in producing the seasonal changes in temperature, and which are not. EQUIPMENT: Gnomon, sunlight meter, heliostat, tape measure, calculator, and a scale. REVIEW: Angles and trigonometry (page 19), using your calculator (page 22). Everybody knows that it s colder in December than in July - but why? Is it because of a change in the number of daylight hours? The height of the Sun above the horizon? The intensity of the sunlight? Or are we simply closer to the Sun in summer than in winter? We can measure each of these factors relatively easily, and will show you how to do so. But seasonal changes occur rather slowly, so we ll need to monitor the Sun over a long period of time before the important factors become apparent. We ll also need to collect a considerable amount of data from all of the lab classes - to gather information at different times of the day, and to make up for missing data on cloudy days. Today you ll learn how to take the solar measurements. Then, every week during the semester, you or your classmates will collect additional observations. At semester s end, you ll return to this exercise to analyze your findings to find out just what factors are responsible for the Earth s heating and cooling. Part I. Start of the Semester: Learning to Make Solar Measurements TIME OF DAY As the Sun moves daily across the sky, the direction of the shadows cast by the Sun move as well. By noting the direction of the shadow cast by a vertical object (called a gnomon), we can determine the time-of-day as defined by the position of the Sun. Such a device, of course, is called a sundial. I.1 Note the time shown by the sundial on the deck of the Observatory. Officially, this is known as local apparent solar time, but we ll just refer to it as sundial time. Determine the time indicated by the shadow to the nearest quarter-hour: Sundial Time =. (Don t be surprised if your watch and the sundial disagree - this is normal and is to be expected due to a number of factors which we won t go into here!) ALTITUDE OF THE SUN When the Sun first appears on the horizon at sunrise, shadows are extremely long; as it rises higher in the sky, the lengths of shadows become shorter. Hence, the length of the shadow cast by a gnomon can also be used to measure the altitude of the Sun (the angle, in degrees, between the Sun and the point on the horizon directly below it). The figure on the next page shows that the shadow cast by a gnomon forms a right-triangle. The Sun s altitude is the angle from the horizontal ground to the top of the gnomon, as seen from the tip of the shadow. The tangent of that angle is the opposite side of the right-triangle (the height of the gnomon, H) divided by the adjacent side of the triangle (the length of the shadow, S).

52 APS 1010 Astronomy Lab 52 Seasons Mathematically, this relationship is: tan(altitude) = H/S. We ve prepared a 1-meter high gnomon (H = 1,000 mm) on a stand to help you make the measurement. I.2 Carry the gnomon and a metric tape-measure to the Observatory deck. Carefully measure the shadow length S from the base of the gnomon to the tip of the shadow: S = mm. I.3 Calculate the tangent value for the solar altitude: tan(altitude) = H S = 1000 mm mm = I.4 Now use the arc-tangent function on your calculator to determine what angle, in degrees, has a tangent equal to the number you obtained in I.3: THE SUNLIGHT METER Solar altitude = The sunlight meter is a device that enables you to deduce the relative intensity of the sunlight striking the flat ground here at the latitude of Boulder, compared to some other place on the Earth s surface where the Sun is, at this moment, directly overhead at the zenith. I.5 On the observing deck, aim the meter by rotating the base and tilting the upper plate until its gnomon (the perpendicular stick) casts no shadow. When properly aligned, the upper surface of the apparatus will directly face the Sun. The opening in the upper plate is a square 10 cm x 10 cm on a side, so that a total area of 100 cm 2 of sunlight passes through it. The beam passing through the opening and striking the horizontal base covers a larger, rectangular area. This is the area on the ground here at Boulder that receives solar energy from 100-square-centimeter s worth of sunlight. I.6 Place a piece of white paper on the horizontal base, and draw an outline of the patch of sunlight that falls onto it. I.7 Measure the width of the rectangular region; is it still 10 cm? Measure the length ( cm), and compute the area of the patch of sunlight (width x length): Area = cm 2. I.8 Now calculate the relative solar intensity - the fraction of sunlight we re receiving here in Boulder compared to how much we would receive if the Sun were directly overhead: Relative Solar Intensity = 100 cm 2 Area THE RELATIVE SIZE OF THE SUN AS SEEN FROM EARTH = Finally, in the lab room your instructor will have an image of the Sun projected onto the wall using the Observatory s heliostat, or solar telescope. As you know, objects appear bigger (we say they subtend a larger angle ) when they are close, and appear smaller at a distance. By measuring the projected size of the Sun using the heliostat throughout the semester, you ll be able to determine whether or not the distance to the Sun is changing - and if so, whether the Earth is getting closer to it, or farther away, and by how much.

53 APS 1010 Astronomy Lab 53 Seasons I.9 Use a meter stick to measure the diameter, to the nearest millimeter, of the solar image that is projected onto the wall. (Note: since the wall isn t perfectly perpendicular to the beam of light, a horizontal measurement will be slightly distorted; so always measure vertically, between the top and bottom of the image). Solar Diameter = mm. PLOTTING YOUR RESULTS You ll use three weekly group charts to record your measurements, which will always be posted on the bulletin board at the front of the lab room: the Solar Altitude Chart, the Solar Intensity Chart, and the Solar Diameter Chart. This first week, your instructor will take a representative average of everyone s measurements and show you how to plot a datum point on each graph. After this week, it will be the responsibility of assigned individuals to measure and plot new data each class period. You yourself will be called upon at least once during the semester to perform these measurements, so it s important for you to understand what you re doing, and to make your measurements and plots as accurately and as neatly as possible! I.10 On the weekly Solar Altitude Chart, carefully plot a symbol showing the altitude (I.4) of the Sun in the vertical direction and the sundial time (I.1) along the horizontal direction, showing when the measurement was made. Use a pencil (to make it easy to correct a mistake) and use the symbol appropriate for your day-of-the-week (M-F) as indicated on the chart. Other classes will have added, or will be adding, their own measurements to the chart as well. I.11 On the weekly Solar Intensity Chart, carefully plot a point that shows the relative solar intensity (I.8) that was measured at the corresponding sundial time (I.1). Again, use the appropriate symbol. I.12 On the weekly Solar Diameter Chart, plot your measurement of the diameter in mm (I.9) vertically for the current date (horizontal axis). (There may be as many as three points plotted in a single day from three different classes.) Part II. During the Semester: Graphing the Behavior of the Sun At the end of each week, the Observatory staff will collect the three weekly charts and construct a best-fit curve through the set of datum points. In addition, the curves will be extrapolated to earlier and later times of the day so that the entire motion of the Sun, from sunrise to sunset, will be represented (adding a few additional early-morning and late-day measurements of our own if necessary). Although the data represent readings over a 5-day period, the curve will represent the best fit for the mid-point of the week, Wednesday. These summaries of everyone s measurements will be available for analysis the following week and throughout the remainder of the semester. Every week take a few moments to analyze the previous week s graphs, and record in the table on the next page: II.1 (a) The date of the mid-point of the week (Wednesday). (b) The greatest altitude above the horizon the Sun reached that week. (c) The number of hours the Sun was above the horizon, to the nearest quarter-hour. (d) The maximum value of the intensity of sunlight received here in Boulder, relative to (on a scale of 0 to 1) the intensity of the Sun if it had been directly overhead. (e) The average measured value of the apparent diameter of the Sun as determined using the heliostat.

54 APS 1010 Astronomy Lab 54 Seasons (a) (b) (c) (d) (e) (f) (g) (h) Week # Date Maximum Solar Altitude (deg) Number of Daylight Hours Maximum Solar Intensity Solar Diam. (mm) Weight of Sunlight (grams) Solar- Const. Hours KWH/ Meter 2 per Day II.2 Also each week, transfer your new data from columns (a) through (e) in the table above to your own personal semester summary graphs on the next two pages: Maximum Solar Altitude, Hours of Daylight, Maximum Solar Intensity, and Solar Diameter. Be sure to include the appropriate date at the bottom of each chart. APS 1010 students using a primitive sundial.

55 APS 1010 Astronomy Lab 55 Seasons Week 90 Maximum Solar Altitude (Semester Summary) Maximum Solar Altitude (degrees) Date: Week Hours of Daylight (Semester Summary) Number of Hours of Daylight Date:

56 APS 1010 Astronomy Lab 56 Seasons Maximum Solar Intensity (relative to sun at zenith) Week Date: Maximum Solar Intensity (Semester Summary) Week 785 Solar Diameter (Semester Summary) Apparent Diameter of the Sun (mm) Date:

57 APS 1010 Astronomy Lab 57 Seasons Part III. End of the Semester: Analyzing Your Results By now, at the end of the semester, your collected data should provide ample evidence to explain the cause of the seasonal change in temperatures. III.1 Draw best-fit curves through your graphed datum points on the previous two pages. The lines should reflect the actual trend of the data, but should smooth out the effects of random errors or bad measurements. Do you expect these downward or upward trends to continue indefinitely, or will they eventually flatten out and then reverse direction? Explain your reasoning. Now, use your graphs to review the trends you've observed: III.2 III.3 III.4 III.5 III.6 III.7 Measured at noontime, did the Sun s altitude become higher or lower in the sky during the course of the semester? On average, how many degrees per week did the Sun's altitude change? Did the number of hours of daylight get greater or less? On average, by how many minutes did daylight increase or decrease each week? What was the maximum altitude of the Sun on the date of the equinox this semester? (Consult the Celestial Calendar at the beginning of this manual for the exact date.) On that date, how many hours of daylight did we have? Did the sunlight meter indicate that we in Boulder received more or less solar intensity at noon as the semester progressed? Did the Sun s apparent size grown bigger or smaller? Does this mean that we are now closer to, or farther from, the Sun as compared to the beginning of the semester? Has the weather, in general, become warmer or colder as the semester progressed? Which factor or factors that you've been plotting (solar altitude, solar intensity, number of daylight hours, distance from the Sun) appear to be correlated with the change in temperature? Which factor or factors seems to be contrary to an explanation of the seasonal change in temperature? If you receive a bill from the power company, you re aware that each kilowatt-hour of electricity you use costs money. One kilowatt-hour (KWH) is the amount of electricity used by a 1000-watt appliance (1 kilowatt) in operation for a full hour. For example, four 100-watt light bulbs left on for 5 hours will consume 2.0 KWH, and will cost you about 15 cents (at a rate of $0.075/KWH). Every day, the Sun delivers energy to the ground, free of charge, and the amount (and value) of that energy can be measured in the same units that power companies use. The amount of energy received by one square meter on the Earth directly facing the Sun is a quantity known as the solar constant, which has a carefully-measured value of 1,388 watts/m 2. That is, a one-square-meter solar panel, if aimed constantly towards the Sun, will collect and convert to electricity KWH of energy every hour (worth slightly more than a dime).

58 APS 1010 Astronomy Lab 58 Seasons Each weekly Solar Intensity Chart contains all the information you need to find out how much energy was delivered by the Sun, in KWH, on a typical day that week. Note that one solarconstant hour is equivalent to the rectangular area on the chart 1.0 intensity units high (the full height of the graph, corresponding to a solar panel that always directly faces the Sun) and one hour wide. The actual number of solar-constant hours delivered in a day to flat ground in Boulder is likewise the total area under the plotted intensity curve, from sunrise to sunset. A simple trick for measuring an irregularly shaped area is to calibrate and weigh the paper itself! Use scissors to cut out a rectangular area corresponding to 10 solar-constant hours, and carefully weigh it on an accurate gram scale. Divide the result by 10 to find out what one solar-constant hour weights : gram. Next, cut out the shape of the area under the curve of a Solar Intensity Chart, and weigh it as well. Divide the latter weight by the former to determine the number of of solar-constant hours. Finally, multiply that number by KWH to obtain the total energy contribution of the Sun to each square meter of ground during the course of a day. III.8 III.9 As a class group exercise, determine the number of KWH delivered on a sunny day to every square meter of ground in Boulder, for each week you ve collected data. Using the table on the previous page, record the weights in column (f), the calculated solar-constant hours in column (g), and finally, the equivalent kilowatt-hours in column (h). From column (h), what is the ratio of the amount of energy received at the end of the semester compared to that at the beginning of the semester? (This ignores any effect due to a change in the distance to the Sun.) (Final Week' s KWH ) (First Week' skwh) = Fractional Change in SolarEnergy A ratio greater than 1 implies than an increase in energy was received over the semester, while a ratio smaller than 1 implies that less solar energy was delivered as the semester progressed. Now let s find out just how important was the change in distance from the Sun: III.10 What is the ratio of the apparent diameter of the Sun between the end and the start of the semester? Diameter ratio = (Final Week' s Diameter) (First Week's Diameter) = The energy delivered to the Earth by the Sun varies inversely as the square of its distance from us. The diameter ratio calculated above is already an inverse relationship (that is, if the diameter appears bigger, the Sun s distance is smaller) - so all we have to do is square that ratio to determine the change in energy from the Sun caused by its changing distance from us. For example, if the ratio is 1.10 (10% closer), the Sun will deliver 21% more energy ( = 1.21). If the ratio is 0.90 (Sun 10% further away), it will deliver = 0.81 = 81% as much energy (or, if you prefer, 19% less energy). III.11 III.12 How much more or less energy (in percent) does the Sun deliver to us now, compared to the start of the semester, solely as a result of its changed distance? If only the distance from the Sun caused the seasonal changes in temperature, would we be warmer or colder in the wintertime? Explain your reasoning. Compare the relative importance of the sunlight intensity-duration effect (III.9) with the solar-distance effect (III.11) in producing seasonal changes in temperature. Which is, by far, the most important? Explain clearly how you arrived at your conclusion.

59 APS 1010 Astronomy Lab 59 Motions of the Sun MOTIONS OF THE SUN SYNOPSIS: The objective of this lab is to become familiar with the apparent motions of the Sun in the Boulder sky. EQUIPMENT: A globe of the Earth, a light box. Part I. Daily Motion of the Sun The daily motion of the Sun is caused by the Earth s rotation rather than the Sun actually moving across the sky. (A subtle point! It took civilization thousands of years to figure this out!) The diagram below show an overhead view of the Earth and Sun: We will now follow a person (the stick figure) as the Earth rotates. At point A our viewer is rotated into view of the Sun, and the Sun appears to rise (i.e. sunrise!) Noon is defined as the time when the viewer is located at point B. This is the point where the Sun will be at its highest point in the sky. At point C our viewer is being rotated out of view of the Sun, and he or she sees sunset. Midnight is defined as point D ; the point opposite Noon. The Sun at points A, B and C as seen on Earth are shown below:

60 APS 1010 Astronomy Lab 60 Motions of the Sun In the next part you will use the globe and light box: I.1 Put the globe at one end of the table. At the other far end position the light box such that it is illuminating the globe; the light box will simulate the Sun. Find Boulder on the globe; and position the globe such that Boulder (latitude 40, longitude 105 ) is facing the light box (at position B, i.e. Noon.) Orient the globe such that the Earth s axis is pointing 90 (in either direction) away from the light box. In a moment you will see that this orientation represents the equinoxes; on these days the Northern and Southern hemispheres each receive 12 hours of sunlight. What fraction of the Earth is illuminated? I.2 At the time Boulder is at Noon: What major cities or small countries are experiencing sunrise and sunset? (pick one for each.) What country is at the same latitude as Boulder but on the other side of the globe? What time is it there? What are the people of Tibet doing right now? Are the Honda Corporation offices in Tokyo likely to be open at this moment? I.3 Rotate the globe such that Boulder is now at sunset. How much of the Earth is illuminated now? What time is it now for the country on the other side of the globe? Part II. The Annual Motion of the Sun The position of the Sun in the sky also changes as the Earth orbits around the Sun. This motion is not to be confused with the daily motion of the Sun described above! The Earth s axis is tilted 23.5 with respect to the perpendicular of its orbital plane (see diagram below). As a consequence different parts of the Earth receive different amounts of sunlight depending on where the Earth is in its orbit. Note: the orbit is circular, but it is shown here in projection: Due to the Earth s tilt the northern hemisphere receives more light during the summer months; and less light during the winter. The Sun also rises higher in the sky during the summer; and this direct sunlight is more warming. These two effects cause the summer to be warmer than the winter. The summer is not warmer than the winter because the Earth is closer to the Sun; in fact, the Earth is slightly closer to the Sun during the Northern hemisphere's winter! The Sun s path across the summer and winter sky is shown on the next page. Note that the winter Sun does not rise as high; nor is it up for as long:

61 APS 1010 Astronomy Lab 61 Motions of the Sun If you were to measure the position of the Sun every day at Noon over the span of a year, you would notice that it slowly moves up and down with the seasons. For example, on June 21st the Sun at Noon is at its highest, northernmost position, while on December 22nd the Sun is at its lowest, southernmost position. These days are called the summer and winter solstices respectively. Solstice literally means Sun stop ; on those two days the Sun appears to stop moving and change directions (e.g. on the Summer solstice the Sun stops moving to the North and starts to descend to the South.) The illustration above shows the Earth at the summer solstice. Position your globe such that Boulder is at Noon and it is the Summer solstice. From the globe and the illustration above answer the following questions: II.1 II.2 II.3 What direction do the stars rotate around Polaris, the North Star, as seen from the Northern hemisphere. Do they go around clockwise or counter-clockwise? Go to the country at the same latitude as Boulder but on the other side of the globe. What country is this? What season is this part of the world in? Now go back to Boulder. Follow the 105 meridian south to a latitude of 40 south. What is there? You should find Easter Island just to the north. (Did you notice South America is much farther east than the U.S.?) What season is this part of the world in?

62 APS 1010 Astronomy Lab 62 Motions of the Sun II.4 II.5 II.6 Finally, find the antipode to Boulder - the point directly opposite on the globe, through the center of the Earth. (Hint: It is not China!) The Tropic of Cancer marks the northernmost points where the Sun can be seen at the zenith (i.e. directly overhead) respectively. On the summer solstice anyone standing on the Tropic of Cancer will see the Sun overhead at Noon. Is there anywhere in the United States where you could see the Sun at the zenith? The Arctic Circle marks the northern region of the Earth where the Sun is sometimes, always (or never!) visible. Find the town of Barrow, Alaska. On the summer solstice at what times will the Sun rise and set here? Part. III The Southern Hemisphere Without changing the orientation of the globe study what is happening down under in Australia. III.1 III.2 III.3 III.4 On the Northern hemisphere's Summer solstice is the Sun to the North or South? What season is Australia experiencing? Would this be a good time to ski the Snowy Mtns. in New South Wales? The Tropic of Capricorn marks the southernmost point at which the Sun can be seen at zenith. Look at the town of Alice Springs in the center of Australia. Is the sun ever directly overhead in Alice Springs? If so, when? (Refer to the dot marking the town.) The Antarctic Circle is the southern equivalent of the Arctic Circle. On our summer solstice what time does the Sun rise at the South Pole? In Australia, do the stars rise in the east and set in the west? Which way do the stars revolve around the south celestial pole? Medieval Noon mark from Bedos de Celles, La Gnomonique pratique (Paris, 1790), a book on the use of sundials. If you look carefully at the shadows you may notice that the artist has made a mistake.

63 APS 1010 Astronomy Lab 63 Motions of the Moon MOTIONS OF THE MOON SYNOPSIS: The objective of this lab is to become familiar with the motion of the Moon and its relation to the motions of the Sun and Earth. EQUIPMENT: A globe of the Earth, light box, styrofoam ball, pinhole camera tube. Part I. The Moon s Orbit In the previous lab you learned how the time of day and the position of the Sun are related to the Earth s daily rotation. Now we will add the Moon and its orbit around the Earth. The diagram below shows the overhead view of the Earth and Sun from before, but now the Moon has been added: The A, B, C and D positions on the Earth are the same as before. The Moon orbits the Earth counter-clockwise (in the same direction the Earth rotates). Note that half of the Moon is always illuminated (just like the Earth); even though it may not appear to be! First let s follow the Moon s progression from new to full (from position #1 to #3). As the Moon starts its orbit (at position #1) it is between the Earth and the Sun. This is a new Moon. The half of the Moon illuminated by sunlight is facing away from us, and we would only see the dark side; however, since the Moon appears close to the Sun in the sky at this time, we cannot see it because the Sun is so bright. As the Moon moves in its orbit, it moves away from the Sun, and we start to see the illuminated half of the Moon in the form of a crescent. At this time the Moon is called a

64 APS 1010 Astronomy Lab 64 Motions of the Moon waxing crescent because each night the crescent appears to grow ( waxing means to grow ). When the Moon reaches position #2 in its orbit half of it will be illuminated - this is 1st Quartercalled as such because the Moon has completed the first quarter of its orbit (a bit confusing since half, not a quarter, of the Moon is illuminated!) As the Moon starts to move behind the Earth (relative to the Sun; look at its orbit above) we see more and more of the illuminated half of the Moon. This is the waxing gibbous (the growing fat Moon!) phase. Finally the Moon moves behind the Earth and we see the entire illuminated face - this is full Moon (position #3). As you can see from the progression above the Moon spends half of its orbit growing from the nonilluminated side to the fully illuminated side. As you will see in the next progression it spends the second half of its orbit doing just the opposite: After reaching full Moon at position #3 the Moon starts to move back in front of the Earth, and the illuminated half begins to disappear. This is the waning gibbous phase. Note that right side of the Moon is dark now; while before it was the left side that was dark. At position #4 only the left half of the Moon is illuminated. The Moon continues on to complete its orbit, going through the waning crescent phase, and then back to the new Moon. You will now experience firsthand the phases of the Moon using the light-box and a ball. I.1 Imagine that your head is the Earth; and that you live on the end of your nose. Position the light-box such that your head is illuminated the same way as the Earth was in the Motions of the Sun lab. Slowly turn your head around counter-clockwise to simulate the daily cycle: sunrise, noon, sunset, midnight and back to sunrise This should give you a feel of what direction in space you re looking during the different times of the day. I.2 Now hold the foam ball in your hand, with your arm extended and the ball at the height of your head. This will simulate the Moon. Position the Moon (foam ball) such that it appears next to the Sun (the light box); this is the new Moon. You should only see the dark side of the Moon. Is it easy to see the Moon next to the bright light? What time of day is it on your nose? I.3 While holding the Moon at arm s length move your arm counter-clockwise (i.e. to your left). Keep your eyes on the Moon the entire time. Watch the phase of the Moon change as you move; can you see the illuminated half of the Moon come into view? Stop turning when you can see exactly half of the Moon illuminated (i.e. 1st quarter). Which side of the Moon is being illuminated? What is the angle between the foam ball, your head, and the light-box? Does this agree with the diagram on the first page? What time is it for you on Earth? I.4 Continue to turn slowly to your left until the Moon is almost right behind you. You should see that the Moon is nearly full - you are now looking at the half of the Moon that is illuminated by the Sun. What time of day is it? If you move the Moon a little more you ll probably move it behind the shadow of your head. This is lunar eclipse - when the shadow of the Earth covers the Moon.

65 APS 1010 Astronomy Lab 65 Motions of the Moon I.5 Again continue to turn to your left, holding the Moon at arm s length. Which side of the Moon is now illuminated? Move until the Moon is half illuminated (3rd quarter). What time is it now? Continue to slowly move the Moon back to new. Part II. Moonrise and Moonset As you observed in the last exercise, there is a relationship between the position of the Moon in its orbit and the time of day on Earth when you see it. When (i.e. what time of day) you can see the Moon depends on where it is in its orbit; and as you just saw the position of the Moon in its orbit also determines the Moon s phase. Now use the globe of the Earth and the light-box as before in the Motions of the Sun lab; but now include the foam ball to simulate the Moon. Position the globe such that it is the summer solstice. Hold the ball and move it around the Earth to simulate the lunar orbit. II.1 II.2 II.3 II.4 II.5 II.6 II.7 Position the globe such that Boulder is at noon and the Moon is at position #1 in its orbit. What phase is the Moon? At what time did the Moon rise; and when will it set? (Hint: You can rotate the Earth to see where Boulder will be when the Moon is on the horizon.) Position Boulder back at noon but now move the Moon to position #2. What is the Moon s phase now? Where in the sky will the Moon appear to be from Boulder? Where in the sky does the Moon appear to be in the country of Kyrgyzstan (remember this place?)? Now put the Moon at position #3. What phase is it? At what time will it rise? (Hint: Think about what position Boulder would have to be at on the Earth to see it on the eastern horizon.) At what time will the Moon set? (This should make sense, as the Moon is on the opposite side of the Earth relative to the Sun.) What phase of the Moon do people in the southern hemisphere see right now? Does the time of moonrise or moonset depend on where your are on the Earth? e.g. does the Moon rise at the same local time for Boulder and Kyrgyzstan? Does the Moon rise earlier or later each night? The Moon completes one lunar orbit in 27.3 days. In this time the moonrise (and moonset) time will have changed by 24 hours - which means it will appear to be right back to where it started. How much earlier or later does the Moon rise each night? The Moon is not the only Solar System object which shows phases - the planets do as well. You ve learned that the Moon shows a crescent phase when it is between the Earth and Sun. Which of the planets can show a crescent phase? Why is this? Even though it is usually regarded as a nighttime object, you can see the Moon during the day! Go outside and check to see if the Moon is visible. If so, hold up the foam ball at arm s length in the direction of the real Moon. The foam ball should have the same phase as the Moon! Explain why this is so.

66 APS 1010 Astronomy Lab 66 Motions of the Moon II.8 What phase is the Moon today? What phase will it be during next week s lab? Part III. The Size of the Sun and Moon Warning! Looking directly at the Sun can damage your eyes! In order to measure the diameter of the Sun we use a pinhole camera - a cardboard tube with a piece of foil at one end with a tiny hole; the other end of the tube is covered in graph paper. Being careful not to look at the Sun directly, aim the tube up to the Sun with the graph paper facing you. You should see an image of the Sun on the graph paper. III.1 Measure the diameter of the Sun s image, counting the marks on the graph paper. Each square on the graph paper is 1 mm across. What is the diameter of the Sun's image? Distance from Sun to Earth Distance from Hole to image The Sun Pinhole Camera Image of The Sun Examining the geometry of the pin-hole camera shown in the figure above, you can see that if the distance to the Sun is known, we can use the similar triangles relationship to solve for the diameter of the Sun. That is, we have the following: Diameter of the Image = Distance of Image from Hole Diameter of Sun Distance of Sun from Earth III.2 Assume that the distance between the Sun and Earth is 150 million kilometers (about 93 million miles). The distance of the image from the hole (i.e. the length of the tube) is 1 meter. Determine the diameter of the Sun and compare this to the true value. The Moon has roughly the same angular size as the Sun. We can use the similar triangles relationship again to determine the size of the Moon: Diameter of the Moon = Distance of Moon to Earth Diameter of Sun Distance of Sun to Earth III.3 If the distance of the Moon to the Earth is about 390 times less than the distance between the Sun and the Earth, how big is the Moon? Check to see if your number makes sense: the Moon's diameter is a little less than the width of the United States.

67 APS 1010 Astronomy Lab 67 Motions of the Moon Part IV. Solar and Lunar Eclipses Nerds watching a Solar eclipse. Since the Sun and Moon have roughly the same angular size, it is possible for the Moon to block out the Sun as seen from Earth, causing a solar eclipse. IV.1 Hold the styrofoam Moon at arm s length and move it through its phases; there is only one phase of the Moon when it is possible for it to block your view of the Sun, causing a solar eclipse. Which phase is this? Now simulate this arrangement with the styrofoam Moon, the Earth globe, and the lightbox. Does the Moon eclipse the entire Earth, or does only a portion of the Earth lie in the Moon s shadow? Does this mean that all people on the sunlit side of the Earth can see a solar eclipse when it happens, or only some people in certain locations? The Moon's orbit is not quite circular. The Earth-Moon distance varies between 56 and 64 Earth radii. If a solar eclipse occurs when the Moon is at the point in its orbit where the distance from Earth is just right, then the Moon's apparent size exactly matches the Sun s. This produces a very brief total eclipse - perhaps lasting only a few seconds. IV.2 If the Moon were at its closest point to the Earth during a solar eclipse, would it appear bigger or smaller than the Sun as seen from Earth? How would this effect the amount of time that the eclipse could be observed? If an eclipse occurred when the Moon was at its farthest distance from the Earth, describe what the eclipse (called an annular eclipse) would look like from the Earth. Balinese Hindus call Rahu, the eclipse demon, Kala Rau. In this scene Kala Rau is losing his head as he is discovered sipping from the elixir of immortality. In anger, he circles the sky in pursuit of the two informers- the Sun and Moon. When he catches either of them, his severed immortal head swallows them and an eclipse takes place. Then the ingested Sun or Moon drops out of Kala Rau s severed throat; and the eclipse is over.

68 APS 1010 Astronomy Lab 68 Motions of the Moon It s also possible for the shadow of the Earth to block the sunlight reaching the Moon, causing a lunar eclipse. IV.3 Once again, move the Moon through its phases around your head and find the one phase where the shadow of the Earth (your head) can fall on the Moon, causing a lunar eclipse. What phase is this? During a lunar eclipse, is it visible to everyone on the (uncloudy) nighttime side of the Earth, or can only a portion of the people see it? (Hint - could anyone standing on your face see the Moon in shadow?) Many people think that a lunar eclipse should occur every time that the Moon is full. This misconception is due to the fact that we usually show the Moon far closer to the Earth than it actually is, making it appear that an eclipse is unavoidable. But as mentioned above, the Moon s actual distance is roughly 30 Earth-diameters away. IV.4 Hold the styrofoam Moon at its true (properly-scaled) distance from the globe of the Earth. How big of an area would the shadow of the Earth be at this distance? Demonstrate how the Moon can easily pass over or under this shadow during its orbit, so that an eclipse does not occur. A lunar eclipse over Tashkent, in what is now Uzbek S.S.R., was witnessed on 16 December With noise of cymbals, tambourines and drums they attempted to drive away whatever it was that was attacking the Moon.

69 APS 1010 Astronomy Lab 69 Gravity GRAVITY AND THE MASS OF THE EARTH To see the world in a grain of sand, And a heaven in a wild flower; Hold infinity in the palm of your hand, And eternity in an hour. -W. Blake SYNOPSIS: By measuring the time taken for an object to fall through a distance, you will determine the acceleration due to Earth's gravity, and will use that information to calculate the mass of the Earth. Using this information, you will compare the Earth s gravity with that on the Moon and on Jupiter. EQUIPMENT: Falling body apparatus, tape measure, calculator. Introduction Acceleration is the change in speed (also called velocity) that a moving body experiences in a given time interval. For example, suppose that an object starts at rest and accelerates at a rate of 10 meters per second per second (written m/sec 2 ). After the first second, it will be traveling at a speed of 10 m/sec. After the next second, its speed will be 10 m/sec plus 10 m/sec, or 20 m/sec, etc. So, for constant acceleration of an object starting at rest, speed = (acceleration) (time). (1) Because an accelerating object s speed is constantly increasing, the distance it covers each second is accordingly greater. For an object starting at rest and undergoing constant acceleration, distance = 1 2 (acceleration) (time) 2. (2) Thus, an object accelerating at 10 m/sec 2 will travel a distance of 5 meters in the first second of time; two seconds after starting, the distance covered is 20 meters, implying that the object travelled 15 meters during the second second. Every particle in the universe exerts a gravitational force on every other particle. A force gives rise to an acceleration. The combined effects of all of the particles in the Earth acting upon us produces an acceleration which we constantly experience; we refer to this acceleration simply as gravity, and we call the force on our bodies weight.. If we drop an object and time how long it takes to fall a certain distance, we can use equation (2) to measure the acceleration due to gravity: acceleration = 2 (distance) (time) 2 (3)

70 APS 1010 Astronomy Lab 70 Gravity Part I. Measuring the Acceleration due to Gravity The falling-body apparatus uses a spring-loaded clamp to hold a steel ball above a landing pad. When we release the clamp, the ball drops and the timer starts. The timer stops when the ball strikes the landing pad, and the elapsed time in seconds appears on the readout. Positioning Clamp Green Pull Knob Dropping Mechanism Timer Red Clamping Knob Ball Table Landing Pad Floor Work in a team of three individuals with one dropping apparatus. Measure the acceleration due to gravity using the small steel ball as described below. After one individual has completed his/her measurements, the other team members should independently conduct their own trial measurements (step I.2). I.1 Position the dropping mechanism over the edge of the table, and the landing pad (inside the catch basin) on the floor directly underneath it. Switch the timer on. I.2 While holding the small steel ball in the clamp of the dropping mechanism, pull on the green knob (against the spring tension) so that the ball is captured. Tighten the red clamping knob to hold the ball in place. Measure the drop-distance to the nearest millimeter: Use a metric tape measure to determine the distance from the bottom of the ball to the top of the landing pad (another team member may assist by holding one end of the tape, but you must actually read the distance). Record your distance measurement in meters (1 mm = meter). Press the reset button on the timer to initialize the display. Release the ball by loosening the red knob. Record the elapsed time in seconds as indicated by the timer. I.3 Write down each individual's name and his/her values for distance and time in Table 1. For each individual trial, calculate the gravitational acceleration experienced by the small ball using equation (3), and record the results in the table.

71 APS 1010 Astronomy Lab 71 Gravity Table 1: Small Ball Long Distance Experimenter Names Distance (meters) Time (seconds) Acceleration (m/sec 2 ) Average Presumably, each of you obtained similar, but not necessarily identical, values for the drop distance, the elapsed time, and the calculated acceleration for each experimental trial. If the measurements were not identical, it does not mean that the distance, time, or acceleration actually changed between trials, nor does it necessarily imply that one or more of you made a mistake. The results simply point out that there is no such thing as a perfect measuring instrument or procedure, and therefore there is no such thing as a perfect measurement! Since every measurement (distance, time) contains an experimental error (meaning an uncertainty, not necessarily a mistake), then any information derived from those measurements (acceleration) also contains an uncertainty. We can never know exactly what the "true" value is; we can only try to get better and better results by improving our measuring equipment or technique, and by averaging the results of our measurements to statistically reduce any random errors that may have occurred. Note: You cannot claim to know the value of the acceleration to any greater accuracy than the measurement error. It is senseless and misleading to list its value to place-values smaller than the uncertainty. For example, if your calculator comes up with a figure of m/sec 2, while your individual trials ranged from to m/sec 2, you should list your result as 9.35 m/sec 2, with an uncertainty of about ±0.01 m/sec 2. It may not look as impressive, but it's honest! I.4 Suggest at least one way in which the measuring equipment or your measurement technique might be improved to produce a smaller experimental error. I.5 Calculate an improved measurement for the gravitational acceleration by averaging all three of your team's individual values, and enter the results in Table 1. Aristotle claimed that heavier objects fall faster than ligher objects (that is, heavy objects experienced a greater gravitational acceleration). Nearly two thousand years later, Galileo was the first to dispute this belief, claiming that all objects fall at the same rate (and asserted that air friction was responsible for the seemingly slow drop of light objects). According to lore, Galileo put his hypothesis to the test by dropping balls of different weights off the leaning tower of Pisa. I.6 Test Galileo's hypothesis. Repeat procedure I.2 using the large steel ball instead of the small one. Once again, each member should make an independent distance measurement (slightly different from the previous, since the size of the ball has changed), time measurement, and calculation of the acceleration. Record all of your teammates results in Table 2, and find the average acceleration.

72 APS 1010 Astronomy Lab 72 Gravity Table 2: Large Ball Long Distance Experimenter Names Distance (meters) Time (seconds) Acceleration (m/sec 2 ) Average I.7 Within your uncertainty of the measurements, does your experimental data support Galileo's contention that the acceleration due to gravity is the same for all objects? Explain. Since both balls fell nearly equal distances, your measurements haven t tested whether gravitational acceleration was a constant value throughout the drop, but merely that it was the same for both objects (it could have changed identically for both balls during the time that they fell). I.8 Determine whether the acceleration due to gravity is a constant that is independent of the drop-distance or duration of the time-of-flight: Reposition the dropping apparatus and landing pad to perform a shorter drop to the tabletop as shown in the diagram. Using the large ball, perform independent measurements as before, and record and average your team's results in Table 3. Table 3: Large Ball Short Distance Experimenter Names Distance (meters) Time (seconds) Acceleration (m/sec 2 ) Average I.9 Within your uncertainty of the measurements, do your results support the contention that all objects experience the same, constant acceleration due to Earth's gravitational attraction? Why or why not? I.10 Average all nine of your separate measurements together (or equivalently, average the three averages) to come up with a final, best estimate of its value.

73 APS 1010 Astronomy Lab 73 Gravity Part II. The Mass of Earth Isaac Newton showed that the acceleration g experienced by an object due to the gravitational attraction of a second body is directly proportional to the mass m of the attracting body, and inversely proportional to the square of the distance r between the bodies (one form of Newton's universal law of gravitation): g = G m r 2. (4) Here G is the constant of proportionality, called the gravitational constant. (The value of G was determined very carefully by measuring the gravitational force between two large blocks of metal hung very close together from wires.) Essentially, G converts the mass and the distance to an amount of gravitational acceleration. In meters-kilograms-second (mks) units, G = x m 3 kg sec 2 (5) Important: When equation (4) is used with the above value for G, the mass m must be in kilograms and r in meters; otherwise, any numerical values you obtain will have nonsense units. Identical Gravitational Acceleration Earth Mass = M E One Earth Mass M E One Earth Radius R E Using calculus (which he invented to enable him to solve his mathematical problems), Newton also showed that the mass of a spherically-symmetric object, such as the Earth, gravitationally attracts other objects as if all of its mass were concentrated at its center. Thus, the acceleration produced by Earth's gravity is the same as that produced by a tiny object having the same mass as the Earth (M E ), and which is located at the center of the Earth a distance of one Earth radius (R E ) away. The Earth's radius is R E = 6,400 km = 6.4 x 10 6 meters. Since you have already measured the acceleration due to gravity, g, we can re-write equation (4) to solve for the mass of the Earth: M E = g R2 E G. (6) II.1 II.2 II.3 Calculate the mass of the Earth using equation (6) and your team's average value for the acceleration of gravity. Compare your result with the accepted value for the mass of the Earth: M E = x kg. Is your result accurate to 50%? 10%? 1%? Is your result too large or too small? If you were to repeat this experiment on a mountaintop, would the acceleration due to Earth's gravity be less than, equal to, or greater than that which you have measured? Explain (hint: which parameters would be different in equation 4)?

74 APS 1010 Astronomy Lab 74 Gravity II.4 Can you think of any reason(s) why your measurement made in Boulder might have given results that were higher or lower than the "official value"? Part III. Gravity on Other Planets Newton's law of gravity (Equation 4) applies to everything and everywhere in the universe, not just on the Earth (that s why they call it the universal law of gravitation!). III.1 III.2 Calculate the gravity (ie. acceleration) felt by the Apollo astronauts as they walked on the Moon. To do this you'll need the mass of the Moon, 7.35 x kg, and its radius, 1738 km. Compare this acceleration to that here on Earth (don t forget to convert from kilometers to meters!). Does this explain why the astronauts "bounced" as they walked? Now, find the surface gravity for Jupiter. Jupiter's mass is 1.9 x kg, and its radius is 71,398 km. Aside from being squashed into a pancake in mere seconds, what other difficulties would we face if we tried to stand on Jupiter's surface? Part IV. Escape Velocity When vehicles are launched into space, the rocket must have a minimum speed at launch to escape the Earth's gravity. We call this velocity the escape velocity (v esc ). If the rocket is moving slower than this velocity, it will fall back to the Earth. From the equations given above, we can calculate the escape velocity from any object, given by the following equation: v esc = 2GM R (7) G is the gravitational constant given in equation (5), and M and R are the mass and radius of the object you are trying to escape. IV.1 IV.2 IV.3 Calculate the velocity needed for a spacecraft to escape from the Earth. (Note that the escape velocity does not depend on the mass of the spacecraft itself!) Now calculate the escape velocity for the Moon. (This should explain why the Apollo astronauts needed only a small vehicle to leave the Moon s surface and return to lunar orbit, while the Saturn-V rocket used to lift everything off of the face of the Earth was so huge!) How fast would your spacecraft have to travel to escape from Jupiter? Individual atoms and molecules of gas in a planet s atmosphere also have to reach these same escape velocities in order to leak off into space; otherwise, they stay trapped close to the planet s surface, just like us. IV.4 Use the concept of escape velocity to explain why the Moon has virtually no atmosphere, Earth has a moderate amount, and Jupiter has so much.

75 APS 1010 Astronomy Lab 75 Kepler's Laws Kepler's Laws SYNOPSIS: Johannes Kepler formulated three laws that described how the planets orbit around the Sun. His work paved the way for Isaac Newton, who derived the underlying physical reasons why the planets behaved as Kepler had described. In this exercise, you'll use computer simulations of orbital motions to experiment with the various aspects of Kepler's three laws of motion. EQUIPMENT: Computer with internet connection to the Solar System Collaboratory. Getting Started Here's how you get your computer up and running: (1) In the Computer Lab, make sure your computer is on the PC side (if on the Macintosh side, simultaneously press the FLOWER and RETURN keys to bring up the PC). (2) Click on the Internet folder (not IE!). (3) Launch Netscape by double-clicking its icon. (4) Do not use "maximized" windows - if you don't see the "desktop" in the background, click on the double-window button at the upper right of the Netscape window. (5) Go to the website (6) Click on "Enter Website - Low Resolution (1024x768)". (7) Click on the Modules option. (8) Click on Kepler's Laws. Note: We intentionally do not give you "cook-book" how-to instructions, but instead allow you to explore around the various available windows to come up with the answers to the questions. But note: use the "applets" on the MAIN window, not the EXTRA window. If you use the EXTRA window, you'll find that the HELP, HINT, and MATH information will be referring to the wrong page. The window placement is designed to facilitate access with one click of the mouse. maximizing or moving windows; otherwise, it will only make your life harder! Avoid

76 APS 1010 Astronomy Lab 76 Kepler's Laws Part I. Kepler's First Law Kepler's First Law states that a planet moves on an ellipse around the Sun. I.1 Where is the Sun with respect to that ellipse? I.2 (a) Could a planet move on a circular orbit? (b) If your answer is "yes", where would the Sun be with respect to that circle? I.3 What is meant by the eccentricity of an ellipse? Give a description (words, not formulae). I.4 What happens to the ellipse when the eccentricity becomes zero? I.5 What happens to the ellipse when the eccentricity becomes one? I.6 On planet Blob the average global temperature stays exactly constant throughout the planet's year. What can you infer about the eccentricity of Blob's orbit? I.7 On planet Blip the average global temperature varies dramatically over the planet's year. What can you infer about the eccentricity of Blip's orbit? I.8 For an ellipse of eccentricity e = 0.9, calculate the ratio of periapsis to apoapsis (you may want to look up periapsis and apoapsis in the ``hints'' section). Use the tick-marks to read distances directly off the screen (to the nearest half-tick). I.9 What is the ratio of periapsis to apoapsis for e = 0.5? I.10 For e = 0.1?

77 APS 1010 Astronomy Lab 77 Kepler's Laws The following questions pertain to our own Solar System. Remember that the orbits of the different planets are not drawn to scale. We have scaled the diagram to the major axis of each orbit. I.11 Which of the Sun's planets has the largest eccentricity? I.12 What is the ratio of perihelion to aphelion for this planet? I.13 Which planet has the second largest eccentricity? I.14 What is the ratio of perihelion to aphelion for that planet? I.15 If Pluto's perihelion is 30 AU, what is its aphelion? I.16 If Saturn's perihelion is 9.0 AU, what is its aphelion? Part II. Kepler's Second Law Kepler's Second Law states that, for each planet, the area swept out in space by a line connecting that planet to the Sun is equal in equal intervals of time. II.1 For eccentricity e = 0.7 count the number of tick-marks on the speedometer between the speed at periapsis and the speed at apoapsis. II.2 Do the same for e = 0.4. II.3 And again for e = 0.1. II.4 For eccentricity e = 0.7, measure the time the planet spends (a) to the left of the vertical line (minor axis):. (b) to the right of the vertical line:. II.5 Do the same again for eccentricity e = 0.2. (a) to the left:. (b) to the right:. II.6 Where does the planet spend most of its time, near periapsis or near apoapsis?

78 APS 1010 Astronomy Lab 78 Kepler's Laws Part III. Kepler's Third Law Kepler's Third Law states the relationship between the size of a planet's orbit (given by itse semimajor axis), and the time required for that planet to complete one orbit around the Sun (its period). III.1 The period of Halley's comet is 76 years. From the graph, what is its semi-major axis? III.2 By clicking on the UP and DOWN buttons, run through all the possible combinations of integer exponents available (1/1, 1/2,, 1/9; 2/1, 2/2,, 2/9; 3/1, 3/2, 3/9; etc). Which combinations give you a good fit to the data? III.3 III.4 Using decimal exponents, find the exponent of a (the semi-major axis) that produces the best fit to the data for the period p raised to the following powers: (a) p 0.6 (b) p 5.4 (c) p 78 Why do you think Kepler chose to phrase his third law as he did, in view of the fact that there are many pairs of exponents that seem to fit the data equally well? Part IV. "Dial-an-Orbit" Applet Here's where you can "play god": create your own planet, and give it a shove to start it into orbit. IV.1 Start the planet at X = -80, Y = 0. (a) Find the initial velocity (both X- and Y-components) that will result in a circular orbit (use the tick marks to judge whether the orbit is circular): V x = V y =. (b) Using the clock, find the period T of that orbit: T =. IV.2 Now start the planet at X = -60, Y = 0. (a) Find the velocity that will result in an elliptical orbit of semi-major axis = 80 (attention: remember the definition of the semi-major axis!). (b) Use the clock to find the period for that orbit. IV.3 Would you expect the period you measured in question IV.2 to be the same as the period you measured in question IV.1? Why?

79 APS 1010 Astronomy Lab 79 Temperature of the Sun MEASURING THE TEMPERATURE OF THE SUN SYNOPSIS: In this lab you will measure the solar flux, the amount of energy per unit area per unit time that reaches the Earth from the Sun. From this you will calculate the temperature of the surface of the Sun. EQUIPMENT: Insulated cup, water, ink, plastic wrap, thermometer, watch, meter stick, gram scale, graph paper, calculator. Review: units (p. 11), temperature (p. 13), energy & power (p. 13), trig (p.19) Introduction The quantity of energy delivered by sunlight, per unit of area and per unit of time, is called the energy flux F (in units of joules per square meter per second). If we multiply the flux F by the area A onto which the light falls, and also multiply by the duration of time t that the area is exposed to the light, we obtain the total amount of energy that has been delivered by the Sun: Energy delivered by Sun = F. A. t. The temperature increase T resulting from the sunshine depends upon two properties of the absorbing material: its heat capacity C, and its total mass M. The more mass there is to be heated, the less the temperature will rise for a given amount of energy. The heat capacity states how much energy is needed to raise the temperature of a kilogram of the material by one degree; for example, the heat capacity of water is C water = 4,186 joules kg. o C, meaning that it takes 4,186 joules of energy to raise the temperature of one kilogram of water by one degree Celsius. The amount of energy needed to produce a temperature increase of T in a material of mass M and heat capacity C is then Energy absorbed from the Sun = C. M. T. If all of the energy delivered by sunlight is completely absorbed, the two quantities above are equal: Energy delivered by Sun = Energy absorbed from Sun F. A. t = C. M. T The change in temperature of the material T is then: T = F A t C M Note that the increase in temperature is directly proportional to the rate F at which energy arrives, the size of the energy-absorbing area A, and the duration of exposure t to the energy; the

80 APS 1010 Astronomy Lab 80 Temperature of the Sun temperature increase is inversely proportional to C, the ability of the material to store energy internally, and to the amount of material M that must be heated. Of course, we don't need to calculate how the temperature of an object exposed to sunlight will increase; all we need is a thermometer. But we can rearrange the equation to find out how to measure the really difficult quantity: F, the energy per unit area per unit time arriving from the Sun: F = C M A T t. (1) Part I. Gathering Data In this experiment, you will place a container of water out in the sunshine, and use a thermometer to measure the increase in the water temperature T that occurs over a time interval t. You already know the heat capacity of the water, C water. A scale will be used to determine the water's mass M, and a meter stick can be used to determine the surface area A of the water. These bits of information can then be combined in equation (1) to yield the solar flux F, the number of joules of energy falling each second onto each square meter of the illuminated surface of the Earth. Prepare your experimental apparatus: I.1 Measure the inside diameter D of the top of the insulated cup in meters, and calculate its surface area A cup in square meters: A cup = π D2 4. (2) The water you use should start out a few degrees cooler than the outside (ambient) air temperature, since the temperature increase will be the most accurate when the air and water temperatures are approximately the same. I.2 Measure the outside air temperature with your thermometer and measure the temperature of the water. If the water is too warm, chill it with ice cubes or use water pre-chilled by your teaching assistant. I.3 Weigh the insulated empty container and write down its mass (in kilograms). Fill the cup roughly three-fourths full with water, and add about three drops of ink to the water to help it absorb energy more efficiently. I.4 Weigh the container again, and calculate the mass of the water M water in kilograms. Cover the top of the container with plastic wrap to help reduce heat losses from evaporation, and poke the thermometer through the top. Carry the works outside to a sunny, level area protected from wind. You are now ready to monitor how the incident solar energy affects the temperature of the water.

81 APS 1010 Astronomy Lab 81 Temperature of the Sun Watch Zenith Angle θ Solar Energy Flux F θ tan ( ) = S/L θ L Thermometer Effective Area A Meter Stick Mass M Cup Area Shadow I.5 As the sunlight warms the water, keep a running record of the temperature T of the water versus elapsed time t. Make a temperature reading once every minute. Between readings, it is good practice to gently stir the water with the tip of the thermometer to keep the temperature uniform. Continue to take measurements until the water is a few degrees warmer than the ambient temperature; you will need about one-half hour of continuously clear skies. I.6 You will also need to know the zenith angle θ of the Sun (how many degrees it is from directly overhead). The angle can be determined by measuring the shadow cast by the meter stick L: hold the meter stick vertically and mark where the tip of its shadow falls on the ground; then use the stick itself to measure the length S of its shadow. The tangent of the zenith angle will be S tan(θ) = S L. (3a) Note: If you ve already measured the solar altitude for the Season s lab, the zenith angle is simply: Zenith Angle θ = 90 - (solar altitude) (3b) You're through gathering data. Carry everything back inside. Part II. Calculating the Solar Energy Flux If the Sun had been directly overhead (which is not possible from Boulder's latitude), the energyabsorbing area of the water would equal the area of the cup A cup. However, the oblique angle of the sunlight reduced the effective area A by an amount equal to the cosine of the solar zenith angle: A = A cup. cos(θ) (4) II.1 Calculate the zenith angle θ from equation (3a) or (3b), and calculate the effective surface area A using equation (4).

82 APS 1010 Astronomy Lab 82 Temperature of the Sun II.2 On the graph paper at the back of this exercise, graph your temperature measurements in degrees Celsius against the elapsed time in seconds, as shown below. (Don t forget to convert minutes into seconds!) x x x x x x x Temperature (degrees C) T x x x x Ambient Temperature x x x x t Time (Seconds) During the period when the water temperature was close to the ambient temperature, the graph should approximate a straight line, indicating a uniform rate of temperature increase. II.3 II.4 Draw a best-fit straight line through this portion of the graph. Determine the slope of this line: find the change in temperature T that occurs over the time interval t. Use your experimentally-determined values for the quantities on the right-hand side of equation (1) to calculate the solar flux F. If you have properly kept track of the units in each of your parameters, the solar flux will have units of joules per square meter per second (joules/(m 2. s)). The watt is a unit of power, or energy per unit of time. One watt is equal to 1 joule per second, so that your measurement of the solar flux in "joules/(m 2. s)" can also be written as "watts/m 2". The meaning of your measurement of the solar flux is then easier to visualize: it is the power in watts delivered by the Sun to each square meter of the Earth's surface. The solar constant E is the name given to the solar energy flux arriving just outside the Earth's atmosphere. A portion of that energy is absorbed by the atmosphere (after all, the air is heated by sunlight just like the water in the cup!), so your measurement of F will be somewhat smaller than the value of E. The amount of energy loss in the atmosphere depends upon the zenith angle θ of the Sun and the amount of water vapor in the atmosphere.

83 APS 1010 Astronomy Lab 83 Temperature of the Sun II.5 Use the chart below to estimate what fraction of the incident solar radiation actually reached the Earth's surface during your experimental measurements. Estimate whether the sky was extremely clear, average, or hazy; then use the corresponding curve and your measured solar zenith angle to determine the atmospheric transmission X. Clear Atmospheric Transmission X Hazy Average Zenith Angle θ (Degrees) II.6 Calculate the solar constant E by dividing your measurement of the flux F below the atmosphere by the atmospheric transmission X : II.7 E = F X (5) Compare your calculated value for the solar constant with the generally accepted value of 1,388 watts/m 2 (that's equivalent to nearly fourteen 100-watt light bulbs shining onto an area 3 feet by 3 feet!). If your value is significantly different, suggest possible sources of error. Part III. The Temperature at the Surface of the Sun Your calculated value of the solar constant E measured the number of watts striking one square meter of surface at a distance of one astronomical unit (1.5 x m) from the Sun. If you multiply the energy hitting one square meter of the Earth by the total number of square meters on a sphere of radius 1 AU (reminder: the area of a sphere of radius R = 4πR 2 ), you obtain the luminosity, or total power output in watts emitted by the Sun! III.1 Calculate the luminosity of the Sun in watts: Luminosity = E x 4π(1.5 x m) 2. (6) Compare your measurement of the total power output from the Sun with the value given in your textbook.

84 APS 1010 Astronomy Lab 84 Temperature of the Sun Earth r = 1 AU Surface Area of Sun E = Solar Constant = Flux at Earth R Surface Area of Sphere of Radius 1 AU Sun E sun = Flux at Sun Surface Now that you know how much total energy the Sun puts out, you can also determine how much energy E sun is emitted by each square meter of the solar photosphere! Since the radius of the Sun is about 7.0 x 10 8 m, we divide the total energy output by its surface area: E sun = Luminosity 4π(7.0 x 10 8 m) 2. (7) III.2 III.3 Calculate the power per unit area E sun, (watts/m 2 ) leaving the Sun's surface. How many 100-watt lightbulbs would be required to equal the energy output from each square meter of the solar photosphere? The Sun radiates energy according to the Stefan-Boltzmann law: the power radiated per unit area (E sun ) is proportional to the fourth power of its absolute temperature T measured in degrees Kelvin: E sun = σ T 4 where σ (called the Stefan-Boltzmann constant) is known from experiment to be 5.69 x 10-8 watts/(m 2 K 4). III.4 Calculate the temperature of the Sun's photosphere in degrees Kelvin: T = (E sun /σ) 1/4 (8) Does your answer make sense? Compare your measured value with the accepted average solar photosphere temperature of 5800 K.

85 APS 1010 Astronomy Lab 85 Temperature of the Sun Solar Heating of a Cup of Water: Temperature versus Time Elapsed Time (seconds) Temperature (degrees C)

86 APS 1010 Astronomy Lab 86 Temperature of the Sun Solar Heating of a Cup of Water: Temperature versus Time Elapsed Time (seconds) Temperature (degrees C)

87 APS 1010 Astronomy Lab 87 Spectroscopy SPECTROSCOPY I ask you to look both ways. For the road to a knowledge of the starts leads through the atom; and important knowledge of the atom has been reached through the stars. - A.S. Eddington SYNOPSIS: In this lab you will explore different types of emission spectra and use a spectroscope to identify an unknown element. You will also observe and analyze the spectrum of the Sun using the observatory's heliostat to study the Sun's composition. EQUIPMENT: Hand-held spectroscope; spectrum tube power supply and stand; helium, neon, nitrogen, air, and "unknown" spectrum tubes; incandescent lamp; and the heliostat. WARNING: There is high voltage on the spectrum tube. You can get a nasty shock if you touch the ends of the tube while it is on. Also, the tubes get hot and you can burn your fingers trying to change tubes. Let the tubes cool or use paper towels to handle them. Most of what astronomers know about stars, galaxies, nebulae, and planetary atmospheres comes from spectroscopy, the study of the colors of light emitted by such objects. Spectroscopy is used to identify compositions, temperatures, velocities, pressures, and magnetic fields. An atom consists of a nucleus and electrons which orbit around the nucleus. An atom emits energy when an electron jumps from a high-energy orbit around the nucleus to a smaller lowenergy orbit. The energy appears as a photon of light having an energy exactly equal to the difference in the energies of the two electron levels. A photon is a wave of electromagnetic radiation whose wavelength (distance from one wave crest to the next) is inversely proportional to its energy: high-energy photons have short wavelengths, low-energy photons have long wavelengths. Since each element has a different electron structure, and therefore different electron orbits, each element emits a unique set of spectral lines. Electron Small Electron Transition Low Energy, Long Wavelength Photon (Red) Nucleus Allowed Electron Orbits Medium Electron Transition Large Electron Transition Medium Energy, Medium Wavelength Photon (Green) High Energy, Short Wavelength Photon (Violet) The light produced when electrons jump from a high-energy orbit to a smaller low-energy orbit is known as an emission line. An absorption line is produced by the opposite phenomenon: a passing photon of light is absorbed by an atom and provides the energy for an electron to jump from a low-energy orbit to a high-energy orbit. The energy of the photon must be exactly equal to the difference in the energies of the two levels; if the energy is too much (wavelength too short) or too little (wavelength too long), the atom can't absorb it and the photon will pass by the atom unaffected. Thus, the atom can selectively absorb light from a continuum source, but only at the very same wavelengths (energies) as it is capable of emitting light. An absorption spectrum appears as dark lines superimposed against a bright continuum of light, indicating that at certain wavelengths the photons are being absorbed by overlying atoms and do not survive passage through the rarefied gas.

88 APS 1010 Astronomy Lab 88 Spectroscopy The human eye perceives different energies (wavelengths) of visible light as different colors. The highest energy (shortest wavelength) photon detectable by the human eye has a wavelength of about 4000 Angstroms (one Angstrom equals meters) and is perceived as "violet". The lowest energy (longest wavelength) photon the eye can detect has a wavelength of about 7000 Angstroms, and appears as "red". A spectroscope is a device which allows you to view a spectrum. Light enters the spectroscope through a slit and strikes a grating (or prism) which disperses the light into its component colors (wavelengths, energies). Each color forms its own separate image of the opening; a slit is used to produce narrow images, so that adjacent colors do not overlap each other. Spectrum Red Green Violet Hand-Held Spectroscope Grating Eye Source of Light Slit A grating is a sheet of material with thousands of evenly spaced parallel openings. In general, the crests and troughs of the light waves passing through adjacent openings destructively interfere with each other: they cancel each other (crest on trough) so that no wave survives. At a unique angle for each wavelength, however, the waves constructively interfere (crests add to crests, troughs to troughs); at that angle we see a color image formed by that wavelength of light. Longer wavelengths of light are "bent" (diffracted) the most, so a spectrum is formed with violet seen at small angles, and red at large angles. Part I. Continuum and Emission Line Spectra I.1 Install the helium discharge tube in the power supply and turn it on. Describe the apparent color of the glowing helium gas. Now view the gas using the hand-held spectroscope, and note the distinctly separate colors (spectral lines) of light emitted by the helium atom. Make a sketch of the spectrum and label the colors. Compare the apparent overall color of the glowing gas with the collection of actual colors contained in its spectrum. I.2 Turn off the helium tube and replace with the neon gas tube. Judging from the appearance of glowing neon, what wavelengths would you expect to dominate its spectrum? Observe and sketch the spectrum using the spectroscope as before. Judging from the number of visible energy-level transitions (lines) in the neon gas, which element would you conclude has the more complex atomic structure: helium or neon? A number of neon spectral lines are so close together that they are difficult to separate or resolve. This blending of lines becomes even more dramatic in molecules of gas: the constituent atoms interact with each other to increase the number of possible electron states, which allows more energy transitions, which in turn produces wide molecular emission bands of color. I.3 Install the nitrogen gas tube containing diatomic (two-atom) nitrogen (N 2 ) molecules. Observe and sketch the spectrum, and identify the broad emission bands caused by its molecular state.

89 APS 1010 Astronomy Lab 89 Spectroscopy A solid glowing object such as the tungsten filament of an incandescent lamp will not show a characteristic atomic spectrum, since the atoms are not free to act independently of each other. Instead, solid objects produce a continuum spectrum of light regardless of composition; that is, all wavelengths of light are emitted rather than certain specific colors. I.4 Look through the spectroscope at the incandescent lamp provided by your instructor. Confirm that no discrete spectral lines are present. What color in the spectrum looks the brightest? How does this color compare to the overall color of the lamp (i.e. the lamp s color without using the spectroscope)? Fluorescent lamps operate by passing electric current through a gas in the tube, which glows with its characteristic spectrum. A portion of that light is then absorbed by the solid material lining the tube, causing the solid to glow or fluoresce in turn. I.5 Point your spectroscope at the ceiling fluorescent lights, and sketch the fluorescent lamp spectrum. Identify which components of the spectrum originate from the gas, and which from the solid. Part II. Identifying an Unknown Gas II.1 II.2 Select one of the unmarked tubes of gas (it will be either hydrogen, mercury, or krypton). Install your "mystery gas" in the holder and inspect the spectrum. Make a sketch of the spectrum and label the colors. Identify the composition of the gas in the tube by comparing your spectrum to the spectra described in the table below. (The numbers to the left of each color are the wavelengths of the spectral lines given in Angstroms). Hydrogen 6563 Red 4861 Blue-Green 4340 Violet 4101 Deep Violet (dim) Mercury 6073 Orange 5780 Yellow 5461 Green 4916 Blue-Green (dim) 4358 Violet 4047 Violet (dim) Krypton 6458 Red 5871 Yellow-Orange 5570 Green 4502 Violet (dim) 4459 Violet (dim) 4368 Violet (dim) 4320 Violet (dim) 4274 Violet (dim) II.3 Install the tube of gas marked air and inspect the spectrum. Compare it to the spectrum for nitrogen. What does this tell you about the composition of our atmosphere? What molecule(s) do you think are responsible for the spectral lines in air?

90 APS 1010 Astronomy Lab 90 Spectroscopy Part III. The Solar Continuum Now you'll apply what you learned about gases in the laboratory to gases in the Sun. First, let's study the Sun's continuum spectrum. The gas in the interior of the Sun is so dense that the atoms cannot act independently of each other and therefore they radiate a continuum spectrum just like a solid. The solar continuum is a blackbody spectrum. Like all blackbody spectra, the shape of the solar continuum depends only on its temperature. The graphs below show the blackbody spectra seen for any object (not just stars!) with different temperatures. The temperatures for the graph on the left are chosen to show the large variation in radiated energy for minor variations in temperature. The graph on the right uses a logarithmic scale to encompass a larger range, and shows the temperatures for O stars (50,000 K - the hottest known stars), the Sun (5783 K), and a person (310 K). Blackbody for Various Temperatures Blackbody Curves near Solar Temperatures 7000 K 6000 K 5000 K Blackbody Curves for Various for Temperatures Various Objects K 5783 K 310 K F l u x 6 6e14 Relative Intensity 4 4e14 2 2e K 6000 K 5000 K Visible Spectrum Wavelength (Å) Wavelength (Angstroms) e3 4e3 6e3 8e3 1e4 Log Relative Intensity L o g 10 F l u x K (O-Star) 5783 K (Sun) visible spectrum 310 K (Human) 2 100A A 4 1µ Log Wavelength (Å) 5 10µ 6 100µ 7 1 mm Wavelength (log scale) III.1 Why do you suppose we humans have evolved to see light in the wavelength range that we do (4000 to 7000 Angstroms?) If the Sun were hotter, would it be useful for us to see at longer or shorter wavelengths? Why can t we see each other glowing in the dark? An object s temperature can be determined from the wavelength at which the peak energy occurs using Wien's Law: Temperature = 2.90 x 107 (degrees kelvin x Angstroms) Peak Wavelength in Angstroms By measuring the peak energy of the solar continuum, we can determine the temperature of the surface of the Sun. III.2 III.3 III.4 Where in the solar spectrum does the continuum emission appear (with your eye) the brightest? Estimate the wavelength using the Fraunhofer Solar Spectrum Chart below the spectrograph screen. Using a photometer (lightmeter) provided by your instructor, measure where the continuum is the brightest. Estimate the wavelength. How does this compare to your estimation with your eye? Using Wien's law, calculate the temperature of the Sun using your measured estimate for the peak wavelength. How does this compare to the accepted value of 5783 K?

91 APS 1010 Astronomy Lab 91 Spectroscopy Part IV. Solar Absorption Lines In the Sun we see both a continuum spectrum and absorption lines from gases in the tenuous solar atmosphere, which selectively absorb certain photons of light where the energy is just right to excite an atom s electron to a higher energy state. Of course, an atom can t absorb light if the atom isn t there. Thus, we can identify the elements that make up the Sun simply by comparing the absorption lines in the solar spectrum with emission lines from gases here on Earth. Your lab instructor will dim the solar spectrum by narrowing the entrance slit, and switch on comparison lamps containing hydrogen and neon; their emission spectra appear above and below the solar spectrum. If an element is present in the Sun (and if the temperature of the gas is "just right"), its absorption line will appear at the same wavelength as the corresponding emission from the comparison source. IV.1 IV.2 Which comparison spectrum (top or bottom) is due to hydrogen, and which is neon? What is your evidence? Do you see evidence that hydrogen gas is present in the Sun? What about neon? Even though your eye can't see it, the solar spectrum extends beyond the visible red portion of the spectrum to include infrared light, and beyond the violet to include ultraviolet light. The spectrum of ultraviolet light can be made visible by fluorescence (remember the solid material in the overhead tube lights?). IV.3 IV.4 Hold a piece of bleached white paper up to the viewing screen where ultraviolet light should be present in the spectrum. Note that there are many additional absorption lines in the solar spectrum at wavelengths that are not normally visible to us! Use the Solar Spectrum Chart to identify the element responsible for the two extremely broad, dark lines in the ultraviolet. Using the Fraunhofer chart, dentify each of the following lines in the solar spectrum - for each, give its wavelength, color, and include a brief descriptive phrase (dark, broad, narrow, fuzzy, etc.). Line Name and Element Abundance per million Wavelength (angstroms) Color Descriptive Appearance Reason B Oxygen (O 2 ) - molecular none C Hydrogen alpha (H α) 900,000 D Sodium (Na) 2 E Iron (Fe) 40 F Hydrogen beta (H β) 900,000 H Calcium (Ca II) - ionized 2 K Calcium (Ca II) - ionized 2 It seems reasonable to assume that stronger (darker, wider) absorption lines would indicate that there are more atoms of that element present in the Sun - but as shown in the abundance column of the table, we would be misleading ourselves. Although an atom must be present in order to show its signature, that doesn t necessarily mean that the element is abundant - otherwise, we would probably assume (incorrectly) that the Sun is mostly made out of calcium!

92 APS 1010 Astronomy Lab 92 Spectroscopy The analysis of spectral features is an extremely complex task, and there are several important factors to consider. First of all, even if many atoms of an element are present, the temperature may be too cool to excite them, so that they won t emit or absorb (remember, the gas in the discharge tubes was completely invisible until you turned on the power). Or, if the temperature is too hot, the atoms will be ionized (electrons stripped away) so that the electrons responsible for the absorption won t be part of the atom anymore. Or, it could be that a spectral feature that we see didn t really come from the Sun at all, but from the gasses in our own Earth s atmosphere! Through careful analysis, physicists have figured out the temperature ranges necessary for certain elemental species to show themselves through absorption, as indicated below. Probability of Absorption He H Ca II Temperature (kelvin) Na Fe O 2 IV.5 IV.6 IV.7 For each spectral line in the table on the previous page give a reason (A, B, C, or D below) why you think it appears in the solar spectrum. A. Although only a very small fraction of the atoms absorb light at any one time, this atom is very abundant and therefore shows its signature. B. This spectral line is actually several lines that are closely spaced together. The sum of the lines makes it appear to be stronger than it really is. It s not really abundant in the Sun. C. This spectral line is strong because the Sun's temperature is just right for this element to absorb light at this wavelength, even though there aren t that may atoms there. D. The spectral line is actually an absorption band from molecules in Earth's atmosphere rather than in the solar atmosphere. The Sun is too hot for molecules to exist. Although 10% (100,000 atoms out of a million) of the Sun is composed of helium (He), we don t see any helium lines in the visible solar spectrum. Inspect the graph of absorption probabilities, and explain why not. However, during total solar eclipses astronomers do see helium in the solar corona, the extremely tenuous outermost region of the Sun s atmosphere (in fact, the element was named for the Greek word helios, meaning the Sun. What does this imply about the temperature of the gas in the corona? (If the answer surprises you, you re not alone - it also surprised astronomers!)

93 APS 1010 Astronomy Lab 93 Telescope Optics TELESCOPE OPTICS SYNOPSIS: You ll explore some image-formation properties of a lens, and then assemble and observe through several different types of telescope designs. EQUIPMENT: Optics bench rail with 3 holders; optics equipment stand (flashlight, mount O, lenses L1 and L2, image screen I, eyepieces E1 and E2, mirror M, diagonal X); object box. NOTE: Optical components are delicate and are easily scratched or damaged. Please handle the components carefully, and avoid touching any optical surfaces. Part I. The Camera In optical terminology, an object is any source of light: it may be self-luminous (a lamp or a star), or may simply be a source of reflected light (a tree or a planet). Light from an object is refracted (bent) when passed through a lens and comes to a focus to form an image of the original object. Lens Image Object Here s what is happening: From each point on the object, rays are emitted in all directions. The rays that pass through the lens are refracted into a new direction - but in such a manner that they all converge through one single point on the opposite side of the lens. The same is true for rays from every other point on the object, although these rays enter the lens at a different angle, and so are bent in a different direction, and again pass through a (different) unique point. The image is composed of an infinite number of points where all of the rays from the different parts of the object converge. To see what this looks like in real-life, arrange the optical bench as shown below: Object O Lens L1 Image Screen I Flashlight d obj = 20 cm dimage Holder 1 Holder 2 (10 cm) (30 cm) Holder 3 First, turn on the flashlight by rotating its handle, and take a look at its illuminated face. The pattern you see serves as the physical object we ll be using in our study. The black ring around the pattern is exactly one centimeter (10 mm) in diameter.

94 APS 1010 Astronomy Lab 94 Telescope Optics Clamp the flashlight into the large opening of mount O as shown. Now install the mount and flashlight into holder #1 so that the flashlight points down the rail. Then slide holder #1 to the 10 cm mark on the rail, and clamp it in place. Position holder #2 at the 30 cm mark on the rail, and clamp it in place. Install lens L1 in the holder so that one of its glass surfaces faces the flashlight. The separation between the lens and the object is called the object distance d object. In this particular arrangement, since the lens is located at the 30 cm mark on the rail while the object is at 10 cm, the difference between the two settings gives the object distance: 20 cm. Finally, put the image screen I (with white card facing the lens) in holder #3 on the opposite side of the lens from the flashlight. On the white screen, you should see a bright circular blob which is the light from the object that is passing through the lens. Slowly slide the screen holder #3 back and forth along the rail while observing the pattern of light formed on the screen. At some one unique point the beam of light coalesces from a fuzzy blob into a sharp image of the object. Position the screen at this location where the image is in best focus. Not surprisingly, the distance from the lens to the in-focus image is called the image distance, d image. You can determine this distance by taking the difference between the location of the image screen (from the rail markings) and the location of the lens (30 cm). Note that distances are always given in terms of how far things are from the lens. I.1 Determine the image distance from the lens to the nearest tenth of a cm (one mm). I.2 Use a ruler to measure the diameter of the outer black circle of the image (remember, the true size of this circle on the object is 1 cm across). The term magnification refers to how many times larger the image appears compared to the true size of the object: Magnification (definition) = Image Size Object Size I.3 What is the magnification produced by this optical arrangement?. (Equation 1) Magnification can also be calculated from the ratio of image distance to the object distance: Magnification = d image / d object. (Equation 2) I.4 Show that equation 2 gives (at least approximately) the same value for the magnification that you measured using equation 1. I.5 Now reposition the object (flashlight) holder so that it is at the 3 cm mark on the rail; the new object distance is now (30-3) = 27 cm. Refocus the image. What is the new image distance (lens to white screen)? The new magnification? Now let s see what will happen if we use a different lens. Replace lens L1 with the new one marked L2; but leave the positions of of the object (holder #1) and the lens (holder #2) unchanged so that the object distance is still 27 cm. I.6 Refocus the image; what s the new image distance? The new magnification? By now you should be convinced that, for any given lens and distance of an object from it, there will be one (and only one) location behind the lens where an image is formed. By changing either

95 APS 1010 Astronomy Lab 95 Telescope Optics the lens or the distance to the object, or both, the location and magnification of the image will also change. The optical arrangement you ve been playing with is the same as that used in a camera, which consists of a lens with a piece of photographic film behind it which chemically records the pattern of light falling onto it. To achieve proper focus, the lens-to film spacing is adjusted by rotating a ring on the barrel of the lens which moves the lens forwards or backwards towards or away from the film, thus changing the image distance. I.7 Where would you place a piece of photographic film in your arrangement in order to take an in-focus picture of the object? In many cameras it is possible to swap lenses so that the same camera will yield larger images of distant objects (a telephoto lens). I.8 Which of the two lenses you ve used produced a larger image? Which would more likely be considered a telephoto lens in a camera? I.9 What modifications or additions to the apparatus would you have to make to built yourself a practical, functional working camera? Part II. The Lens Equation There is a mathematical relationship between the object and image distances for any given lens, called the lens equation: 1 f = 1 1 d object + d image. (Equation 3) The value f in the formula is called the focal length of the particular lens being used - it is a property of the lens itself, regardless of the location of the object or the image. II.1 II.2 Calculate the focal length f of lens L1, using your measured image distance d image and object distance d object (either from step I.1, or step I.5, or both). What is the focal length of lens L2 (from step I.6)? HELPFUL HINT: When using your calculator with the lens formula, it is simpler to deal with reciprocals of numbers rather than with the numbers themselves. Look for the calculator reciprocal key labelled 1/x. To compute , hit the keys 2 1/x + 4 1/x =. You should get the result 0.75 ( = 3/4 ). Now if 1/f equals this quantity, just hit 1/x again to get f = = II.3 Which lens, L1 or L2, has the longer focal length? Considering what you found in I.8, does a telephoto lens have a longer or shorter focal length than a normal lens?

96 APS 1010 Astronomy Lab 96 Telescope Optics Part III. The Refracting Telescope In astronomy, we look at objects that are extremely far away - for all practical purposes, we can say that the object distance is infinitely large. This means that the value 1/d object in the lens equation is extremely small, and for all practical purposes can be said to equal zero. Thus, for the special case where an object is very far away, the lens equation simplifies to: 1 f = dimage or simply d image = f In other words, when we look at an object very far away, the image that is formed comes to a focus at a distance behind the lens equal to the value of the focal length of the lens Since everything we look at in astronomy is very far away, images through a telescope are always formed at the focal length of the lens. Let s now look at an object that is far enough away to treat it as being at infinity. Remove the flashlight and mount from holder #1. Instead, use the large object box at the other end of the table. It should be at least 3 meters (10 feet) from your optics bench. Focus the screen. Your arrangement should look like the following: Large Object Box Lens L2 Focal Plane I III.1 d d obj 300 cm image f Holder 2 Holder 3 Measure the image distance from the markings on the optics rail. Confirm that this is approximately the same as the focal length of lens L2 that you calculated in II.2. If the screen were not present, the light rays would continue to pass through and beyond the image. In fact, the rays would diverge from the image as if it were a real object, suggesting that the image formed by one lens can be used as the object for a second lens. III.2 III.3 Remove the white card from the screen to expose the central hole. Aim the optics bench so that the image disappears through the opening. Place your eye along the optical axis about 20 cm behind the opening in the screen. You'll be able to see the image once again, "floating in space" in the middle of the opening! Move your head slightly from side-to-side to confirm that the image appears to remain rigidly fixed in space at the center of the hole. (By sliding the screen back and forth along the rail, you can also observe that the opening passes around the image, while the image itself remains stationary as if it were an actual object.) Notice that the image is quite tiny compared to the size of the original object (a situation that is always true when looking at distant objects). In order to see the image more clearly, you ll need a magnifying glass: III.4 Remove screen I from its holder and replace it with the magnifying lens E1. Observe through the magnifier as you slowly slide it back away from the image. At some point, a greatly enlarged image will come into focus. Clamp the lens in place where the image appears sharpest. Your arrangement will be as follows:

97 APS 1010 Astronomy Lab 97 Telescope Optics Light from Object at Infinity Objective Lens Eyepiece Lens Eye f obj f eye L You have assembled a refracting telescope, an apparatus which uses two lenses to observe distant objects. The main telescope lens, called the objective lens, takes light from the object at infinity and produces an image exactly at its focal length f obj behind the lens. Properly focused, the magnifier lens (the eyepiece) does just the opposite: it takes the light from the image and makes it appear to come from infinity. The telescope itself never forms a final image; it requires another optical component (the lens in your eye) to bring the image to a focus on your retina. To make the image appear to be located at infinity (and hence observable without eyestrain), the eyepiece must be positioned behind the image at a distance exactly equal to its focal length, f eye. Therefore, the total separation L between the two lenses must equal the sum of their focal lengths: III.5 L = f obj + f eye. (Equation 4) Measure the separation between the two lenses, and use your value for the objective lens focal length to calculate the focal length of eyepiece E1. Earlier, we used the term "magnification" to refer to the actual size of the image compared to the actual size of the object. This can't be applied to telescopes, since no final image is formed. Instead, we use the concept of angular magnification: the ratio of the angular size of an image appearing in the eyepiece compared to the object's actual angular size. The angular magnification M produced by a telescope can be shown to be equal to the ratio of the focal length of the objective to the focal length of the eyepiece: M = f obj f eye. (Equation 5) III.6 Calculate the magnification using the ratio of the focal lengths of the two lenses. Equation 5 implies that if you used a telescope with a longer focal length objective lens (make f obj bigger), the magnification would be greater. This, however, would require that the eyepiece be located farther from the objective lens, so that the entire telescope would be longer, bulkier, and more costly. But the equation also implies that you can increase the magnification of your telescope simply by using an eyepiece with a shorter focal length (make f eye smaller). III.7 III.8 Eyepiece E2 has a focal length of 1.8 cm. Use equation 5 to calculate the magnification resulting from using eyepiece E2 with objective lens L2. Replace eyepiece E1 with E2, and refocus. Did the image get bigger or smaller than before? Is your observation consistent with your prediction in III.7? A note to the telescope shopper: Some inexpensive telescopes are advertised on the basis of their high power ( large magnification ), because many consumers think that this means a good

98 APS 1010 Astronomy Lab 98 Telescope Optics telescope. You now know that a telescope can exhibit a large magnification simply by switching to an eyepiece with a very short focal length - it has nothing to do with the quality of the most important part of the telescope: the objective lens that gathers the light and forms the initial image. Part IV. The Reflecting Telescope Concave mirrored surfaces can be used in place of lenses to form reflecting telescopes rather than refracting telescopes. All of the image-forming properties of lenses also apply to reflectors, except that the image is formed in front of a mirror rather than behind. As we'll see, this poses some problems! Reflecting telescopes can be organized in a variety of configurations, three of which you will assemble below. The prime focus arrangement is the simplest form of reflector, consisting of the image-forming objective mirror and a flat surface located at the focal plane. A variation on this arrangement is used in a Schmidt camera to achieve wide-field photography of the sky. Light from Object at Infinity Focal Plane Screen X Concave Mirror M f obj IV.1 IV.2 IV.3 Assemble the prime-focus reflector shown above: First, return all components from the optical bench to the stand. Then move holder #2 to the 80 cm position on the optics rail, and install the large mirror M into it. Carefully aim the mirror so that the light from the object is reflected straight back down the bench rail. Place the mirror/screen X into holder #1, with the white screen facing the mirror M. Finally, move the screen along the rail until the image of the object box is focused onto the screen. Is the image right-side-up, or inverted? Measure the focal length of the mirror M (the mirror-to-screen spacing). Since the screen X obstructs light from the object and prevents it from illuminating the center of the mirror, many people are surprised that the image doesn't have a "hole" in its middle. IV.4 Hold the white card partially in front of a portion of the objective mirror in order to block a portion of the beam, as shown on the next page. Demonstrate that each small portion of the mirror forms a complete and identical image of the object at the focus. When you block some of the light, does the image change in brightness?

99 APS 1010 Astronomy Lab 99 Telescope Optics White Card Light from Object Focal Plane light is blocked light reaches mirror Mirror The previous arrangement can't be used for eyepiece viewing, since the image falls inside the telescope tube; if you tried to see the image with an eyepiece your head would also block all of the incoming light. (This wouldn't be the case, of course, if the mirror were extremely large: for example, the 200-inch diameter telescope at Mount Palomar has a cage in which the observer can actually sit inside the telescope at prime focus, as shown here!) Isaac Newton solved the obstruction problem for small telescopes with his Newtonian reflector, which uses a flat mirror oriented diagonally to redirect the light to the side of the telescope, as shown below. The image-forming mirror is called the primary mirror, while the small additional mirror is called the secondary or diagonal mirror. Light from Object at Infinity Diagonal Mirror Focal Plane Eyepiece Primary Mirror IV.5 IV.6 Eye Convert the telescope to a Newtonian arrangement. Reverse the mirror/screen X so that the mirror side faces the primary mirror M and is oriented at a 45 angle to it. Slide the diagonal approximately 5 cm closer towards primary. Hold the image screen I at the focal plane (see diagram) to convince yourself that an image is still being formed. Now remove the image screen and look into the diagonal mirror; if your eye is properly placed and the optics are properly arranged, you can directly observe the image. You ll also be able to see the outline of the primary mirror, and the shadow of the diagonal.

100 APS 1010 Astronomy Lab 100 Telescope Optics IV.7 IV.8 Now try observing the image through the (hand-held) eyepiece E1. When the image is in focus, why do you think that the primary mirror and the diagonal are no longer visible? Calculate the magnification produced by this arrangement. Large reflecting telescopes (including the 16-inch, 18-inch, and 24-inch diameter telescopes at Sommers-Bausch Observatory) are usually of the Cassegrain design, in which the small secondary redirects the light back towards the primary. A central hole in the primary mirror permits the light to pass to the rear of the telescope, where the image is viewed with an eyepiece, camera, or other instrumentation. Light from Object at Infinity Secondary Mirror Eyepiece Eye Primary Mirror IV.9 IV.10 IV.11 IV.12 IV.13 Arrange the telescope in the Cassegrain configuration: Move the secondary mirror X closer to the primary mirror M until the separation is only about 35% of the primary's focal length. Carefully reorient the secondary mirror to reflect light squarely back through the hole in the primary, and visually verify the presence of the image from behind the mirror. Install eyepiece E1 into holder #3, and focus the telescope (be patient - this can be a rather tricky operation). How does the magnification here compare to that in the Newtonian arrangement? How does the overall length of the Cassegrain telescope design compare with that of the Newtonian style? Explain your reasoning. Why doesn't the hole in the primary mirror cause any additional loss in the lightcollecting ability of the telescope?

101 APS 1010 Astronomy Lab 101 Planetary Temperatures PLANETARY TEMPERATURES Mars is essentially in the same orbit. Mars is somewhat the same distance from the Sun, which is very important. We have seen pictures where there are canals, we believe, and water. If there is water, that means there is oxygen. If oxygen, that means we can breathe. -D. Quayle SYNOPSIS: In the next two lab sessions we will explore the factors that contribute to the average temperature of a planet using the EARTH/VENUS/MARS module of the Solar System Collaboratory. EQUIPMENT: Computer with internet connection to the Solar System Collaboratory, photometer with light shade, soil/rock samples, calculator. Part I. Temperature of a Planet The module provides the tools you need to attack one of the grand questions of planetary science. In this case, the grand question of the EARTH/VENUS/MARS module can be phrased in two different but related ways: Why can Earth support abundant life but Venus and Mars cannot? - or - What determines the habitable region around a star? Although both questions are truly grand (meaning that it would probably take a number of major research projects to answer them in detail) they can be broken down into a number of component parts, each one of which is quite accessible. The module concentrates on one of these parts, planetary temperature. Why temperature? Of all the factors that affect the presence of abundant life on a planet (chemistry, radiation, biology, etc.) the presence of liquid water is of paramount importance, and liquid water can only exist in a narrow temperature range. I.1 Why do you think liquid water is thought to be so critical for life? (Of course, nobody really knows for sure.) I.2 Over what approximate range of temperatures do you think you could find liquid water? I.3 Over what approximate range of temperatures would you expect to find life? We will now explore the factors that determine the temperature of a planet, and to find the range of parameters that would result in an average planetary temperature that allows liquid water. In the Computer Lab, make sure your computer is on the PC side. Click on the Internet folder, and launch Netscape (be sure that the window is not maximized). Now go to the website Click on "Enter Website - Low Resolution (1024x768)", click on the Modules option, and finally, select the Earth/Venus/Mars module.

102 APS 1010 Astronomy Lab 102 Planetary Temperatures There are five parts to the module. In this lab we will concentrate on the first one (PLANET TEMPERATURE - click on the words and you should bring up an applet - short for little application ) and use it to explore the way the temperature of a planet depends on 1) its distance from the Sun. 2) its albedo. We will explore the effect of the atmosphere on a planet's temperature in the next lab session. Part II. Distance from the Sun This is the simplest and most obvious way to determine a planet's temperature. Like hikers who build a fire and huddle around it at night, the inner planets huddle around the central fire in the solar system. The closer you get to the fire, the warmer you get. Notice that the model used to calculate the temperature of a planet in this applet is displayed at the bottom of the applet. It should be set on fast-rotating, dark planet. The fast-rotating part of this just ensures that the planet rotates fast enough that day-vs.- night temperatures are not too terribly different. The dark just means that the planet absorbs (rather than reflects) all the sunlight that hits it. The PHYSICS PAGE link provides background information on the physical processes that go into the model. SHOW ME THE MATH provides the mathematical formulation that is programmed into the computer. Select the "Fast rotating dark planet" model from the menu at the bottom of the applet. Let s explore how the distance of a planetary orbit from the Sun affects the planet s temperature. II.1 Move Planet X to the orbit of the Earth (1 AU). What is the temperature of Planet X? II.2 II.3 We know that if we move the planet to a larger orbit, its temperature will go down. But by how much? Make a prediction: what do you think will happen if you double the size of the Earth s orbit? Think about it before you move Planet X! Here are come possibilities: (a) If the temperature follows an inverse law, doubling the radius should cause the temperature to drop by a factor of 2. (b) If the temperature follows an inverse square law, doubling the radius should cause the temperature to go down by a factor of 4. (c) If the temperature follows an inverse square-root law, doubling the radius should cause the temperature to drop by a factor of square root of 2 which is about Your prediction: Now go ahead and move Planet X to 2 AU (twice Earth s orbital distance) - what is the temperature? Which of the above laws does temperature follow? (To check, look at SHOW ME THE MATH.)

103 APS 1010 Astronomy Lab 103 Planetary Temperatures II.4 Do you think the temperature of a planet depends on the size of the planet in this model? Have a look at the PHYSICS PAGE and/or SHOW ME THE MATH, and explain why (or why not). II.5 II.6 How good is this model? Bring up the FACT SHEET from the quick navigation frame (the gray frame on the left). How does the temperature calculated by the model compare to the measured average temperature of Mars? What about Earth? Venus? So - is this model any good? Does it do what it claims to do (calculate the average temperature of a dark body)? How can you tell? HINT: Of all the bodies mentioned in the FACT SHEET, which is best described by the dark planet model? Is the temperature of that body calculated accurately by the model? So, what do you conclude about how well the model works? Part III. Adding Albedo to the Model Albedo (represented by the symbol A) is the fraction of sunlight falling on a surface that is reflected back into space. (The word albedo comes from the Latin word for "white" - albus.) The albedo represents the average reflectivity over the entire visible surface; hence it differs slightly from the reflectivity of different portions of it. For example, the surface of the Moon has an albedo of 0.07 (on average, 7% of the incident sunlight is reflected, 93% is absorbed), even though there are bright and dark regions that have reflectivities different from the average. Now let's consider how the planet's albedo affects its temperature. If you haven't done this already, you may want to get more background information on the physics behind this applet. Click on the PHYSICS PAGE link in the quick navigation frame (the gray strip on the left) and look up albedo. Select the "Fast rotating dark planet with adjustable albedo" model from the menu at the bottom of the applet. III.1 What value of albedo does the previous model ("Fast rotating dark planet") assume? III.2 What is the present day albedo of Mars? (Hint: use the Fact Sheet) III.3 What happens to the temperature of Mars if you increase its present day albedo by 0.05? The temperature goes from to.

104 APS 1010 Astronomy Lab 104 Planetary Temperatures III.4 III.5 What happens to the temperature of Mars if you increase its albedo from to ? The temperature goes from to. In general, if you increase the albedo, you the temperature. Explain why this is the case. III.6 If you put in the correct albedo for Mars, does the model give the correct temperature? How about for the Earth? And for Venus? III.7 So does this model do what it claims to do (calculate the average temperature of a planet with a non-zero albedo)? How can you tell? Part IV. Measuring Albedos of Samples The albedo of a planet or moon provides valuable information about its composition and temperature. You will measure the albedos of various soil and rock specimens; this information will be used to provide clues as to the nature of the surfaces of the planets and moons in our Solar System. A photometer (light meter) with a sunshade can be used to measure the reflectivity of different materials, as shown below. The measurements are made as follows: Measure the brightness of white paper illuminated by sunlight. The paper has a reflectivity of approximately 100%, corresponding to an albedo of 1.00, and thus gives you a convenient standard against which to compare the reflectivity of other surfaces. Be sure that nothing (including you or the photometer) is casting shadows onto the area under observation! Incident Sunlight Detector Light Shade Photometer Meter Measure the brightness of the sample. Be sure to hold the photometer close enough to the sample so that its detector only "sees" the sample, not the surrounding area. Reflected Sunlight Divide your sample reading by the value you obtained for the white paper. The resulting fraction is the reflectivity of the material. Specimen

105 APS 1010 Astronomy Lab 105 Planetary Temperatures IV.1 Measure the reflectivities of the various specimens provided by your lab instructor: rocks (vesicular basalt, dark basalt, marble, limestone, breccia), charcoal, wet and dry sand, crushed ice or snow (if available). Enter your data in the table below. Also note the color of the specimen. These samples have been chosen because they are likely to be found in other objects in the Solar System. IV.2 In addition, measure the reflectivity of some materials commonly found on the Earth's surface which you think might significantly contribute to the Earth's albedo: e.g., water, snow, grass and other plant life, etc. Add these data in the table below as well. Specimen Identification Sample Reading Paper Reference Reflectivity (albedo) Color (A) (B) (A) / (B) Granite Basalt Soil/Loam Charcoal Limestone Sand Marble Sandstone Mars Soil (Simulated)

106 APS 1010 Astronomy Lab 106 Planetary Temperatures Part V. Comparing Solar System Albedos We can measure the albedo of a planet or moon by comparing its brightness to how much sunlight it receives. We know how much sunlight it receives because we know its distance from the Sun (remember the 1/ R 2 rule!); and we can measure how much light is coming from the object with a photometer on a telescope. If the object has an albedo of 100% it will reflect all the sunlight incident upon it. Note: We are assuming that all of the light coming from the object is reflected sunlight; i.e. the object is not producing its own light. Planetary scientists are interested in knowing the albedo of a planet or moon because it provides information on the composition of the object. By comparing the albedo of a planet or moon to the albedos of substances found here on Earth we can learn what substances may or may not be on that object. V.1 What assumption are we making when we compare the albedos of substances on the Earth to other objects in space? The table below contains information regarding the measured albedo of various planets and their moons. Use the table and information in the textbook to answer the following questions. Object Albedo MERCURY 0.06 VENUS 0.76 EARTH 0.40 Moon 0.07 MARS 0.16 JUPITER 0.51 Io 0.60 Europa 0.60 Ganymede 0.40 Callisto 0.20 SATURN 0.50 Mimas 0.70 Iapetus 0.05, 0.50 URANUS 0.66 NEPTUNE 0.62 PLUTO 0.50 V.2 Why do you think the albedos of Mercury and the Moon are so close? Look at photos of these two; do the pictures confirm your hypothesis?

107 APS 1010 Astronomy Lab 107 Planetary Temperatures V.3 What material that you measured is closest to the albedo of Mercury and the Moon? Does it have the same color as well? Do you think the Moon's surface contains this material? V.4 The Moon has a very low albedo, meaning that it is very dark. Why then do you suppose the Moon appear to be so bright? V.5 Compare the albedos of the terrestrial planets: why do Venus and the Earth have much higher albedos than Mercury and Mars? What, if any, of the substances you measured in IV.2 might cause the Earth to have a higher albedo than Mars? Why does Venus have a higher albedo than the Earth? V.6 The albedos of Earth and Mars are averages over the planet's disk as well as averages over time. Average the albedos you measured of substances on the Earth s surface in IV.2 and compare it to the Earth s average albedo. Why might they be different? How does the Earth's reflectivity vary over the surface? And Mars? What is the likely reflectivity of the polar regions? How do their reflectivities change with time? On Earth we see basalt in several forms. When it is first created (i.e. when it comes out of the Earth in the form of lava) it is very dark; however, over time it gets weathered; exposure to oxygen oxidizes basalt and turns it reddish.

108 APS 1010 Astronomy Lab 108 Planetary Temperatures V.7 What planet do you think might have oxidized basalt based upon its color? What can you say about that planet s atmosphere? V.8 The Moon contains basalt in its lunar maria which is very old. Why hasn't it turned red? V.9 Compare the Jovian planets to the terrestrial planets: on average, why do the Jovian planets have a higher albedo? From this and your answer for question V.5 what can you conclude is the most important factor in determining a planet's albedo?

109 APS 1010 Astronomy Lab 109 Galilean Moons ENCOUNTER WITH THE GALILEAN MOONS All these worlds are yours, except Europa. - A.C. Clarke SYNOPSIS: Jupiter's four large moons were first discovered by Galileo in 1610 and looked at in close detail by the Voyager I and II spacecraft in Launched in October 1989, NASA's Galileo spacecraft entered orbit around Jupiter on December 7, Its mission is to conduct detailed studies of the giant planet, focusing on its largest moons and the Jovian magnetic environment. The objective of this lab is for you to have a look at some of the pictures of these distant worlds and to learn what such pictures tell us about their surfaces, interiors and past histories. EQUIPMENT: Galileo photographs of the Galilean moons, a ruler and a calculator. The images come from the Galileo website Please do NOT mark on the photographs! Part I. Properties of the Galilean Satellites Radius (km) Average Density (kg/m 3 ) Albedo (reflectivity) Orbital Distance, a (R jupiter ) Orbital period, P (days) Orbital period (P/P Io ) Moon Io Europa Ganymede Callisto Mercury The table above shows properties of the Galilean satellites as well as the Moon and Mercury for comparison. Figure 1 in the folder shows family portrait of the four Galilean moons. Note that Io and Europa are similar in size to the Moon while Ganymede and Callisto are comparable to Mercury in size. But when we look at other properties, such as density and albedo, the similarities do not hold up. Each of the four Galilean moons are believed to have some iron at their center, surrounded by rock with perhaps a layer of water/ice on top. The density of iron is about 8000 kg/m 3, the density of rock is 2000 to 3000 kg/m 3, the density of water/ice is about 1000 kg/m 3. I.1 Considering just the average densities in the table above, (a) which Galilean moon would you expect to have the most ice (least rock/iron); and (b) which moon could be all rock and iron, with no ice on the surface? I.2 All of the Galilean moons are phase locked with Jupiter. That is to say, one side of each moon always faces towards Jupiter, and one side always faces away. Can you think of another moon in the solar system that is also phase locked with the planet that it orbits? What is its name?

110 APS 1010 Astronomy Lab 110 Galilean Moons Part II. Io: The Jovian Cauldron Io, the Galilean moon closest to Jupiter, is the most volcanically active body in the Solar System. What makes Io's volcanic activity so interesting is the mechanism that causes it. For instance, our Moon's interior cooled and most volcanic activity stopped over 3 billion years ago. Since Io is about the same size as the Moon, its interior must have also cooled. So, why hasn't Io's volcanic activity stopped? The answer lies with Jupiter and the other Jovian moons. Their strong gravitational pull on Io stretches and squeezes the interior of Io, thus melting the interior and causing volcanic activity. The process (known as tidal heating) is the same as the gravitational effect of the Sun and Moon on the Earth, causing the oceans' tides. Figure 2 shows Io photographed by the Galileo spacecraft in front of Jupiter's cloudy atmosphere. The image is centered on the side of Io that always faces away from Jupiter. The color in the image was derived using the near-infrared, green and violet filters of the Galileo camera, and has been enhanced to emphasize variations in color and brightness that characterize Io's volcanopocked face. The near-infrared filter makes Jupiter's atmosphere look blue. The white patches are sulfur dioxide frost. The black and bright red materials correspond to the most recent volcanic deposits, some less than a few years old. II.1 The dark spots are volcanoes. Make a rough count of the number of volcanoes in the image. The active volcano Prometheus is seen near the center of the disk (arrow). To appreciate the size of the volcanoes on Io, we have to determine the scale of the photograph: II.2 II.3 Measure the diameter of Io on photo #2 (measure in millimeters). Io is actually 3,630 km in diameter. Determine the scale factor S, of the image: How many (real) kilometers correspond to 1 millimeter on the photo? S (km / mm) = Diameter of Io in km / Diameter of image in mm Measure the diameter of the volcano Prometheus as seen on photo #2, including the bright ring around it. Use the scale factor above to determine its actual size. What is its actual size in kilometers? Compare this to the sizes of the volcano Mauna Kea in Hawaii (~80 km across, about the size of a metropolitan area) and Olympus Mons on Mars (the largest volcano in the solar system at 700 km across, about the size of Colorado). Look at Photo #3. This image of Io, also taken by Galileo, shows a new blue-colored volcanic plume, named Pillan, extending into space (see the upper inset, the lower inset is of Prometheus.) The blue color of the plume is consistent with the presence of sulfur dioxide gas erupting from the volcano, scattering sunlight (similar to water molecules making the Earth's sky blue). The sulfur dioxide freezes into snow in Io's extremely tenuous atmosphere and makes the white patches on the surface. These eruptions are common on Io and were first discovered when Voyager passed Io in Interestingly, they were not discovered by Voyager scientists, but rather by Linda Morabito, a young member of the Navigation Team. Morabito discovered them when she had difficulties matching the edge of Io's image with a circle, and then enhanced the images to investigate the problem. These volcanic eruptions on Io are far larger than any on Earth. Because Io's atmosphere is exceedingly thin, there is no air resistance and the gas molecules that erupt from a volcano follow paths like shells fired from a cannon. These paths are called ballistic trajectories (after ballista, an engine used in ancient warfare for hurling stones). The maximum height H an object on a ballistic trajectory can reach is given by: H = v2 2 g

111 APS 1010 Astronomy Lab 111 Galilean Moons where v is the initial velocity of material exiting the volcano and g is the acceleration of gravity which is 9.80 m/sec 2 on Earth, but only 1.81 m/sec 2, about a factor of 5 less, on Io. II.4 II.5 II.6 II.7 The scale factor S for the upper inset of photo #3 is about 10 km per millimeter. Measure the height of the blue plume and determine its actual physical height. Convert this height to meters (1 kilometer = 1000 meters). Using your value for the height (in meters) of the blue plume, determine the initial vent eruption velocity of the plume (in meters / second). For comparison, 1000 m/s equals about 2000 mph. Volcanic eruptions on Earth cannot throw materials to such high altitudes because of atmospheric resistance and stronger gravity. Ignoring atmospheric friction and considering the factor of 5 greater gravity on Earth, what would be the height of the Pillan plume be if it had erupted from a similar volcano on Earth? (That is, what would H be on Earth if the initial v were the same, but with the Earth value of g?) For comparison, Mount Everest is just over 8 km high, commercial jets fly at about 15 km, and the Space Shuttle orbits the Earth at km. Would such plumes be a hazard to commercial jets or the Shuttle? Tall plumes (and high velocities of ejected material) are due to the pressures that build up because of internal sources of heat. Compare the height of the Pillan plume, scaled down to the Earth's gravity, with the height of the geyser Old Faithful (around 70 meters - about the height of the Gamow Tower) and the plume from the eruption of Mt. St. Helens (1000 meters). What does this tell us about the pressures that build up inside Io compared with inside volcanoes on Earth? Scientists are noting many changes that have occurred on Io's surface since the Voyager flybys 17 years ago, and even a few changes from month to month between Galileo images. Figure 4 shows two images taken in 1997 on April 4 (upper) and September 19 (lower). The large black area in the lower picture is material that has been ejected by the Pillan plume. II.8 II.9 The diameter of the new black patch of volcanic material is 400 kilometers (half the state of Colorado). This corresponds to about 1% of the surface area of Io. If such eruptions occur at random over the surface every 6 months, estimate how many years it would take to resurface the moon. Do you see any impact craters on any of the Io pictures? Explain. Part III. Europa: Water World? Jupiter's moon Europa has a density closer to that of rock than water, yet spectroscopic analysis had shown that the surface of Europa is composed almost entirely of water ice. The ice seen on the surface can be the top of only a thin layer of water/ice over a rocky interior. Recent measurements of the effects of Europa's gravitational pull on the Galileo spacecraft allow us to put an upper limit of about 170 km for the thickness of the water/ice shell. III.1 What percentage of Europa's radius is this outer water /ice shell?

112 APS 1010 Astronomy Lab 112 Galilean Moons In Figure 5, Galileo pictures of Europa show an icy crust that has been severely fractured. The upper image covers part of the equatorial zone of Europa, an area of about 360 by 770 kilometers (220 by 475 miles, or about the size of Nebraska), and the smallest visible feature is about 1.6 kilometers (1 mile) across. In the lower image the color has been greatly exaggerated to enhance the visibility of certain features. The fractures, called linea, and the mottled terrain appear brown/red, indicating the presence of contaminants in the ice. The blue icy plains are subdivide into units with different albedos at infrared wavelengths, probably because of differences in the grain size of the ice. The area shown is about 1,260 km across (about 780 miles - the size of Texas). III.2 III.3 From these two images, does it look like the contaminants come from below (e.g. seeping through the cracks) or from above (e.g. meteorite dust deposited on the surface)? Figure 6 shows global views of Europa and of the Moon - Europa is only 10% smaller than the Moon. Which moon has the older surface? When asteroids and comets collide with planets and moons, the explosions resulting from the collisions are extremely violent. Matter is excavated from great depths and can be flung wide distances from the resulting crater. Larger impacts create larger craters and expose materials from greater depths. The appearance of the crater resulting from such an impact depends, among many things, upon the material properties of the material in which crater is formed. In Figure 7 there are four examples of impact features, two on the Moon and two on Europa. III.4 At 5.2 AU from the Sun, and having an albedo of 0.64, the temperature on the surface of Europa is nearly two hundred degrees Celsius below the freezing point of water. The lunar surface is composed primarily of a volcanically-derived type of rock known as basalt. Given the similar appearance of the two small craters, what can you conclude about the material properties of water ice at Europan temperatures and those of basalt? Also shown in Figure 7 is the aftermath of two much larger impacts. The Europan impact feature, known as Tyre Macula, looks very different from the lunar crater, but it can still be identified as an impact feature from the clusters of surrounding small secondary craters that were created during the big (primary) impact. III.5 From seismology experiments carried out during the Apollo missions, we know that the Moon's crust is very thick and is composed of the same material throughout. This is why, up to a certain size, most lunar craters look very similar. Since larger impacts excavate material from greater depths and "see" more of the interior, what does the dissimilar appearances of these large impact structures lead you to conclude about the water/ice layer of Europa? Do you think it is frozen solid all the way through? What do you think happened to the impactor that made Tyre Macula? Figure 8 shows an image of "chaos terrain" which looks as if it were created when the surface surrounding the ice blocks was slushy and the ice blocks, or "ice rafts" were free to float about. The thickness of these ice rafts probably does not exceed their width. (Why not? Think of a pencil floating in water. In which way would it orient itself?) III.6 III.7 The image covers an area of 35 by 55 kilometers. Pick the smallest "ice raft" that still looks as if it was broken off from neighboring ice blocks. Measure a typical width for this ice raft. From this measurement, make a rough estimate of the thickness the ice crust (in kilometers) at the time that the "chaos terrain" froze. The next issue is how long ago did the "chaos terrain" freeze? Could there be just a thin layer of ice over a liquid ocean today? What is the evidence in Figure 8 that the chaos terrain froze over relatively recently? (Millions rather than billions of years ago.)

113 APS 1010 Astronomy Lab 113 Galilean Moons If such an ocean does exist, it might be a possible place for life to exist. Life, as we know from studies of life here on the Earth, can be very hardy and can adapt to survive in many regions. Life has been found near volcanic vents at the bottom of the ocean where no sunlight can reach, the frozen lakes of Antarctica and even inside rocks! III.8 What difficulties do you think life in a hypothetical Europan ocean would have to overcome in order to survive? Part IV. Ganymede: The Giant Moon Ganymede is the largest moon in the Jovian system and also the entire Solar System. In fact, it is even larger than Pluto and Mercury! Furthermore, the Galileo spacecraft detected a magnetic field near Ganymede that indicates that the moon has a liquid iron core (similar to the Earth and to Mercury). However, the average density of Ganymede is close to that of water so that the outer layers of Ganymede must be water/ice rather than rock. IV.1 Figure 9 shows global pictures of Ganymede and of Moon. Superficially, they look rather similar. For the Moon, which is older: the lighter or darker regions? Figures 10 and 11 are close ups of a darker and lighter region on Ganymede respectively. When we look closer, any resemblance to the Moon disappears. IV.2 The dark regions on Ganymede are older than the newer, lighter regions. The dark material is probably meteorite dust that has accumulated on the surface. Looking at the close up of the dark region in Figure 10, how do the craters on the icy surface of Ganymede change as they get older? (Compare them to the "fresh" lunar craters shown in Figure 7.) IV.3 What has happened to the crust in the blown-up image of the light region in Figure 11? The high-resolution image from the light region on Ganymede covers a region about the same size as San Francisco Bay - compared in Figure 12. On the left the resolution is that of the best images taken by Voyager in 1979 and on the right the images are at the Galileo resolution. IV.4 For the cases of (a) San Francisco Bay and (b) Ganymede, describe how the higher resolution images change our interpretation of the surfaces of these two regions. You probably remember Comet Shoemaker-Levy-9 making a spectacular display when it bombarded Jupiter in A couple of years before, the comet had been broken up into about 21 fragments when it had passed close by Jupiter. When it came back to Jupiter in 1994, the comet fragments plunged (and exploded) in Jupiter's atmosphere. It was realized at this time that comets are probably frequently broken up by Jupiter's gravity. Sometimes these broken up comets hit the moons rather than the planet. IV.5 Figure 13 shows a chain of craters on Ganymede that may have been produced by a broken up comet. How many pieces of comet impacted Ganymede?

114 APS 1010 Astronomy Lab 114 Galilean Moons Part V. Callisto: A Battered World Callisto, the fourth Galilean moon, has the dubious distinction of being the most cratered moon in the solar system. Callisto is a little smaller than Ganymede (about the size of the planet Mercury) and is apparently composed of a mixture of ice and rock similar to Ganymede. Unlike the other Galilean moons, Callisto has endured virtually no tidal heating. Callisto's albedo is about half that of Ganymede but Callisto is still more reflective than the Moon. The darker color of Callisto suggests that its upper surface is dirty ice or water rich rock frozen at Callisto's cold surface. The abundance of craters on its surface suggests that its surface is the oldest in the Galilean system, possibly dating back to final accretion stages of planet formation 4 to 4.5 billion years ago. And, unlike the other Galilean moons, Callisto's surface shows no signs of volcanism, tectonics or other geologic activity, further supporting the hypothesis that Callisto's surface took its present form long ago, and is hence very old. Valhalla, the prominent bullseye type feature in the top left image in Figure 14, is believed to be a large impact basin, similar to Mare Oriental on the Moon and the Caloris Basin on Mercury. The ridges resemble the ripples made when a stone hits water, but here they probably are the result of a large meteorite. The fractured ice surface was partially melted by the impact, but they re-solidified before the ripple could subside. V.1 The four images in Figure 14 show increasing detail as Galileo zoomed in to smaller and smaller scales. Notice how the top two pictures show the surface of Callisto to be saturated with craters so that if another impactor hit, it would probably cover up on old crater. But when we go to smaller scales, does the surface remain saturated with craters? V.2 The dark material is probably dust produced by the break up of micro-meteroites (tiny, dust-sized meteorites). It is probably very similar to the dust on the surface of the Moon. What is the approximate size of the smallest crater that you can distinguish as a crater in the bottom left image? If all smaller craters are covered up with meteorite dust, roughly how thick must the dust layer be? Earlier we learned that Io s volcanic activity (hence resurfacing activity) is a result of the gravitational interaction with Jupiter and its moons. The tidal heating which causes Io s volcanic activity is due to Io s orbital resonance with the other Galilean moons. A moon is in orbital resonance if its orbital period is (or nearly is) a whole-number multiple of the orbital period of another moon (e.g. if one moon has twice the period of another moon they are in orbital resonance with each other). V.5 From the table at the beginning of this exercise, which of the Galilean moons is not in orbital resonance with any of the other Galilean moons? How does the surface age of this non-resonant moon s surface compare to the others? V.6 Now you are equipped to make some very general statements about how the characteristics of the four Galilean moons vary with distance from Jupiter. First, how does the degree of tidal heating vary with distance from Jupiter? How might this lead to the observed differences in the amount of water on these four moons? How might this result in the observed ages of their surfaces?

115 APS 1010 Astronomy Lab 115 Observing Projects OBSERVING PROJECTS The Moon SBO 16 Telescope

116 APS 1010 Astronomy Lab 116 Observing Projects Messier 31, nearest Spiral Galaxy - CCD image using 180mm Telephoto Lens mounted on the SBO 18 Telescope

117 APS 1010 Astronomy Lab 117 Constellation Identification - Fall CONSTELLATION AND BRIGHT STAR IDENTIFICATION SYNOPSIS: In this self-paced lab, you will teach yourself to recognize and identify a number of constellations, bright stars, planets, and other celestial objects in the current evening sky. EQUIPMENT: A planisphere (rotating star wheel) or other star chart. A small pocket flashlight may be useful to help you read the chart. Part I: Preparation, Practice, and Procedures Part II contains a list of 30 or more celestial objects which are visible to the naked eye this semester. You are expected to learn to recognize these objects through independent study, and to demonstrate your knowledge of the night sky by identifying them. Depending upon the method chosen by the course instructor, you may have the opportunity to identify these objects one-on-one with your lab instructor during one of your scheduled evening observing sessions. Alternatively, there may be the opportunity to take an examination over these objects in Fiske Planetarium near the end of the semester. In addition, there may be the opportunity to do both, in which case the better of your two scores would be counted. If you are given the option, and if you wait until the end of the semester to take the verbal quiz and then are clouded out, you have no recourse but to take the Planetarium exam. Do not expect your TA to schedule additional time for you. If you have not taken the oral test and are unable to attend the special exam session at Fiske, you will not receive credit for this lab!!! "Poor planning on your part does not constitute an emergency on our part." You can learn the objects by any method you desire: Independent stargazing by yourself or with a friend. Attending the nighttime observing sessions at the Observatory, and receiving assistance from the teaching assistant(s) or classmates. Attending Fiske Planetarium sessions. All of the above. Observing and study tips: It is generally be to your advantage to take the nighttime verbal quiz if it is an option, since you control the method and order of the objects to be identified. In addition, it is easier to orient yourself and recognize objects under the real sky rather than the synthetic sky, since that is the way that you learned to recognize the objects in the first place. It may also be possible to later take the Fiske written quiz and use it to replace your oral quiz score if you feel it will improve your grade.

118 APS 1010 Astronomy Lab 118 Constellation Identification - Fall The Celestial Coordinates section at the beginning of this lab manual (page 27) may help you visualize the night sky and the location of objects in it. We recommend using the large, 10" diameter Miller planisphere available from Fiske Planetarium: it is plastic coated for durability, is easiest to read, and includes sidereal times. The smaller Miller planisphere is more difficult to use but is handier to carry. Other planispheres are available from the bookstore or area astronomy stores. To set the correct sky view on your planisphere, rotate the top disk until the current time lines up with the current date at the edge of the wheel. Planispheres indicate local "standard" time, not local "daylight savings" time. If daylight savings time is in effect, subtract one hour from the time before you set the wheel. (For example, if you are observing on June 15th at 11 p.m. Mountain Daylight Time, line up 10 p.m. with the June 15th marker). The planisphere shows the current appearance of the entire sky down to the horizon. It is correctly oriented when held overhead so that you can read the chart, with North on the chart pointing in the north direction. The center of the window corresponds to the zenith (the point directly overhead). When you face a particular direction, orient the chart so that the corresponding horizon appears at the bottom. As with all flat skymaps, there will be some distortion in appearance, particularly near the horizons. Be aware that faint stars are difficult to see on a hazy evening from Boulder, or if there is a bright moon in the sky. On the other hand, a dark moonless night in the mountains can show so many stars that it may be difficult to pick out the constellation patterns. In either case, experience and practice are needed to help you become comfortable with the objects on the celestial sphere. Learn relationships between patterns in the sky. For example, on a bright night it may be virtually impossible to see the faint stars in the constellation of Pisces; however, you can still point it out as "that empty patch of sky below Andromeda and Pegasus". You can envision Deneb, Vega, and Altair as vertices of "the Summer Triangle", and think of Lyra the harp playing "Swan Lake" as Cygnus flies down into the murky pool of the Milky Way. If you merely "cram" to pass the quiz, you will be doing yourself a great disservice. The stars will be around for the rest of your life; if you learn them now rather than just memorize them, they will be yours forever. Good luck, good seeing, and clear skies...

119 APS 1010 Astronomy Lab 119 Constellation Identification - Fall Part II. Fall Naked-Eye Observing List Constellations Ursa Minor (little bear, little dipper) Lyra (lyre, harp) Cygnus (swan, northern cross) Aquila (eagle) Cepheus (king, doghouse) Capricornus Aquarius Pegasus (horse, great square) Andromeda (princess) Pisces (fishes) Aries (ram) Cassiopeia (queen, 'W') Perseus (hero, wishbone) Taurus (bull) Auriga (charioteer, pentagon) Orion (hunter) Gemini (twins) Bright Stars Polaris Vega Deneb Altair Aldebaran Capella Betelgeuse, Rigel Castor, Pollux Mercury, Venus, Mars, Jupiter, Saturn, Uranus, Neptune, Pluto, Asteroids, Comets Ecliptic or Zodiac Celestial Equator Great Andromeda Galaxy (M31) Pleiades (seven sisters) Hyades (closest star cluster) Great Nebula in Orion (M42) Other Celestial Objects or Regions any planets visible in the sky (check the Celestial Calendar at the beginning of this manual) trace its path across sky trace its path across the sky fuzzy patch in Andromeda star cluster in Taurus near Aldebaran center 'star' in Orion's sword

120 APS 1010 Astronomy Lab 120 Constellation Identification - Fall The Boulder night sky at 10 pm October 15, 1999

121 APS 1010 Astronomy Lab 121 Telescope Observing TELESCOPE OBSERVING SYNOPSIS: You will view and sketch a number of different astronomical objects through the SBO telescopes. The requirements for credit for telescope observing may vary from instructor to instructor. The following is given only as a guideline. EQUIPMENT: Observatory telescopes, observing forms, and a pencil. Be sure to dress warmly - the observing deck is not heated! Part I. Observing Deep Sky Objects The two main SBO observing telescopes (the 16-inch and 18-inch) are both operated by computer. The user may tell the computer to point at, for example, object number 206, or s/he may specify the coordinates at which s/he wants the telescope to point. Deep sky objects are easily selected from the SBO Catalog of Objects found in the operations manual of each telescope. Additional objects may also easily be located with the 18-inch telescope using TheSky planetarium program. Your instructor may point the telescopes to at least one of each of the following different types of deep-sky objects (provided that weather cooperates and appropriate objects are "up" at the time); distinguishing characteristics to look for have been included. Double or multiple stars. Separation of the stars, relative brightness, orientation, and color of each component. Open clusters. Distribution, concentration, and relative brightness and color of the stars. Globular clusters. Shape, symmetry, and central condensation of stars. Diffuse nebulae. Shape, intensity, color, possible association with stars or clusters. Planetary nebulae. Shape (ring, circular, oblong, etc.), size, possible central star visible. Galaxies. Type (spiral, elliptical, irregular), components (nucleus, arms), shape and size. For each of the above objects that you observe: I.1 In the spaces provided on the observing form, fill in the object's name, type, position in the sky (R.A. and Dec.), etc. Make sure you note what constellation the object is in; this information is almost essential when using the reference books! I.2 Observe through the telescope and get a good mental image of the appearance of the object. You may wish to try averted vision (looking out of the corner of your eye) to aid you in seeing faint detail. Take your time; the longer you look, the more detail you will be able to see.

122 APS 1010 Astronomy Lab 122 Telescope Observing I.3 Using a pencil, carefully sketch the object from memory, using the circle on the observing form to represent the view in the eyepiece. Be as detailed and accuracy as possible, indicating color, brightness, and relative size. I.4 Include an "eyepiece impression" of what you observed: a brief statement of your impressions and interpretations; feel free to draw upon comparisons (eg., "like a smoke ring", "a little cotton ball", etc.), and to express your own enthusiam or disappointment in the view. I.5 If you wish, or if your instructor has required it, research some additional information on your objects. The Observatory lab room has some sources, as does the Math-Physics Library. Specific useful books are Burnham's Celestial Handbook, the Messier Album, and textbooks. Read about the object, then provide any additional information you think is particularly pertinent or interesting. Part II. Planetary Observations Most of the other eight planets (besides the Earth) are readily observed with the SBO telescopes. The difficult ones are Pluto (tiny and faint) and Mercury (usually too close to the Sun). Provided that they are available in the sky this semester (consult the Celestial Calendar section at the beginning of this manual): II.1 Observe, sketch, and research at least two of the solar system planets as in paragraphs I.1 through I.5 above. Pay particular attention to relative size, surface markings, phase, and of course any special features such as moons, shadows, rings. You may wish to use different magnifications (different eyepieces) to attempt to pick out more detail.

123 APS 1010 Astronomy Lab 123 Telescope Observing NAME: Object Name Object Type Constellation R.A. Dec. Date Time Telescope size Sky Condition Description of Observation Additional Information Object Name Object Type Constellation R.A. Dec. Date Time Telescope size Sky Condition Description of Observation Additional Information

124 APS 1010 Astronomy Lab 124 Telescope Observing NAME: Object Name Object Type Constellation R.A. Dec. Date Time Telescope size Sky Condition Description of Observation Additional Information Object Name Object Type Constellation R.A. Dec. Date Time Telescope size Sky Condition Description of Observation Additional Information

125 APS 1010 Astronomy Lab 125 Telescope Observing NAME: Object Name Object Type Constellation R.A. Dec. Date Time Telescope size Sky Condition Description of Observation Additional Information Object Name Object Type Constellation R.A. Dec. Date Time Telescope size Sky Condition Description of Observation Additional Information

126 APS 1010 Astronomy Lab 126 Telescope Observing NAME: Object Name Object Type Constellation R.A. Dec. Date Time Telescope size Sky Condition Description of Observation Additional Information Object Name Object Type Constellation R.A. Dec. Date Time Telescope size Sky Condition Description of Observation Additional Information

127 APS 1010 Astronomy Lab 127 Telescope Observing NAME: Object Name Object Type Constellation R.A. Dec. Date Time Telescope size Sky Condition Description of Observation Additional Information Object Name Object Type Constellation R.A. Dec. Date Time Telescope size Sky Condition Description of Observation Additional Information

128 APS 1010 Astronomy Lab 128 Telescope Observing NAME: Object Name Object Type Constellation R.A. Dec. Date Time Telescope size Sky Condition Description of Observation Additional Information Object Name Object Type Constellation R.A. Dec. Date Time Telescope size Sky Condition Description of Observation Additional Information

129 APS 1010 Astronomy Lab 129 Observing Lunar Features OBSERVING LUNAR FEATURES SYNOPSIS: You will investigate the moon through telescopes and binoculars, and identify and sketch several of the lunar features. EQUIPMENT: Sommers-Bausch Observatory telescopes and binoculars, lunar map, lunar observing forms, and a pencil. Be sure to dress warmly - the observing deck is not heated! Part I. Lunar Features Listed below are several types of lunar features. Read the description of feature types, and identify at least one example of each using either a telescope or binoculars. Locate and label each feature on one of the lunar outline charts below. (One of the charts is presented in "normal" view, which resembles the appearance of the Moon as seen through binoculars. The other is a "telescope view", which is a mirror image of the Moon as it may appear through the telescopes. Use either or both charts at your convenience.) You will encounter a number of additional objects not shown on the outline charts, such as small craters. Feel free to add them as you encounter them. Feature types marked with "T" are best seen through a telescope, while those marked with "B" can be seen with binoculars. I.1 Maria: These are relatively smooth areas which comprise the "man-in-the-moon". They were thought to be seas during the early days of the telescope, but are now known to be lava flows. (B) Shade in these dark patches with your pencil. I.2 Craters with central peaks: Many large craters have mountain peaks in their centers which reach 5000 meters in height. These peaks are produced by a rebound shock wave produced by the impact that formed the crater. (T) I.3 Craters with terraced walls: Often the inner walls of a crater collapse as in a landslide. This sometimes happens several times, giving the inner crater wall a stairstepped appearance. (T) 1.4 Overlapping craters: An impact crater may be partially obliterated by a subsequent impact, giving clear evidence of which impact occurred at an earlier time in the Moon's history. (T) I.5 Craters with rays: Some younger craters have bright streaks of light material radiating from their centers. The rays are debris splashed out by the impact which formed the crater that have not been obliterated by subsequent geologic or impact history. Rays are most prominent near the time of the full Moon. (B) I.6 Walled plains: A few craters are very large with bottoms partially filled by lava. The appearance is that of a large flat area surrounded by a low circular wall. (T)

130 APS 1010 Astronomy Lab 130 Observing Lunar Features I.7 Rilles: Rilles are trenches in the lunar surface which can be straight or irregular. Some of them look like dried river beds on the Earth. It is generally believed that they were not formed by water erosion, but rather by flowing liquid lava. Straight rilles are probably geological faults, formed when the lunar surface collapsed on one side of the rille. (T) I.8 Mountains and mountain ranges: Due to the lack of erosion processes on the Moon, mountain peaks can reach heights of 10,000 meters. (B or T) Part II. The Terminator The terminator is the sharp line dividing the sunlit and dark sides of the Moon's front face. II.1 II.2 II.3 If the Moon is not full on the night of your observations, carefully sketch the terminator on the chart. Include irregularities in the line which give visual clues to the different heights in the lunar features: high mountains, crater edges, low plains. (B) Inspect the appearance of craters near the terminator, and those which are far from it. How does the angle of sunlight make the craters in the two regions appear different? In which case is it easier to identify the depth and detail of the crater? (If the Moon is full, look at craters near the edge of the Moon and contrast with those near the center.) (T) If you were standing on the Moon at the terminator, describe what would be happening. Part III. Lunar Details III.1 Select two lunar features of particular interest to you, and use the attached lunar sketch sheet to make a detailed pencil sketch of their telescope appearance. Be sure to indicate their locations on an outline chart so that you may later identify the features. (T) Part IV. Lunar Map Identification III.1 Compare your finished lunar outline charts and observing sheets with a lunar map, and determine the proper names for the features you have identified and sketched.

131 APS 1010 Astronomy Lab 131 Observing Lunar Features N E W S Binocular View

132 APS 1010 Astronomy Lab 132 Observing Lunar Features N W E S Telescope (Inverted) View North may not be "up" in the eyepiece

133 APS 1010 Astronomy Lab 133 Observing Lunar Features NAME: Object Name Object Type Comments Object Name Object Type Comments

134 APS 1010 Astronomy Lab 134 Observing Lunar Features NAME: Object Name Object Type Comments Object Name Object Type Comments

135 APS 1010 Astronomy Lab 135 The Messier Catalog THE MESSIER CATALOG (CCD IMAGING) SYNOPSIS: You have the opportunity to use the SBO telescopes to do electronic imaging of celestial objects from the Messier catalog using a CCD camera. EQUIPMENT: Sommers-Bausch Observatory telescopes, CCD camera, and image processing software, a planisphere (rotating star wheel) or other star chart. NOTE: This is an advanced lab exercise which may be possible only if a sufficient number of clear nights are available. Students who pursue this exercise should be willing and prepared to spend additional time and effort in order to process their work. Part I. The Messier Catalog During the years from 1758 to 1782 Charles Messier, a French astronomer (b d. 1817), compiled a list of approximately 100 diffuse objects that were difficult to distinguish from comets through the telescopes of the day. Discovering comets was the way to make a name for yourself in astronomy in the 18th century, so Messier's aim was to catalog objects that were often mistaken for comets such that they would not be bothered with again. Ironically these are perhaps the most interesting objects in the night sky and are well worth looking at! The Messier Catalog soon became well-known as a collection of the most beautiful objects in the night sky, including a supernova remnant, diffuse and planetary nebulae, open and globular star clusters, and spiral and elliptical galaxies. It was one of the first major milestones in the history of the discovery of deep sky objects, as it was the first comprehensive and reliable list of its kind. The study of these objects by astronomers has, and continues to, lead to important discoveries such as the life cycles of stars, the reality of galaxies as separate island universes and the age of the universe. Many of the beautiful pictures taken by the Hubble Space Telescope are of Messier objects. Today's versions of the catalog usually also include additional of objects observed by Messier and his collegial friend, Pierre Mechain, but were not included in his original list. Objects in the Messier catalog are given a number preceded by the letter M (for Messier, of course!) For example, the Andromeda Galaxy is the 31st object in the Messier catalog and is hence also known as M31. The table below lists all the Messier objects in order. The object type, angular size (in arcminutes) and common name are listed, as well as the constellation in which the object resides. Interestingly, for some of the catalog entries it has been difficult to determine which object Messier originally saw, as his notes were sloppy! Thus the identity of some objects are still under debate. For example, there is some question as to the identity of M102. Some believe it is an accidental re-labeling of M101 while others believe it to be the galaxy NGC 5866 (NGC, the new general catalog, is another catalog of non-stellar objects). M104 through M110 are objects that were believed to have been originally seen by Messier but for some reason not cataloged. They were later added to the Messier catalog by Mechain and other astronomers.

136 APS 1010 Astronomy Lab 136 The Messier Catalog Object Object Type Angular Size ( ) Distance (kly) Constellation Common Name M1 Supernova Remnant Taurus Crab Nebula M2 Globular Cluster Aquarius M3 Globular Cluster Canes Venatici M4 Globular Cluster Scorpius M5 Globular Cluster Serpens Caput M6 Open Cluster 15 2 Scorpius Butterfly Cluster M7 Open Cluster 80 1 Scorpius Ptolemy's Cluster M8 Diffuse Nebula Sagittarius Lagoon Nebula M9 Globular Cluster Ophiuchus M10 Globular Cluster Ophiuchus M11 Open Cluster 14 6 Scutum Wild Duck Cluster M12 Globular Cluster Ophiuchus M13 Globular Cluster Hercules Hercules Cluster M14 Globular Cluster Ophiuchus M15 Globular Cluster Pegasus M16 Open Cluster 7 7 Serpens Cauda Eagle Nebula M17 Diffuse Nebula 11 5 Sagittarius Omega Nebula M18 Open Cluster 9 6 Sagittarius M19 Globular Cluster Ophiuchus M20 Diffuse Nebula Sagittarius Triffid Nebula M21 Open Cluster Sagittarius M22 Globular Cluster Sagittarius M23 Open Cluster Sagittarius M24 Open Cluster 5 10 Sagittarius M25 Open Cluster 40 2 Sagittarius M26 Open Cluster 15 5 Scutum M27 Planetary Nebula Vulpecula Dumbbell Nebula M28 Globular Cluster Sagittarius M29 Open Cluster Cygnus M30 Globular Cluster Capricornus M31 Spiral Galaxy Andromeda Andromeda Galaxy M32 Elliptical Galaxy Andromeda M33 Spiral Galaxy Triangulum M34 Open Cluster Perseus M35 Open Cluster Gemini M36 Open Cluster Auriga M37 Open Cluster Auriga M38 Open Cluster Auriga M39 Open Cluster Cygnus M40 Double Star Ursa Major Winnecke 4 M41 Open Cluster Canis Major M42 Diffuse Nebula Orion Orion Nebula M43 Diffuse Nebula Orion M44 Open Cluster Cancer Praesepe M45 Open Cluster Taurus Pleiades M46 Open Cluster Puppis M47 Open Cluster Puppis M48 Open Cluster Hydra M49 Elliptical Galaxy 9 60,000 Virgo M50 Open Cluster 16 3 Monoceros M51 Spiral Galaxy 11 37,000 Canes Venatici Whirlpool Galaxy M52 Open Cluster 13 7 Cassiopeia M53 Globular Cluster Coma Berenices M54 Globular Cluster Sagittarius M55 Globular Cluster Sagittarius

137 APS 1010 Astronomy Lab 137 The Messier Catalog Object Object Type Angular Size ( ) Distance (kly) Constellation Common Name M56 Globular Cluster Lyra M57 Planetary Nebula Lyra Ring Nebula M58 Spiral Galaxy 6 60,000 Virgo M59 Elliptical Galaxy 5 60,000 Virgo M60 Elliptical Galaxy 7 60,000 Virgo M61 Spiral Galaxy 6 60,000 Virgo M62 Globular Cluster Ophiuchus M63 Spiral Galaxy 10 37,000 Canes Venatici Sunflower Galaxy M64 Spiral Galaxy 9 12,000 Coma Berenices Blackeye Galaxy M65 Spiral Galaxy 8 35,000 Leo M66 Spiral Galaxy 8 35,000 Leo M67 Open Cluster Cancer M68 Globular Cluster Hydra M69 Globular Cluster Sagittarius M70 Globular Cluster Sagittarius M71 Globular Cluster Sagitta M72 Globular Cluster Aquarius M73 Open Cluster 3? Aquarius M74 Spiral Galaxy 10 35,000 Pisces M75 Globular Cluster Sagittarius M76 Planetary Nebula Perseus M77 Spiral Galaxy 7 60,000 Cetus M78 Diffuse Nebula Orion M79 Globular Cluster Lepus M80 Globular Cluster Scorpius M81 Spiral Galaxy 21 11,000 Ursa Major Bode's Galaxy M82 Irregular Galaxy 9 11,000 Ursa Major M83 Spiral Galaxy 11 10,000 Hydra M84 Elliptical Galaxy 5 60,000 Virgo M85 Spiral Galaxy 7 60,000 Coma Berenices M86 Elliptical Galaxy 8 60,000 Virgo M87 Elliptical Galaxy 7 60,000 Virgo Virgo A M88 Spiral Galaxy 7 60,000 Coma Berenices M89 Elliptical Galaxy 4 60,000 Virgo M90 Spiral Galaxy 10 60,000 Virgo M91 Spiral Galaxy 6 60,000 Coma Berenices M92 Globular Cluster Hercules M93 Open Cluster Puppis M94 Spiral Galaxy 7 14,500 Canes Venatici M95 Spiral Galaxy 5 38,000 Leo M96 Spiral Galaxy 6 38,000 Leo M97 Planetary Nebula Ursa Major Owl Nebula M98 Spiral Galaxy 10 60,000 Coma Berenices M99 Spiral Galaxy 6 60,000 Coma Berenices M100 Spiral Galaxy 7 60,000 Coma Berenices M101 Spiral Galaxy 22 24,000 Ursa Major Pinwheel Galaxy M102 Spiral Galaxy 5 40,000 Draco M103 Open Cluster 6 8 Cassopeia M104 Spiral Galaxy 9 50,000 Virgo Sombrero Galaxy M105 Spiral Galaxy 2 38,000 Leo M106 Spiral Galaxy 19 25,000 Canes Venatici M107 Globular Cluster Ophiuchus M108 Spiral Galaxy 8 45,000 Ursa Major M109 Spiral Galaxy 7 55,000 Ursa Major M110 Elliptical Galaxy Andromeda

138 APS 1010 Astronomy Lab 138 The Messier Catalog I.1 Read through the Messier catalog. Which objects are the farthest away? Is this what you'd expect for the types of objects that are included? I.2 Which types of object are the most nearby? Why don't we (or, more specifically, why didn t Messier) see these types of objects at greater distances? Part II. The CCD Camera Rather than use conventional photography, you will use a special type of electronic camera, known as a CCD. In the last 15 years, the CCD ( charge-coupled device ) camera has revolutionized the way astronomers do astronomy. Rather than preparing photographic plates or film using specialized sensitizing techniques and then exposing for many hours to capture the sky, observatories now use these electronic detectors to reconstruct an image of the sky in the form of computer bytes and data arrays. The advantages of using a CCD camera instead of conventional photographic film are numerous: Sensitivity - An astronomical CCD detector is 20 to 60 times more sensitive to light than film - allowing exposures to be made in seconds or minutes rather than hours. Linearity - Twice the amount of light produces twice the signal value in a CCD, while the behavior of photographic film is much more complex; it is therefore much easier to analyze the results in a quantitative manner. Dynamic range - The CCD detector can accommodate a far larger range of intensity than film; useful information on both bright and dim objects can be obtained simultaneously in the same field and at the same time. Threshold - While photography requires a certain minimum of light before anything at all is recorded, CCDs respond to any level of light reaching the detector. Digital processing - Photography is a form of "analog" data, exhibiting a continuous range of gray-scale brightness that does not lend itself well to quantitative analysis. Further, development of film takes time and noxious chemicals, so you are unable to see your results (or worse, mistakes) until well after the fact. CCDs produce "digital" data: the image is acquired directly by a computer and the information is in the form of an array of digital values, ready for immediate analysis and processing. However, photography still offers some advantages over electronic imaging: Size - The largest CCD detectors currently available are about the same size as an exposed square of 35mm film; most are much smaller. This means that film can photograph much larger regions of the sky, producing "panoramas" while CCDs usually concentrate on "close-up" shots. Resolution - The size of an individual CCD picture element, or "pixel", determines the smallest feature that can be resolved. Photographic grain sizes are much smaller than current-technology pixel sizes, so that photographs contain more spatial detail. You will use the CCD camera on the 8-inch telescope that is mounted piggyback on the 18-inch telescope; this permits the small ST-6 detector to see a larger patch of the sky, thus it is useful for deep-sky imaging. Even though the 8-inch telescope has less light-gathering capability than the 18-inch, the sensitivity of the CCD detector allows you to get a much brighter image than what you can see with your eye through the 18-inch. The field of view of the CCD on the 8-inch is similar

139 APS 1010 Astronomy Lab 139 The Messier Catalog to that of the 16 or 18-inch with a 55mm eyepiece. This allows you to find your object with the 16 or 18-inch before taking a picture with the CCD. II.1 How many times more light does the 18-inch telescope collect compared to the 8-inch? Of prime importance is the field of view of the CCD camera. How much of the sky can it see? To determine this you must know two things: the plate scale and the size of the detector. The plate scale is a measure of the angular extent each pixel sees, which depends on the size of the pixels and the telescope to which the CCD camera is attached. II.2 For the ST-6 CCD camera on the 8-inch f/6.3 telescope the plate scale is 3.8 arcseconds per pixel. The ST-6 camera is a 375 x 242 pixel array (meaning it has 375 pixels in each East-West row and 242 pixels in each North-South column). What is the field of view of the ST-6 camera when it is on the 8-inch? III. Observations The goal of this lab is to get pictures of at least three Messier objects. Depending on the size of the class, your instructor will gather you into groups of 2 to 4 students. Once in a group, follow the following steps for each object. Note: It is essential that you keep good records on each exposure and include all pertinent background information regarding equipment, technique, and exposure with each image or photograph. Don't make the same mistakes that Messier made! It s very frustrating to create a beautiful image but not know what it is or how it was acquired. Fill in all the information in the table on the next page. III.1 III.2 III.3 III.4 Before you can look at an object you must first make sure that it is currently visible in the night sky. Use the planisphere on the South wall of the observing deck (or your own if you have one) to determine what constellations are currently visible. Also make sure the constellation is visible to the 16 and 18-inch telescopes. For example, constellations just now on the eastern horizon will not be visible (although they may be in a few hours.) Also, the roof makes it difficult to see objects to the North. Look at the Messier catalog and find objects within the constellations that you think are visible. Want help finding objects that look interesting? There are several books at the observatory that have pictures of many of the Messier objects. The display wall near the entrance of SBO may also help. And of course your instructor will have his or her favorites. Will your object be too big to look at? Some of the Messier objects are very large and they may not fit in the field of view of the CCD camera. The Messier catalog in this lab lists the largest angular size for each object in arcminutes (1 arcminute = 60 arcseconds). Make sure your object will fit in the field of view of the CCD camera. If it doesn't you may want to choose another object. Once you have an object you'd like to observe, ask the instructor or the assistant to move the 16-inch telescope to your object. This will confirm that your object is indeed visible to and accessible by the telescopes. If not, return to step III.1 and start over. Look at the object through the main eyepiece and confirm that it is there. It may be very faint and hard to see. Allow your eye a few minutes to let your eye adjust and use the averted vision technique to help you see it. Hopefully this will later give you an appreciation for the power of the CCD camera! Now go to the 18-inch telescope and ask your instructor or assistant to move the telescope to your object. Guide the telescope so that your object is near the center of the field of view as seen through the 18-inch eyepiece. Ask your instructor to take a 30- second exposure. The picture will shortly appear on the screen. Ask the instructor to

140 APS 1010 Astronomy Lab 140 The Messier Catalog save the image to disk. Be sure to record the filename of your object. Otherwise you will be unable to later determine which file is yours! III.5 Repeat steps III.1 through III.4 for at least two more objects. If time permits you may do more if you like. Catalog Number Object Type Object Name (if any) Constellation Weather (e.g. clear, hazy, etc.) Image Filename IV. Image Analysis Your instructor will return to you printed copies of you images. These are yours to keep so don't write on them! But before you take them home and hang them on your wall there's some science to be done with them. A property of an object that is of fundamental interest is its actual physical size. IV.1 IV.2 Determine the largest angular size of three objects you observed. Do this by measuring the width of your image to determining the scale of the image in arcminutes/cm (remember that you already know the field of view from II.2). Now measure your object along is longest length, and use the image scale to determine its largest angular size. How do these compare to the values given in the Messier catalog? Why might there be some discrepancy? Use the small angle approximation relationship (as discussed in other labs as well as a section in the introductory section of the manual) to determine the actual physical size of your three objects. The distances to each object are also listed in the Messier catalog in units of kilo-light years (kly). Give your answers in appropriate units (light years, Astronomical Units, etc.) e.g., centimeters are not suitable for galaxies! V. Fame and Fortune The Observatory conducts a contest for the Best Astrophoto of the Month, which may be either a CCD image taken at Sommers-Bausch, or a standard photograph of a celestial object. If you think your finished work is of sufficient quality to have it exhibited for others to see, consult the contest rules on the observatory s website (located at ) and make an entry or two! Besides notoriety, you ll also receive a (very) modest reward if you win!

141 APS 1010 Astronomy Lab University of Colorado COURSE INFORMATION NAME: ADDRESS: TELEPHONE: COURSE TITLE: LECTURE Section Number: Class Time: Location: Instructor: Office Location: Office Hours: Telephone: Lecture Teaching Assistant: Office Location: Office Hours: Telephone: LABORATORY Section Number: Lab Meets (Day & Time): Lab Location: Lab Instructor/TA: Office Location: Office Hours: Telephone: NIGHT OBSERVING SESSIONS Dates and Times:

142 APS 1010 Astronomy Lab University of Colorado