Lab Title: Studying Solar and Lunar Eclipses Using Voyager II Equipment: Macintosh computer and the Voyager II planetarium program from Carina Software. Purpose: To learn about the differences between solar and lunar eclipses. Requirements: This lab is to be performed individually (or in groups of no more than two if there are not enough computers). If you must work in pairs, take turns manipulating the computer and taking the data. You should switch off from time to time so everyone gets a chance to use the computer. Although you may use the computer and the program with your partner to collect data, all calculations, graphing, and any narratives in your lab report must be your own original work! At the end of the lab write-up, you will find a Project Report form on which to do all of your work. Hand in only the Project Report form (including any additional sheets of paper if you need to) along with any computer printouts requested in the lab write-up. Do NOT hand in the lab write-up itself! -1-
Introduction: COVER UP: SOLAR ECLIPSE CONDITIONS As the Moon revolves about the Earth, it sometimes passes between the Earth and the Sun. When this happens a solar eclipse results. As you can see from the Figure 1, a necessary condition for a solar eclipse is that the Moon be in a new phase. But although the Moon goes through the new phase once each month, there is not a solar eclipse each month. This implies that the Moon does not usually pass directly between the Earth and Sun at new moon. Sun Earth Umbra Eclipse Path Cross Section of the Moon's Shadow Penumbra Figure 1. Solar Eclipse Geometry Usually at new Moon, the Moon passes either above or below the Sun. Hence, the Moon being in a new phase is a necessary but not a sufficient condition for a solar eclipse. The other required condition for a total solar eclipse is that the Moon must pass directly between the Earth and Sun, which can happen only if the Moon is in the ecliptic plane. The reason that the Moon is not always in the ecliptic is that the Moon's orbital plane is inclined to the ecliptic plane by about 5 degrees. Just as the Earth's shadow has two parts, so does the shadow of the Moon. The inner, darker region is called the umbra and the outer, lighter region is called the penumbra. Figure 2 shows the possible types and duration of solar eclipses. Notice that the Moon's shadow covers a relatively small area on the Earth's surface. Only those few people who are in the shadow region will actually see a solar eclipse. Individuals in the penumbra will see a partial solar eclipse while those in the umbra will view a total solar eclipse. The -2-
Moon's shadow sweeps across the Earth's surface from west to east, and a solar eclipse is seen at different times by people at different locations. The path traveled by the Moon's umbra is known as the solar eclipse path. A. Longest Duration B. Shortest Duration C. Annular Eclipse Figure 2. Solar Eclipse Types and Duration Because the Moon revolves about the Earth in an elliptical orbit, its distance from the Earth varies. When the Moon is close to the Earth its apparent size is larger than when it is far from the Earth. If a solar eclipse occurs when the Moon is close, its apparent size will be somewhat larger than that of the Sun, the solar eclipse path will be wider, and the duration of the solar eclipse will be longer (Figure 2, A). The maximum possible duration of totality is around 8 minutes. The reverse is true when the Moon is far from the Earth (Figure 2, B). From time to time the Moon can be so far away that its apparent size is less than the Sun's. When this happens, the Moon does not completely cover up the Sun, and a ring (annulus) of sunlight remains visible around the Moon. This type of solar eclipse is called an annular eclipse (Figure 2, C). The outermost part of the Sun's atmosphere, the corona, is a very faint, tenuous gas that is difficult to observe with ground-based telescopes except during a total solar eclipse. For this reason, astronomers have historically gone to great lengths and great distances to observe solar eclipses. Now that orbiting instruments have made it possible to produce artificial solar eclipses with some ease, the scientific importance of natural solar eclipses is not quite as great. However, the esthetic aspects of solar eclipses still make them one of the most striking and exciting of astronomical events. -3-
Procedure: Your instructor will inform you about which computers on campus currently have the program installed on their hard drives. Position the mouse cursor arrow over the icon (picture) of the Mac's hard disk and double click on the mouse button. A list of the contents of the hard disk will appear. Move the mouse cursor over the Astronomy 30 folder's icon and again double click the mouse button to reveal the contents. Clicking the mouse button twice when the cursor arrow is on the picture of the Voyager folder will open the folder and reveal a picture (icon) of the program itself called Voyager II in the file list. Position the mouse cursor over the Voyager II icon and double click to run the program. SET LOCATION AND TIME Set your location to the nearest major city to your school: Control Set Location Location Lists... Scroll to City in Major Cities dialog window Highlight city and Double Click or press return Control Define Horizon... Select Use Standard Horizon For now, you do not have to change the date and time. Use whatever values Voyager has entered. PREDICTING SOLAR ECLIPSES If the angular separation between two celestial objects is small and they therefore appear close together in the sky, they are said to be in conjunction. To determine the dates and times of solar eclipses you will search for conjunctions between the Moon and Sun. Chart Chart Coordinates Local Horizon Chart Chart Coordinates 180 Projection to 180 Time Step 2 minutes in the Control Panel Click to view Planet Panel On the left side of the Planet Panel is an area containing 16 little symbol boxes. From left to right in the first row, these symbols represent the Sun, Mercury, Venus, and Earth. Under these are the symbols for Mars, -4-
Jupiter, Saturn, and Uranus. The next-to-the-last row has Neptune, Pluto, the Moon, and the Earth's (or the Moon's) shadow. Notice that the planets' symbol boxes are ordered according to their distance from the Sun. When these symbol boxes are black, the corresponding objects can be viewed. Note that above, only the Sun and Moon symbol boxes are turned on (black), so only the Sun and Moon will be visible and the planets will not be visible. You can turn off objects by clicking on each symbol one at a time or by holding down the mouse button and dragging across the symbols so that the cursor acts like an eraser. Clicking once on a turned off (white) symbol box will turn it on (black). When you double click on a symbol box, that object is centered on the screen. Double click on the Sun symbol to center the Sun. You will find that when you center an object, that object's symbol appears in the Lock box. Click the Lock box and it turns black meaning that object will always remain centered on the screen. The Lock box containing the Sun's symbol is also black and hence the Sun will always remain centered on the screen. When the Lock box is not black, an object will not remain centered. Turn off all planets Turn ON only Moon and Sun Center (Double click) Sun Lock Sun Options Conjunction Search... Conjunction Search dialog window Select Sun and Moon Search From This Year Search To Next Year Separation 0.50 degrees Click Search As the search proceeds, the date and time of each conjunction (possible solar eclipse) is displayed. Note that the separation angle you entered in the Conjunction Search dialog window is an upper limit so that the list will contain all conjunctions with a separation angle less than or equal to this number. -5-
The type and visibility of a solar eclipse may be different at different locations on the Earth. If your search did not find any total or partial solar eclipses that were above your local horizon, it might be that there were none in the specified time interval. Try a longer time interval from this year onward. Keep extending the ending year search date until you find one that IS visible above your local horizon! An asterisk (*) next to a conjunction date indicates that one or both objects are below the horizon at your particular location when the conjunction takes place. If this is the case, all or some of the solar eclipse will NOT be visible from your location. If you wish to stop the search before it is completed you can click the Cancel button. Double click on the listed conjunction to display the sky with the objects centered on the screen. You can also highlight the listed conjunction and click the Set Time button. When your search is completed, to 5 and look at a few of the possible solar eclipse dates (conjunctions) that are above the horizon at your location and use the advance time (+) and/or the reverse time ( ) arrows in the Control Panel to watch the motion of the Moon near its new phase. To stop the motion, click once anywhere else in the Sky Chart window. To determine more accurately when a solar eclipse begins and ends, you may want to shorten the Time Step to 1 minute. Project Result 1: Hand in a printout showing the next solar eclipse occurring nearest today's date (from today ONWARD) that is visible above the horizon at your location and answer the related questions. But, before you make a printout select: File Print Options... Select Use Black Stars with White Sky Click OK or press return To print the Voyager screen, choose: File Print Sky Chart... Click OK or press return Note that since you are using a white sky, the new Moon will appear white and the Sun will appear black on your printout! Clearly label the Sun and the Moon. Project Result 2: Search for all solar eclipses beginning this year over the next 20 years with a separation of 0.50 or less during this time interval. Divide the total number (including those below your local horizon) of these Sun-Moon conjunctions (solar eclipses) you found by 20 to find an estimate for the average yearly frequency of all types of solar eclipses. -6-
THE SOLAR ECLIPSE OF JULY 1991 A relatively long solar eclipse visible from the northern hemisphere took place in July 1991. The eclipse path passed over one of the largest observatories in the world, situated on top of an extinct volcano. To view this solar eclipse from this site, Mauna Kea, Hawaii: Control Set Location Location Lists... Scroll to Mauna Kea in the Major Cities dialog window Highlight city and Double Click or press return Control Set Time Local Mean Time... Set Local Mean Time dialog window 7/11/1991 AD 6:20 AM Daylight Saving Time OFF Click OK or press return Time Step 5 minutes Field Center on Planet Sun Click to display Planet Panel Sun and Moon ON Center Sun Lock Sun Chart Chart Coordinates Local Horizon Chart Chart Coordinates 180 Projection to 5 Project Result 3: Use the advance time (+) and/or the reverse time ( ) arrows in the Control Panel to watch the eclipse. To determine more accurately when the eclipse begins and ends, you may want to shorten the Time Step to 1 minute. Hand in a white sky printout showing the solar eclipse as the Moon passes in front of the Sun as viewed from Mauna Kea, Hawaii and answer the related questions. Clearly label the Sun and the Moon on your printout. Project Result 4: The type and visibility of a solar eclipse may be different at different locations on the Earth. Repeat for La Paz, Mexico which is located on the southernmost tip of the Baja peninsula. Clearly label the Sun and the Moon. Project Result 5: The type and visibility of a solar eclipse may be different at different locations on the Earth. Repeat for San Francisco, California. Clearly label the Sun and the Moon. -7-
FROM THE MOON'S POINT OF VIEW With Voyager you can view a solar eclipse from the Moon and see the solar eclipse path as the Moon's shadow sweeps across the Earth's surface. Control Observe from Planet... Moon Control Set Time Universal Time... Set Universal Time dialog window 7/11/1991 AD 17:00 hours Click OK or press return Time Step 2 minutes Earth On Moon's Shadow On (the symbol just to the right of the Moon's symbol) Double click Earth to Center Lock Earth to 2 Project Result 6: Use the advance time (+) and/or the reverse time ( ) arrows in the Control Panel to watch the Moon's shadow move across the Earth. To determine more accurately when the shadow crosses a particular location, you may want to shorten the Time Step. Complete the sketch for the direction of motion of the small dark umbra of the Moon's shadow and note the approximate Universal Times that the shadow crosses Mauna Kea, Hawaii and then La Paz, Mexico. -8-
SHADOWING THE MOON: LUNAR ECLIPSE CONDITIONS When the Moon is in a full phase, it sometimes passes through the Earth's shadow. When this happens, a lunar eclipse occurs (see Figure 3). But although the Moon goes through the full phase once each month, there is not a lunar eclipse each month. Generally, the Moon passes either above or below the shadow. Hence, the Moon being in a full phase is a necessary but not a sufficient condition for a lunar eclipse. Sun Cross Section of the Earth's Shadow Umbra Penumbra Figure 3. Lunar Eclipse Geometry The other required condition is, of course, that the Moon must pass through the Earth's shadow, which can happen only if the Moon is in or close to the Earth's orbital plane. This plane, called the ecliptic derives its name from the requirement that the Moon be near the plane for a lunar eclipse to occur. The reason that the Moon is not always in the ecliptic is that the Moon's orbital plane is inclined to the ecliptic plane by about 5 degrees. The Earth's shadow has two parts. The inner, darker region is called the umbra and the outer, lighter region is called the penumbra. Neither the umbra nor the penumbra is completely dark because the Earth's atmosphere scatters sunlight into the shadow. During a lunar eclipse, the Moon darkens and becomes redder, but does not completely disappear. Figure 4 shows the possible types of lunar eclipses. When the Moon is in the penumbra, only a very small darkening occurs, so penumbral lunar eclipses are difficult to detect with the naked eye. It is partial and total umbral lunar eclipses that are most easily seen. -9-
Partial Penumbral Eclipse Partial Umbral Eclipse Total Umbral Eclipse Total Penumbral Eclipse No Eclipse Figure 4. Types of Lunar Eclipses SET LOCATION AND TIME Set your location to the nearest major city to your school: Control Return to Earth Control Set Location Location Lists... Scroll to City in Major Cities dialog window Highlight city and Double Click or press return For now, you do not have to change the date and time. Use whatever values Voyager has entered. PREDICTING LUNAR ECLIPSES To determine the dates and times of lunar eclipses, you will search for conjunctions between the Moon and the shadow of the Earth. Chart Chart Coordinates Local Horizon Chart Chart Coordinates 180 Projection to 180 Time Step 4 minutes in the Control Panel Click for Planet Panel -10-
Moon ON Earth's Shadow ON Center (Double click) Earth's Shadow Lock Earth's Shadow Options Conjunction Search... Conjunction Search dialog window Select Moon and Earth's Shadow Search From This Year Search To Next Year Separation 1.0 degrees Click Search As the search proceeds, the date, time, and angular separation of each conjunction are displayed. The type and visibility of a lunar eclipse may be different at different locations on the Earth. If your search did not find any total or partial umbral lunar eclipses that were above your local horizon, it might be that there were none in the specified time interval. Try a longer time interval from this year onward. Keep extending the ending year search date until you find one that IS visible above your local horizon! An asterisk (*) next to a conjunction indicates that one or both objects are below the horizon at your location when the conjunction takes place. If this is the case, all or some of the lunar eclipse will not be visible from your location. If you wish to stop the search before it is completed, you can click the Cancel button. Double click on the listed conjunction to display the sky with the objects centered on the screen. You can also highlight the listed conjunction and click the Set Time button. When your search is completed, to 10 and look at a few of the possible lunar eclipse dates (conjunctions) that are above the horizon at your location and use the advance time (+) and/or the reverse time ( ) arrows in the Control Panel to watch the motion of the Moon near its full phase. To stop the motion, click once anywhere else in the Sky Chart window. To determine more accurately when the Moon enters and leaves different parts of the Earth's shadow, you may want to shorten the Time Step to 1 minute. -11-
Project Result 7: Hand in a printout showing the next lunar eclipse occurring nearest today's date (from today ONWARD) that is visible above the horizon at your location and answer the related questions. Be sure to make a White Sky printout as you did in Project Result 1. Note that since you are using a white sky, the full Moon will appear black and the eclipsed Moon will appear white on your printout! Clearly label the Moon and both the umbra and the penumbra of the Earth's shadow. Project Result 8: Search for all lunar eclipses beginning this year over the next 20 years with a separation of 1.0 or less during this time interval. Divide the total number (including those below your local horizon) of these conjunctions (lunar eclipses) you found by 20 to find an estimate for the average yearly frequency of all types of lunar eclipses. FROM THE MOON'S POINT OF VIEW, AGAIN With Voyager you can also view a lunar eclipse from the Moon and watch the Earth pass in front of the Sun. Control Observe from Planet... Moon Control Set Time Universal Time... Set Universal Time dialog window 12/21/1991 AD 7:30 hours Click OK or press return Time Step 2 minutes Earth On Sun On Center (Double click) Sun Lock Sun to 5 Project Result 9: Use the advance time (+) and/or the reverse time ( ) arrows in the Control Panel to watch the Earth move across the Sun. To determine more accurately when the eclipse begins and ends, you may want to shorten the Time Step. Hand in a printout showing the lunar eclipse just before the Earth passes in front of the Sun as viewed from the Moon and answer the related questions. Be sure to make a White Sky printout as you did in Project Result 1. Note that since you are using a white sky, the Sun will appear black on your printout! Clearly label the Earth and the Sun. -12-
Project Report Studying Solar and Lunar Eclipses Name: Lab Partners: Date: PROJECT RESULTS 1. Printout showing the next solar eclipse nearest to today's date (from TODAY ONWARD) that is above your local horizon. Clearly label the Sun and the Moon. A. Solar eclipse data (Local Time and Date) City Longitude (W, E) Latitude (N, S) Date Type of solar eclipse Start of solar eclipse Middle of solar eclipse End of solar eclipse B. About how long did the solar eclipse last? If the solar eclipse was total, estimate the duration of totality, that is, the time that the Sun was totally covered by the Moon. 2. Solar eclipse frequency A. Time interval of search = years -13-
B. Separation angle = degrees C. Total number of all solar eclipses for the next 20 years = D. Average yearly frequency of solar eclipses = per year. 3. Printout of the July 1991 solar eclipse as viewed from Mauna Kea, Hawaii A. Solar eclipse data (Local Time and Date) City Longitude (W, E) Latitude (N, S) Date Type of solar eclipse Start of solar eclipse Middle of solar eclipse End of solar eclipse B. About how long did the solar eclipse last in Mauna Kea from beginning to end? If the solar eclipse was total, estimate the duration of totality, that is, the time that the Sun was totally covered by the Moon. C. Draw an arrow on your printout showing the apparent path of the Moon before, during, and after the solar eclipse as viewed from this location. 4. Printout of the July 1991 solar eclipse as viewed from La Paz, Mexico A. Solar eclipse data (Local Time and Date) City Longitude (W, E) Latitude (N, S) Date Type of solar eclipse Start of solar eclipse Middle of solar eclipse End of solar eclipse -14-
B. About how long did the solar eclipse last in La Paz from beginning to end? If the solar eclipse was total, estimate the duration of totality, that is, the time that the Sun was totally covered by the Moon. C. What are the angular sizes of the Sun and the Moon during the total solar eclipse in La Paz? (Clicking in the center of each object will bring up a Data Window with information that will help you.) Angular size of Moon = arc minutes (') Angular size of Sun = arc minutes (') D. If the solar eclipse in La Paz had instead been an annular eclipse, how would the two angular sizes shown above have compared? Which one of the angular sizes would have changed? Why? 5. Printout of the July 1991 solar eclipse as viewed from San Francisco A. Solar eclipse data (Local Time and Date) City Longitude (W, E) Latitude (N, S) Date Type of solar eclipse Start of solar eclipse Middle of solar eclipse End of solar eclipse B. About how long did the solar eclipse last in San Francisco from beginning to end? If the solar eclipse was total, estimate the duration of totality, that is, the time that the Sun was totally covered by the Moon. C. Describe the differences between the view of the July 1991 solar eclipse from San Francisco and the view from Mauna Kea, Hawaii. -15-
6. July 1991 solar eclipse as seen from the Moon A. Sketch the path and direction of motion of the small dark umbra of the Moon's shadow on the map below. Show the eclipse path and indicate with an arrow the direction of motion of the Moon's umbral shadow on the picture of the Earth's surface: B. Illumination of the Earth % Phase of the Earth C. Universal Time that the umbra of the Moon's shadow crosses Mauna Kea, Hawaii UT La Paz, Mexico UT D. Knowing that the distance from Mauna Kea to La Paz is 2970 miles, use the time difference between Mauna Kea and La Paz from part C to calculate approximately how fast (in miles per hour) that the shadow of the Moon moves across the Earth's surface. Show your work below. -16-
7. Printout showing the next lunar eclipse nearest to today's date (from TODAY ONWARD) that is above your local horizon. Clearly label the Moon and both the umbra and the penumbra of the Earth's shadow. A. Lunar eclipse data (Local Time and Date) City Longitude (W, E) Latitude (N, S) Date Type of lunar eclipse Moon entered: Penumbra at Umbra at Mid lunar eclipse time Moon left: Umbra at Penumbra at B. About how long was part or all of the Moon in the Earth's shadow regions? C. About how long was part or all of the Moon in the smaller umbra? D. Recalling that the apparent angular diameter of the Moon is about 0.5 degrees, use your printout of this lunar eclipse to estimate the angular diameter of the umbra and of the penumbra in degrees. Show your technique and work directly on the printout using a metric ruler to make the necessary measurements. Angular diameter of umbra degrees Angular diameter of penumbra degrees -17-
E. The Moon moves eastward about one-half a degree per hour. If the Moon passed directly through the center of the Earth's shadow, how long would the Moon remain completely within the umbra? Show your work below. Time in umbra How long would the Moon remain completely within the penumbra? Time in penumbra 8. Lunar eclipse frequency A. Time interval of search = years B. Separation angle = degrees C. Total number of all lunar eclipses for the next 20 years = D. Average yearly frequency of lunar eclipses = per year. E. Divide your result for question 8D by your result for question 2D to see how the average yearly frequency of lunar eclipses compares to the average yearly frequency of solar eclipses. F. Which type of eclipse happens more often? -18-
9. Printout of the December 1991 lunar eclipse as viewed from the Moon. Clearly label the Earth and the Sun. A. Use your printout of this lunar eclipse to estimate the angular diameter of the Earth when viewed from the Moon using the fact that the angular diameter of the Sun is about 0.5 (= 30 arc minutes). Show your technique and work directly on the printout. Angular diameter of Earth degrees B. Illumination of the Earth % Phase of the Earth C. Universal Time that the Earth First starts to pass in front of the Sun UT Completes its trip across the face of the Sun UT D. Carefully study the relative sizes of the Sun and the Earth during the eclipse. Can there be an annular lunar eclipse? Why or why not? -19-
Conclusions and Comments -20-
Name: Lab Partner: Pre-lab Exercises: Studying Solar and Lunar Eclipses Using Voyager II 1. Carefully define each of the following terms: (a) Penumbral shadow (b) Umbral shadow (c) Ecliptic (d) Line of Nodes (e) Annular eclipse 2. (a) Describe the apparent motion of the Earth through the lunar sky as viewed from a point on the surface of the Moon that is facing the Earth. (Remember that the Moon always presents the same side toward the Earth because it's gravitationally locked into a 1:1 spin-orbit resonance.) (b) Would you always see the same side of the Earth from the Moon? Why or why not? -21-
3. Does the Earth go through phases when viewed from the surface of the Moon? Why or why not? 4. Viewed from Mare Imbrium on the surface of the Moon, the Earth: (i) rises and sets every 24 hours, (ii) is always below the horizon, (iii) is always at the same place in the sky but goes through monthly phases, (iv) rises and sets every 29.5 days. Which of the above choices are true? Why? 5. The Sun is actually 400 times larger in diameter than the Moon but in a remarkable cosmic coincidence it happens that the Sun is also 400 times farther away from the Earth than the Moon. As a consequence, the Sun and the Moon appear to be the same size in the sky when viewed from the Earth! (a) The diameter of the Earth is 12,800 km and the diameter of the Moon is 3400 km. How many times larger is the Earth than the Moon? -22-
(b) Use a drawing compass and a metric ruler to make three circles below showing the correct relative sizes of the Sun, the Moon, and the Earth as viewed from different vantage points. Make the Sun (as viewed from either the Earth or the Moon) a circle of diameter 2 cm (about the size of a nickel): The Moon as viewed from the Earth: The Earth as viewed from the Moon: -23-