Astronomy 101 Lab Manual Victor Andersen Community College of Aurora victor.andersen@ccaurora.edu January 8, 2013
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Contents 1 Angular Measures 5 1.1 Introduction............................ 5 1.1.1 Degrees, Arc-minutes, and Arc-Seconds......... 5 1.1.2 Using Your Body to Measure Angles.......... 6 1.2 Questions............................. 7 2 Latitude and Longitude 11 2.1 Terrestrial Coordinates...................... 11 2.2 Questions............................. 13 3 The Celestial Globe 15 3.1 Introduction............................ 15 3.2 Constellations........................... 15 3.3 Star Names............................ 15 3.4 Celestial Coordinates....................... 16 3.5 Time Systems........................... 17 3.5.1 Solar Time........................ 17 3.5.2 Sidereal Time....................... 17 3.5.3 Units for Right Ascension and Declination....... 17 3.6 Questions............................. 19 4 Phases of the Moon 21 4.1 Introduction............................ 21 4.2 Procedure............................. 21 4.3 Questions............................. 23 3
4 CONTENTS
Chapter 1 Angular Measures 1.1 Introduction In astronomy, we frequently measure the positions and distances between objects on the sky using angles. 1.1.1 Degrees, Arc-minutes, and Arc-Seconds You are probably familiar with angles measured in degrees, where we divide a circle into 360 equal parts. You may not be familiar with the traditional system for expressing fractions of degrees. Each degree is divided into 60 equal pieces, each of these pieces is called an arc-minute, and denoted with a single tick mark, that is: 1 = 60. Furthermore, if we need a fraction even smaller than 1/60 of a degree, we divide each arc-minute in to 60 pieces, and call that an arc-second, that we denote with a double tick mark: 1 = 60. As an example, lets look at specifying an angle of 1/8 of a degree in arc-minutes and arc-seconds. First lets figure out the number of arc-minutes this angle corresponds to. Because there are 60 arc-minutes in 1 degree, this angle is 1 60 8 1 = 7.5. 5
6 CHAPTER 1. ANGULAR MEASURES This means that there are 7 whole arc-minutes in 1/8 of a degree, but we need to convert the 0.5 into arc-seconds: (0.5 ) 60 1 = 30. Therefore, 1/8 a degree is equal to 7 30. 1.1.2 Using Your Body to Measure Angles A useful way to make a rough estimate of angles is to use your own body. The index finger on your hand has an angular size of 1 when held at arms length, while your closed fist held at arms length is approximately 10 across.
1.2. QUESTIONS 7 1.2 Questions 1. Write the angle 64 12 56 in decimal form. 2. Write the angle 9 48 12 in decimal form. 3. Write the angle 16.423 in degrees, arc-minutes, and arc-seconds. 4. Write the angle 114.088 in degrees, arc-minutes, and arc-seconds.
8 CHAPTER 1. ANGULAR MEASURES 5. Go out the back of the building, and from the place where the sidewalk and road meet, measure the angle between the top and the bottom of the dome. 6. Now walk up near the Fine Arts Building, and stand near the garage door at its back. Measure the angle between the top and the bottom of the dome. 7. Approximately how many times closer to the dome are you at the second spot you measured than the first?
1.2. QUESTIONS 9 8. Go out in the hallway, and from near the classroom door measure the angle between the top and the bottom of the door at the south-east end of the hallway. 9. Now walk down the hallway until you are near the doorway to room C307, and measure the angle between the top and the bottom of the SE door. 10. Approximately how many times farther from the door are you at the second spot you measured than the first? Write your answer as a complete sentence (e.g. I was x times farther away at the second door than the first. )
10 CHAPTER 1. ANGULAR MEASURES
Chapter 2 Latitude and Longitude 2.1 Terrestrial Coordinates In order to locate points on the surface of the earth, we can divide Earth up using lines of longitude and latitude. Lines of longitude are great circles (a great circle is any circle that you can draw on the surface of a sphere that will cut the sphere in half) running north-south on the globe. Lines of latitude run east-west on the globe, most of them aren t great circles. We define the equator as 0 degrees latitude, and define the longitude line through Greenwich, England as 0 degrees longitude. This line of longitude is known as the Prime Meridian. Measurements of both longitude and latitude are given by angles measured form the center of the earth, normally specified in degrees ( ), arcminutes ( ), and arc-seconds ( ). Longitude is measured along Earth s equator, and latitude is measured north or south from the equator. Latitudes are thus measured as a number of degrees north or south of the equator. North latitudes are denoted as positive values, while latitudes south of the equator are denoted as negative values. Longitudes are typically written as a number of degrees east or west of the prime meridian. For example Denver is at latitude +39 45 00, and longitude 104 52 12 West. 11
12 CHAPTER 2. LATITUDE AND LONGITUDE
2.2. QUESTIONS 13 2.2 Questions 1. Find the approximate longitudes and latitudes of the following places: (a) Los Angeles, California (b) Cape Town, South Africa (c) Tokyo, Japan (d) Honolulu, Hawaii (e) Paris, France (f) Nome, Alaska 2. Which is farther east, Now York City, or Rio De Janeiro, Brazil? 3. Which is farther north, Minneapolis Minnesota, or London, England? 4. What is the latitude of the south pole? What is the longitude?
14 CHAPTER 2. LATITUDE AND LONGITUDE 5. Can you find a point on the globe where the latitude of that point is ambiguous or undefined? 6. Can you find a point on the globe where the longitude of that point is ambiguous or undefined?
Chapter 3 The Celestial Globe 3.1 Introduction The observed motions and phases of different objects on the sky provides the basis the systems we use to keep time. As such, keeping of time is linked with the way we keep track of positions of things, both on the surface of the earth and the sky. 3.2 Constellations Constellations are areas on the sky, usually defined by distinctive groupings of stars (Modern astronomers define 88, if you are interested a complete list is given in appendix I of the textbook). Constellations have boundaries in the same way that countries on the earth do. 1 3.3 Star Names Most bright stars have names (often Arabic). Stars are also named using the Greek alphabet along with the name of the constellation of which the star is a member. The first five lower case letters of the Greek alphabet are: α (alpha), β (beta), γ (gamma), δ 1 Prominent groupings of stars that do not comprise an entire constellation are called asterisms (for example, the Big Dipper is just part of the constellation Ursa Majoris). 15
16 CHAPTER 3. THE CELESTIAL GLOBE (delta), and ɛ (epsilon). The normal convention is for the brightest star in a constellation to be designated as the α star of that constellation, the next brightest the β star, and so on (although there are one or two counter examples.) For example, the Brightest star in Scorpius is named Antares, but is also called α Scorpii. 3.4 Celestial Coordinates Remember that we can think of the sky as single spherical surface, centered on the earth, called the celestial sphere. The celestial sphere is an imaginary surface on which we can keep track of the positions of all celestial objects. Imagine projecting lines of longitude and latitude upward from the surface of the earth onto the celestial sphere. Astronomers call the coordinate analogous to the longitude the right ascension (RA) and and that analogous to the latitude the declination (Dec). Any object s position on the sky can be given in terms of these two coordinates.
3.5. TIME SYSTEMS 17 3.5 Time Systems 3.5.1 Solar Time The earth rotates around an axis through its north and south poles. This means that celestial objects seem to move across the sky with time. In fact, many of our basic time divisions (days, months, and years for example) are based on this apparent motion of celestial objects as seen from a fixed point on the earth. Notice that this means that we can define at least two different time systems using the apparent position of different types of objects on the sky. If we use the sun as our reference object, the time system is called solar time. If we use stars as our references, we call the time sidereal time. The length of time between two successive meridian crossings for the sun is called an apparent solar day (the meridian is the north-south great circle on the sky that runs through the point directly over your head.) The length of an apparent solar day varies from one day to the next throughout the year, mainly because Earth s orbit is elliptical in shape. For everyday use we define a mean solar day as average length of all the apparent solar days over the entire year. 3.5.2 Sidereal Time The time for a star to make two successive meridian crossings takes only about 23 hours 56 minutes (as measured on a clock keeping mean solar time); the orbital motion of the earth around the sun means that the earth most rotate about 361 to return the sun to the meridian, while the earth must rotate only 360 in order to have a star return to the meridian. 3.5.3 Units for Right Ascension and Declination Astronomers normally use units of sidereal time for Right Ascension. 24 hours of sidereal time is defined to be the time separating two successive
18 CHAPTER 3. THE CELESTIAL GLOBE meridian crossings as seen from a fixed location on the surface of the earth for any star. Zero hours right ascension is defined by the position of the vernal equinox. The local sidereal time of zero hours thus occurs at any position on the surface of the earth when the vernal equinox is on the meridian at that location. A star s right ascension is then defined to be the amount of sidereal time between when the vernal equinox crosses the meridian and time the star crosses meridian. (Example: A star with a RA of 21 hours will cross meridian 21 (sidereal) hours after the vernal equinox. The vernal equinox will then cross the meridian again 3 (sidereal) hours after this star.) Notice that the local sidereal time at any location is just the right ascension of the stars on the meridian at that location at that instant. A star s declination is measured as the number of degrees away from the equator (just like latitude on the surface of the earth), with declinations north of the equator having positive values and those south of the equator having negative values.
3.6. QUESTIONS 19 3.6 Questions 1. For the following 5 sets of coordinates, indicate whether they could be or could not be valid coordinates for a celestial object, such as a star (in other words, do the following coordinates represent actual points on the celestial sphere?).if not, explain why not. (a) RA: 0 h 0 m, Dec: 0 0 (b) RA: 34 h 26 m, Dec: 90 0 (c) RA: 12 h 34 m, Dec: 92 42 (d) RA: 7 h 18 m, Dec: 87 22 (e) RA: 7 h 18 m, Dec: 87 22 2. What bright stars are at the following positions (give both their common name as well as their designation within their constellation, for example α Virginis (Virginis = Virgo...))? (a) RA: 6h43m, Dec: 16 39 (b) RA: 19h48m, Dec: 8 44 (c) RA: 1h36m, Dec: 57 29
20 CHAPTER 3. THE CELESTIAL GLOBE 3. What are the coordinates of the following stars? (a) Vega (α Lyrae). (b) Rigel (β Orionis). (c) Spica (α Virginis). 4. Locate the constellation Orion on the Celestial Globe. What is the RA and Dec of Betelgeuse (also known as α Orionis?) 5. Locate the ecliptic (the path that the Sun follows with respect to the stars over one year). What is the Sun s RA and Dec today?
Chapter 4 Phases of the Moon 4.1 Introduction This lab is designed to help you understand how the phase cycle of the Moon is produced, and give you a model that will allow you to predict moon and planetary phases in a number of situations. 4.2 Procedure The figure below shows the phases of the moon, as they appear from Earth. 1. You will need two balls for your group, one to represent Earth and the other to represent the moon. The light colored side of each will represent the side of the object facing the Sun. 2. We will take the direction of the Sun to be toward front of the room. 3. Hold the ball representing Earth in one place, and move the ball representing the moon around your Earth. 4. The person holding Earth stands in one spot for the entire lesson (but can turn around to see the Moon). The person holding the Moon stands 21
22 CHAPTER 4. PHASES OF THE MOON relative to the Earth so that the styrofoam ball appears to the Earth in each phase. The Moon must make sure that the white side of the ball always faces towards the Sun! The person holding Earth decides when the appropriate phase is shown. The other team members should mark where the Moon is relative to the Earth. All people in each group should take turns being Earth and the in order to clearly visualize what is producing the different phases seen from Earth.
4.3. QUESTIONS 23 4.3 Questions 1. Record the location of the Moon necessary to each phase of the Moon below. Waning Crescent New Waxing Crescent First Quarter Waxing Gibbous Full Waning Gibbous Third Quarter Waning Crescent 2. In which direction does the Moon orbit the Earth? CLOCKWISE or COUNTERCLOCKWISE 3. For observers from the Northern hemisphere, which side of the Moon is illuminated when the Moon is just past new phase? RIGHT or LEFT 4. If you were to observe a crescent moon with the horns of the crescent pointing right, is the Moon WAXING or WANING? Hint: consider the previous question!
24 CHAPTER 4. PHASES OF THE MOON 5. When an earth-bound person observes the Moon in its full phase, which phase of Earth is observed by a person on the Moon? NEW, FULL or SOME OTHER PHASE 6. In the following three pictures, fill in the missing piece (either in the top or the bottom panel). 7. Mars has two moons, Phobos and Deimos. In the following picture, (a) What is the phase of Phobos as seen from Mars? (b) What is the phase of Deimos as seen from Mars?
4.3. QUESTIONS 25 (c) What is the phase of Deimos as seen from Phobos? 8. For each of the following pictures, what is the time for the observer (the solid black line), what phase is the Moon in, and where is the Moon in the observer s sky? Lab adapted from Phases of the Moon at the University of Washington Astronomy Clearinghouse: http://www.astro.washington.edu/courses/labs/clearinghouse/labs/phasesmoon/lab.html