Physics 1401 Introduction to Astronomy Laboratory Manual Fall 2006 Dr. Keith Mon 5:30-8:30 Wed 2:30-5:30 Thurs 5:30-8:30 Text by R. Thompson, J. Christensen, T. Bykov, and W. Keith, and for the Virtual Astronomy Lab text, M. Guidry and K. Lee. 1
The Celestial Sphere By using a globe that displays the celestial sphere, we can learn many things about the apparent movements of the stars throughout the year. With your celestial sphere, carry out the following exercises and answer all accompanying questions. Notice that there is a difference between the star names and the constellation names. Your write-up will not be in the usual lab format. Please write a concise paragraph with complete sentences and/or lists as appropriate to explain and describe the relevant information from each section. 1. By spinning the sphere, the effects on the celestial sphere due to the rotation of the earth are simulated. To show your ability to correlate the Celestial Sphere with the real sky, please point out to the instructor the following points of reference on the globe. Your report should explain how to find these features in the sky. (a) the zenith (Is there a star at this point? Is there always a star at this point?) (b) the celestial poles (Find both the celestial north pole and the celestial south pole. When can we see each pole?) (c) the celestial equator (How is this different than the Earth s equator?) (d) the horizon (e) the ecliptic (Why would all the planets, the moon, and the sun all follow essentially the same path in the sky? Distinguish between the sun s daily path and the sun s yearly path across the sky.) 2. Spin the sphere so that the stars appear to rise in the east and set in the west. Notice that for any particular setting of the sphere, some stars never rise above the horizon and some never set below the horizon. Such stars are known as northern and southern circumpolar stars. Using the scale on the sphere s support ring, set the sphere for the latitude of Abilene (32 ). Spin the sphere and determine which stars are always visible from Abilene (northern circumpolar). Which stars never rise (southern circumpolar)? Record both groups of stars. (List enough that I can distinguish the region of the celestial sphere to which you are referring.) 3. Using the scale printed on the ecliptic, set the sphere for sundown on today s date. Which constellations are visible from Abilene at sundown on this date? Which are visible at midnight? Set the sphere for sundown six months from today. Which constellations are visible? 4. Set the sphere for sunrise on March 21st. What season is this? Where is the sun in relation to the observer s horizon (due east, north of east, south of east)? Set the sphere for sunrise on June 21st. What season is this? Where is the sun in relation to the observer s horizon? Repeat for September 21st and for December 21st. 5. Place the sun on its correct position for today. Place the new moon where it would be in the sky in relation to the sun s position. Place the 1st quarter, full, and 3rd quarter moons where they would be in relation to the sun. Have your instructor verify that they are on the correct positions. Set the sphere for sunrise and slowly spin the sphere moving the sun toward the west. Notice where the sun is when each different-phase moon rises. Record your observations. 2
Earth and Sky This lab will take a more detailed look at some of the topics discussed in the Celestial Sphere lab. In particular, it will investigate the differences in sunrise and moonrise times across the country and the effects of latitude on the length of day. You will be asked to make several predictions during this lab. Please note that your predictions will not be graded. I simply want to see what your initial thoughts were on these topics and, if the results happen to disagree with your initial guess, how well you explain the difference. Your data will be collected from the internet using the Weather Underground website: http:\\www.wunderground.com You will need to select at least 20 cities widely distributed across the country. Though there are no restrictions on which cities you pick, it is necessary that you: pick some pairs of widely separated cities that are at the same latitude (at least four pairs) pick some pairs that are at the same longitude (at least two pairs) pick at least one pair that are on the opposite ends of the same time zone (use either the Central or the Mountain time zones) A United States map is available at the front of the room for your use. Using the Weather Underground web site, you will need to record the following data for each city: sunrise, sunset, moonrise, moonset, longitude, latitude. All times will need to be converted to eastern time (eastern = central +1, mountain +2, pacific +3) Before actually taking your data, please carry out the following instructions: 1. Sketch a plot of your prediction of sunrise time vs. longitude. 2. Sketch a plot of your prediction of length of daytime vs. latitude. 3. Predict how the sunrise times will compare for cities at the same longitude. 4. Predict how the length of daytime for a particular city will compare with the length of time that the moon is up for this same city. (Note: the length of time the moon is up should not be confused with the length of nighttime ) 5. Calculate what the rotation rate of the earth should be (in degrees per hour). 6. For two cities at the same latitude, predict how the delay time for moonrise (i.e., how much later the moon will rise for the western city compared to the eastern city) will compare with the delay time for sunrise. (Note: if the moon rises at 6pm for the eastern city and at 7pm for the western city, the delay time is one hour) 7. Predict how much delay time there will be for sunrise between two cities at opposite ends of the same time zone. 3
Once all of these predictions have been made, please have the instructor initial your paper. Please turn this sheet in with your report. Remember, you will not be graded on the accuracy of these predictions. Now go to the website and take your data. Remember to convert all times to eastern time. Once your data have been collected: 1. Plot sunrise time vs. longitude. Discuss how this plot compares with your prediction. Attempt to explain any differences. 2. Calculate the length of day for each city. 3. Plot length of day vs. latitude. Discuss how this plot compares with your prediction. Attempt to explain any differences. 4. Compare sunrise times for cities at the same longitude. How do they compare to your prediction? 5. Compare length of daytime for a city to the length of time the moon will be up. How does your answer compare to your prediction? 6. For each pair of cities at the same latitude, calculate the rotation rate of the earth in degrees per hour. Take an average of all of your city pairs. How does this answer compare to your prediction? 7. For two cities at same latitude, calculate the delay time for sunrise and for moonrise. How do they compare? How does your result compare to your earlier prediction? Attempt to explain any difference. 8. For a pair of cities at opposite ends of the same time zone, how much is the delay in sunrise? Compare with your earlier prediction. 9. Discuss the moonrise time (local time) and the current phase of the moon. Do they correspond to what was discussed in the Celestial Sphere lab last week? Which of your predictions were right? Which turned out to be wrong? In those cases where your predictions were wrong, what did you learn about the relationship between the earth and sky? 4
The Laws of Refraction and Reflection Most data collection in astronomy involves the collection of light by using some type of telescope. Most types of telescopes use lenses or mirrors to bend and focus light rays to form an image. This lab illustrates the property of lenses and mirrors to bend light, known as Refraction for lenses and Reflection for mirrors. We will begin by considering Refraction. When light, or any other type of wave, crosses the boundary between two media in which the speed of the wave differs, the phenomenon of refraction will occur. How much refraction occurs depends on the types of media and on the shape of the boundary. We may study the effect by observing what happens when a ray of light crosses the boundary from air into glass. The phenomenon can be most easily studied with the aid of a piece of glass having parallel sides. 1. Place a piece of paper and a square piece of glass on the cardboard. 2. Place pins in positions 1 and 2 as shown in Figure 1 (on the chalkboard) 3. Looking through the opposite side of the glass, line up a pin with the images of the original two pins. Place this pin at position 3. 4. Place a pin at position 4 so that it lines up with pin 3 and the images of pins 1 and 2. 5. Remove the glass and draw a line from pin 1 to pin 2, from pin 2 to pin 3, and from pin 3 to pin 4. 6. At pin 2, draw a line perpendicular to the edge of the glass as in Figure 1. 7. Measure the angles t and i as shown in Figure 1. The effect of the type of material is described by its Index of Refraction. Calculate the index of refraction using Snell s Law: n = sin i sin t The index of refraction is related to the speed of light within the material in the following manner: n = c v The velocity of light in air, c, is approximately 3x 10 8 m/sec. Calculate the velocity of light in the glass. Repeat the previous steps with a prism, tracing the path of light through the prism (see Figure 2 on board). 5
The Law of Reflection is much simpler. It states that the angle of reflection r is equal to the angle of incidence i, or: i = r We are very familiar with flat mirrors like the one we will use today, but these mirrors do not focus or magnify light. Astronomers use curved mirrors, just like lenses use curved glass, to bend the light in a particular way so that objects appear bigger and brighter than normal. For example, look at the magnifying mirror at the front of the room and think about how the law of reflection works on a curved mirror. In order to demonstrate the law of reflection for a flat mirror, follow the procedure listed below. 1. Using a fresh sheet of paper, stand up the mirror on the cardboard and draw a line along the reflecting surface (use extra pins to keep the mirror upright). 2. Place pins in positions 1 and 2 according to Figure 3 (on the board). 3. Position pin 3 such that it lines up with the image of pin 1 and the point halfway between pin 2 and its image. 4. Remove the mirror and draw a line from pin 1 to pin 2, and from pin 2 to pin 3. 5. At pin 2, draw a line perpendicular to the edge of the mirror as in Figure 3. 6. Measure the angles r and i as shown in Figure 3. How well does your experimental data agree with the law of reflection? Be sure to discuss possible sources of error in your lab write up. 6
Telescope Observing This lab will give you a chance to do what you took this class for in the first place; observe through a telescope. Along the way, you will be expected to learn about the various types of telescopes, how they work, and how they influence the quality of the image that you see through the eyepiece. This lab will make use of at least two different types of telescopes as well as binoculars and the naked eye. for each optical instrument, you should pay attention to how it collects the light. (Does it use lenses or mirrors?) How big are the lenses/mirrors? Does it work by reflection or refraction? You will be observing different celestial objects through the different instruments. Each time you look through an eyepiece, draw a simple sketch of what you see. Make any notes necessary to remind yourself later as to what instrument you were using and what object you were viewing. Notice the difference in the images between the different instruments. Notice also the differences due to differing magnifications of the same instrument. How does magnification affect such things as field of view, image brightness, image clarity? In your report you should discuss all of these issues as well as presenting your sketches. 7
A Study of the Simple Lens Everyone knows that lenses form images, but do you know how or why? What factors influence the size, location, and orientation of the image? In this lab, we will learn how properties such as the focal length and index of refraction affect the formation of images for different shaped lenses. These properties will be measured by the following procedure: 1. Place a converging lens on the optical bench between the illuminated object and the screen. Adjust the positions of the lens and screen until a good image is formed on the screen. Measure the distances between the lens and the image (image distance), and between the lens and the object (object distance). Measure the height of the object and of the image. Is there a relationship between the four quantities? 2. The lens equation 1 i + 1 o = 1 f shows the relationship between the image distance, i object distance, o, and the focal length of the lens, f. Using your data from part 1, determine the focal length of each lens. Notice that there are two places between the object and the screen at which the lens may be located and still give a sharp image. Find both these positions and determine the focal length of the lens in each case. Compare these two focal lengths. Do they agree? Should they? The magnification of the image is equal to i/o. Compare this calculated value to your measured value from part 1. 3. The focal length of a lens may also be determined by forming the image of a very distant object on a screen. In this case, the object distance, o, becomes very large and therefore 1/o becomes very small. When this is the case, the lens equation may be written as 1/i = 1/f or i = f. Measure the focal length of each lens using this method and compare with your results from part 2. 4. A simple refracting telescope can be constructed using two converging lenses; one as the objective and one as the eyepiece. The magnification of the telescope is given by the formula m = f o /f e. Choose two lenses which, when used together, will give you the largest magnification. The lenses are normally placed so that distant (parallel) light rays into the objective lens emerge from the eyepiece as parallel rays. First, determine how far they should be placed apart and then build your telescope. Describe how well it functions. 8
VLab 11: The Spectral Sequence and the HR Diagram This lab investigates how the Hertzsprung-Russell (HR) diagram orders stellar structure, how it may be used with certain assumptions to determine distances to clusters of stars, and how the distribution of stars in the HR diagram for a cluster is closely tied to an understanding of stellar evolution and is a measure of the age of the cluster. Learning Objectives: Students completing this laboratory should have a basic understanding of spectral classes, apparent and absolute magnitudes, color index, the HR diagram, the distance modulus, how matching of observed main sequences with expected ones permits the distance to clusters to be determined, and how the turnoff point in the HR diagram for a cluster is related closely to the age of the cluster. VLab 12: Binary Stars This lab explores some basic properties of visual, eclipsing, and spectroscopic binary star systems. Learning Objectives: Students completing this laboratory should have a basic understanding of how mass information may be extracted from visual, eclipsing, and spectroscopic binary systems. 9
The Intensity-Distance Relationship of Light An object that emits light, such as a light bulb, our Sun, or a distant star, is said to have a certain intensity. This is a measure of the amount of energy given off by the object. For the objects mentioned above, the light is emitted isotropically, that is, equally in all directions. We can imagine the emitted light forming a constantly expanding sphere around the light source. As the sphere of light expands, the amount of energy per unit area on the surface of the sphere decreases. This amount of energy per unit area is known as the observed flux. At the distance of an observer, the area of the light sphere is given by 4πr 2 where r is the distance from the light source to the observer. The observed flux is the intensity of the light source divided by the surface area of the light sphere, flux = intensity. This shows 4πr 2 that the flux decreases as 1. That is, if we move 2 times farther from the light source, the r 2 flux (or the apparent brightness) decreases to 1 = 1 2 2 4 its original value. In this lab, we will first confirm the 1 property of light and will then use it to determine the intensity of some r 2 light sources. Section I: Confirm the 1/r 2 property of light Using a light bulb, a meter stick, and a light meter, make measurements of the brightness of the bulb at various distances from the bulb. Keep a table of the reading of the light meter for each distance. Using your calculator, take the log of the distances and the light meter meter reading and make a plot of log (distance) vs. log (reading). Draw a straight line through your data points and measure the slope of this line. The slope represents the exponent of r. You should come close to -2.0 (note: r 2 is the same as 1/r 2 ). Section II: Use the 1/r 2 property of light to determine the wattage of unknown bulbs Using sets of light bulbs (some with a known wattage and some with unknown wattages), a meter stick, and a paraffin photometer, you will determine the wattage of the unknown bulbs. The paraffin photometer is used to determine when two bulbs appear to shine with equal brightness. First you will confirm that the paraffin photometer works as it should, then you will test the theory, then you will carry out your measurements of the unknown wattage bulbs. Confirm this use of the photometer using a pair of identical wattage bulbs, one on either side of the paraffin block. When the bulbs are at equal distances from the block, both sides will appear equally bright. If one is closer, the paraffin block will appear brighter on that side. Now, try it with a 40 watt and a 60 watt bulb. How do the distances from each bulb to the center of the paraffin block compare? If the halves of the block shine with equal brightness, then they are receiving equal flux from the bulbs. This means that flux 40watt = flux 60watt. Since flux = intensity r 2, intensity 60 r 2 60 = intensity 40 r 2 40 Plug your values for the distances from each bulb to the center of the paraffin into the equation and see if this relation holds. Now that you ve confirmed both the apparatus and the theory, use a known wattage bulb and one of the four bulbs of unknown wattage. Set them at distances from the paraffin so that both sides are of equal brightness. Use the above relation to determine the wattage (or intensity) of the unknown bulb (note: use the wattage of the bulb as the intensity). Be sure to record the number of the unknown bulb 10
written on the attached masking tape. Now repeat the procedure for the other unknown bulbs. Be very careful removing the bulbs from the sockets as they will be very hot. In your report, sum up what you have learned about the relationship between the intensity of a light source, and how its apparent brightness varies with distance. Describe how this relationship might be used to determine the true brightness of a distant star. The results from each group will be written on the board. Discuss how well the groups results agreed. Discuss how this situation is similar to that encountered in real scientific investigations. 11
VLab 14: Neutron Stars and Pulsars This lab surveys basic characteristics of neutron stars and pulsars. placed upon the period and period change of pulsars. Special emphasis is Learning Objectives: Students should have a good grasp of the characteristics of a pulsar and understand the special importance of period and the spin-down rate. VLab 16: Astronomical Distance Scales Distances are crucial in astronomy. This lab introduces the units used by astronomers to measure large distances (astronomical units, light years, and parsecs) and illustrates some methods such as parallax and Cepheid variables by which distances may be determined. Learning Objectives: Students completing this laboratory should understand the basic distance units used in astronomy and how to convert between them, the method of parallax, and the method of using Cepheid period-luminosity relations to determine astronomical distances. VLab 17: Evidence for Dark Matter There is strong evidence that the major fraction of the matter contained in the Universe does not interact significantly with normal matter, except through gravitation. This lab introduces the concept of such dark matter and explores two types of observations suggesting the existence of unseen matter in large amounts: galaxy rotation curves and gravitational lenses. Learning Objectives: Students completing this lab will have a quantitative understanding of how galaxy rotation curves and gravitational lensing may be used to determine the total mass in a region of space, and how both techniques suggest the presence of far more mass in the Universe than can be explained by the visible mass. 12