Exercises Using a Planisphere

Transcription

1 Astro 1H, Spring 2009 Dr. Richard Wade Exercises Using a Planisphere These Exercises use the Edmund Scientific Star and Planet Locator, an inexpensive planisphere. The Exercises gradually introduce the various ways a planisphere can be used. They will help you learn things about the sky, the motions of Sun, Moon, stars, and planets. We will work through the beginning Exercises in class, but you should gradually become skilled enough to use the planisphere on your own to do the later Exercises, and to use it for your own personal exploration of the sky. The instruction booklet that comes with the planisphere is another way to learn how to use it. Each Exercise has a Goal or Goals, and something specific to do. After you have done the specifics, reflect on whether the Exercise has helped you get closer to the Goals. Feedback is welcome, so that future versions of these Exercises can be improved! I strongly recommend taping a string or thread across the face of the planisphere, to represent the meridian line which divides the eastern sky from the west. EXERCISE 1. What s the sky like tonight? Goals: (1) to learn how to set up the planisphere to show the sky for a particular time; (2) to learn how to orient the planisphere to correspond to the real sky; (3) to learn a bit about what constellations are, and how they are distorted on the planisphere; (4) to learn how to locate the bright planets, using the table on the reverse side. To setup the planisphere for a particular calendar date and time, rotate the wheel so that the date and time line up. Be aware that the planisphere shows the sky as it appears for a particular local time, which is usually not the same as clock time (local time at State College is about 11 minutes earlier than Eastern Standard Time as shown on a clock, and you need to watch out for Daylight Savings Time!). To see what the sky looks like tonight at 8 p.m. (EST) from State College, you would want to align the wheel so that today s date matches 7:49 p.m. on the planisphere. The directions (North, South, East, West) printed on the planisphere correspond to directions on your horizon. If you are facing N, then E should be on your right, and you need to hold the planisphere so that the printing is upside down. Then the pattern of stars will correspond to what you see in the sky. The table on the reverse (upper right) gives the constellation that a particular planet will appear in, month by month. For example, where is Saturn tonight? In mid-april 2009, Jupiter is in Capricornus, close to the ecliptic. Find this area on your planisphere. Is Jupiter visible at 10 p.m. in mid-april? What time doe Jupiter rise in mid-april?

2 EXERCISE 2. What changes through the night? Goals: (1) to notice which way the stars appear to move from hour to hour; (2) to learn about the diurnal cycle of the stars, as they rise, transit, and set; and (3) to notice that some stars never set. To mimic the motion of the stars as time progresses, rotate the wheel so that the date successively lines up with later and later clock times. If you are facing South, do stars near the horizon appear to move from left to right, or from right to left? If you are facing North, which way do stars near the horizon move? Do stars appear to rise in the East, or the West? If a star rises in the Northeast, does it set in the Northwest, or in the Southwest? Concentrate on the stars in the constellation Orion. The solid white line is the Celestial Equator. How much time elapses between when an equatorial star rises, and when it sets? Do stars further South take a longer or a shorter time to cross the sky? Find some constellations whose stars never rise or set: are they in a particular part of the sky? These diurnal or daily apparent motions of things in the sky are a result of the actual motion of the Earth, spinning on its axis.

3 EXERCISE 3. Where is the Sun now, and throughout the year? Goals: To learn to use the planisphere to find the Sun s position among the stars, and to see how this changes from month to month. The dashed line on the planisphere wheel is the Sun s apparent path among the stars, called the Ecliptic. But where along this path is the Sun on any given day? To find this, set your planisphere so that it is local Noon on the date of interest. Since the Sun crosses the meridian at local Noon, the Sun s position must be where the ecliptic and the meridian line intersect at Noon. For mid-january, what constellation is this in? At Noon, the sky is bright and you can t see the stars of that constellation, but they are there all the same! (You could see them if the Sun were eclipsed.) What constellation is the Sun in during mid-february? mid-march? mid-april? Notice how from day to day the Sun appears to drift slowly EASTWARD among the stars along the ecliptic. At the same time its more rapid hour-to-hour motion is WESTWARD (along with the stars). We refer to these different apparent motions as annual and diurnal motions. They are actually due to two separate motions of the Earth: its annual revolution around the Sun and its daily (diurnal) rotation on its own axis. Use your planisphere to find the approximate date when the Sun appears to cross the Celestial Equator, moving from South to North. What date is the Sun farthest North? When does it cross the Equator moving Southwards? When is it farthest South? Have you noticed that on your birthday, the Sun is not in the constellation that corresponds to your astrological Sun Sign? This is due to precession of the Earth s rotation axis (see C&M, page 11).

4 EXERCISE 4. When is Orion due South? Goal: to learn that the stars complete one apparent rotation around the sky in less than 24 hours, so they appear to drift WESTWARD compared to the Sun. Recall that you always need to read the time of an event at the position on the rim of the planisphere that matches the calendar date. Find the constellation Orion on the planisphere wheel and place it on the meridian (when it will appear due South in the sky). Objects on the meridian are transiting from the eastern sky to the western sky. In mid-january, at what local time does Orion transit? At what time does it transit in mid-february? in mid-march? (Note that in mid-march the Sun sets at about 6 p.m. local time.) Note that each month, Orion (or any other constellation) transits 2 hours earlier than the preceding month. This is a difference of about 120 minutes, accumulated slowly over an interval of about 30 days. This is really telling us that each night, Orion (or any other constellation) transits about 4 minutes earlier than the previous night. That is, it only takes the stars 23 hours and 56 minutes to appear to revolve through a complete circle on the sky. We refer to this shortened day as the sidereal day divided into 24 (shortened) sidereal hours in contrast to the solar day of 24 (solar) hours by which we set our clocks. Note that since the stars gain about 2 hours per month compared with the Sun, then in 12 months the stars will have gained about 24 hours. In other words, the same stars would appear in the sky as appeared one year earlier at the same time of day. (That s why your planisphere is good not only in 2007, but also in other years.) Another way of saying that the stars complete one rotation in less time than the Sun, is to say that the stars drift WESTWARD with respect to the Sun. You already saw this in Exercise 3, when you looked to see what constellation the Sun was in, only then we talked about the Sun drifting EASTWARD with respect to the stars. Do you see that these are the same thing? If you prefer to think in terms of angles rather than time, the stars drift westward compared against the Sun by a bit less than 1 degree of arc per day, so that in 365 days they have drifted by a complete circle of 360 degrees. Or, the Sun has drifted eastward compared with the stars (if you prefer). Either way of describing things works, and either way, the phenomenon is a consequence of the Earth s motion around the Sun.

5 EXERCISE 5. When are the Pointer stars pointing directly down? Goals: To look again at the changing position of the stars through the night and from month to month; and to look at the part of the sky near the Pole. Hold your planisphere upside down so that the West is to the left, East to the right, and the Northern horizon is straight ahead. Find the Big Dipper, which is part of the constellation Ursa Major (the Big Bear). Two stars that form part of the bowl of the Dipper happen to point toward Polaris, the Pole Star (which is missing from your chart because of the brass grommet that holds the planisphere together at the Pole). At 9 p.m. in late January, the Pointer stars are east of Polaris. What time will they be straight above Polaris (on the meridian line)? How long does it take the Pointers to go completely around Polaris? (You already know this from Exercise 4, but try it with the planisphere anyway.) In late February, when are they straight above Polaris? In late March? Could you use the Pointer stars to tell the time, if you knew the date? Do the Pointer stars ever set? Stars that are so close to the North Celestial Pole that they don t set are called circumpolar stars. There are circumpolar stars near the South Celestial Pole that we (at 40 degrees North latitude on the Earth) never see, because they never rise above our horizon. Try to imagine what the sky looks like for someone observing from the Earth s North Pole, the Earth s equator, or from Australia. Would the Star and Planet Locator work for latitudes that are very different from 40 degrees North? EXERCISE 6. If Mercury is east of the Sun, is it a morning star or an evening star? Goals: to reinforce knowledge of directions on sky, and associate this with the sequence of rising or setting of objects. It so happens that on April 24, 2009, the planet Mercury will appear in Taurus, just south of the Pleiades star cluster. (The table on the planisphere is a bit unhelpful for Mercury, because it moves so quickly from one constellation to another. Set up your planisphere to show Noon on April 24 (this will help you locate the Sun, see Exercise 3). Is Mercury to the East or West of the Sun? Will it set before or after the Sun? What are the times of sunset and Mercuryset on April 24, 2009? Mercury is never very far from the Sun, as they appear in Earth s sky. Sometimes Mercury is to the East of the Sun, sometimes to the West. To see Mercury in a relatively dark sky, one has to have the Sun below the horizon, but Mercury above the horizon. In late April 2009, does this happen in the morning (before sunrise) or in the evening (after sunset)?

6 EXERCISE 7. How high up is the Sun at Noon? Goals: to trace the Declination of the Sun through the year, and to learn how the position of an object on the Celestial Sphere is related to its altitude when transiting the meridian. For this Exercise you will use the Meridian Scale printed on page 5 of the instruction booklet for your planisphere. This scale lets you measure the Declination of any object, provided it is on the meridian (but nowhere else in the sky, because the planisphere has some distortion of positions). The Declination of a star on the Celestial Sphere is like the Latitude of a place on Earth: it measures how far north or south of the Celestial Equator that star is. Set up your planisphere for local Noon on December 20. The Sun will be on the meridian, and of course also on the Ecliptic (as you learned in Exercise 3). Use the Meridian Scale to find the Sun s Declination on this date. For most accurate results, make sure to place the scale so that 0 corresponds to the Celestial Equator. Is the Sun north or south of the Equator? At what locations on Earth will the Sun pass overhead on this date? Now set up the situation at local Noon on June 22, and measure the Sun s Declination. Since you are in the Northern Hemisphere of the Earth, the noontime Sun is closer to overhead (it has a higher elevation or altitude) if it is north of the Celestial Equator, rather than south of it. The point directly overhead is called the zenith. To be in the zenith (at transit) as seen by an observer at latitude 40 North, an object in the sky must have a Declination of 40 North. This same relationship holds for other latitudes as well, as shown by the diagrams in the instruction booklet. Question: at what latitude on Earth would Polaris be overhead at Noon? what about Sirius? (N.B. The latitude of State College is North, so the planisphere, designed for 40, works quite well for us.) EXERCISE 8. When does the Sun rise and set? Goals: to compare the length of the day and the Noon elevation of the Sun in December, March, and June. Use the local Noon setup on December 20 to find the celestial position of the Sun on that date. Keeping track of where the Sun is among the stars, determine the local time of sunrise and sunset, and figure out the length of the day. Do this also for March 21 and June 22. How much longer is a day in mid-summer than a day in mid-winter, at 40 North? Also, for each of these three calendar dates, find the Declination of the Sun, and figure out the Sun s noontime elevation for an observer at 40 North. You did some of these measurements in Exercise 7. Remember that the elevation of an object is 90 minus its angular distance from the zenith, and the Declination of the zenith is the observer s latitude. (N.B. We will treat the terms altitude and elevation as synonymous.)

7 EXERCISE 9. Where is the summer Milky Way? Goals: to notice that the Milky Way is a great circle on the sky, and to understand the relation of this appearance to the actual situation in 3-dimensional space. The Milky Way is a faint band of light that stretches across the sky, best seen on a clear, moonless night from a dark location. The summer Milky Way passes through the constellations of Cygnus and Sagittarius. Find these star groupings on your planisphere. What other constellations does the Milky Way pass through? Can you explain the origin of the term summer Milky Way? (think about observing in the late evening!) Is there a winter Milky Way? What are some of the constellations through which it passes? Try to find the Milky Way the next time conditions are favorable! EXERCISE 10. What is the Moon s path? Goals: (1) to discover that the Moon moves (approximately) along the Ecliptic, as the Sun does; (2) to see that the Moon moves eastward among the stars from night to night, although its motion during the night is toward the west. Find the following bright stars on your planisphere: Aldebaran (in the constellation Taurus), Regulus (in Leo), Spica (in Virgo), Antares (in Scorpius). Notice that all of these stars are close to the dashed line (the Ecliptic, which is the Sun s path among the stars). The Moon sometimes occults (moves in front of) these stars, and always passes close to them in its own progression across the sky. Use the planet table on the reverse of the planisphere to find Saturn s constellation during March 2009 (it will be near the Ecliptic as well). Now use the table of Astronomical Phenomena (at the front of these Exercises) to find what objects the Moon is close to on March 11, March 17, and March 22. Using your planisphere, find these objects. Then determine which direction the Moon is moving from night to night. Does the Moon move very far (with respect to the stars) in the course of 24 hours? For the night of February 2, what is the Moon s path across the sky (i.e., relative to your horizon and zenith) from hour-to-hour? Is this in the same or opposite direction to its slower, night-to-night motion among the stars?

8 EXERCISE 11. What is the length of the sidereal month, and the synodic month? Goals: to distinguish between the Moon s motion with respect to the distant stars and its motion with respect to the Sun. This exercise can be done without using the planisphere. You will use the table of Astronomical Phenomena, and it may help to have a calendar to refer to. First, find the dates when the Moon passes Antares. What is the average number of days between one passage and the next? (The Moon s motion is slightly non-uniform, so it helps to take an average value over more than one interval.) The name we give to this interval of time is the sidereal month, after the Latin words sidereus (adj.) and sidus (n.), or star. Next, find the dates of New Moon, and figure out the average number of days between one New Moon and the next. Is the number the same or different for the time from Full Moon to the next Full Moon? The name for this time interval is the synodic month, based on the Greek prefix syn- which means together (a synod of bishops is a gathering together of bishops, for instance). The synodic month is the time interval between moments when the Sun and Moon appear together in the sky. Can you explain why the synodic month is longer than the sidereal month? (Here is where your planisphere may be useful: during one month, how has the Sun moved with respect to the stars, and how far must the Moon move to come around to the Sun s new location?) EXERCISE 12. When does the Moon rise? Goal: to learn how the time of day that the Moon rises or sets is related to the phase of the Moon. The New Moon obviously rises at sunrise and sets at sunset, since the Moon and the Sun are together in the sky at that time. Equally clear, the New Moon transits at (local) Noon. What about the Last Quarter Moon? On the date of Last Quarter Moon in March 2009, the Moon is near Antares and easy to locate on the planisphere. For this date, determine the approximate hour when the Moon transits. Your answer should be that the Last Quarter Moon transits about 6 hours (or one quarter of a day) before the Sun does. [A small technical point: on this date of Last Quarter the Moon has moved a bit past Antares, so you may not get exactly 6 hours, but something close to it.] Now use the March Full Moon (when the Moon is near Saturn) to find the time of day that Full Moons transit. Your answer should be that the Full Moon (which is halfway around the sky from New Moon) transits about one half day after the Sun does. Can you find a suitable month and object to figure out the time that a First Quarter Moon would transit, or deduce this by other means?

9 EXERCISE 13. What path is Mars following among the stars? Goals: to see that planets are not called wanderers for nothing, and to discover that the paths of planets sometimes have them moving from East to West (retrograde) against the stars, rather than prograde (West to East) as usual. Use the planet table on the reverse of the planisphere to find the constellations in which Mars appears, as the months of 2007 and 2008 (!) go by. Is Mars usually moving from West to East among the stars, or in the other direction? Which months is it moving from East to West? This motion is called retrograde, because it is backwards compared to the usual motion of the planets, the Sun, and the Moon. During the middle of its retrograde period (December 18, 2007), when did Mars transit? (Your answer will be pretty rough, but you should find a transit close to the middle of the night.) We can understand retrograde motion of Mars and other planets by considering the motion of both the Earth and the planets around the Sun, and then asking how that true motion in space corresponds to the apparent motion of the planets on Earth s sky. C&M Sections 1.1 discusses modern and ancient views of planetary motion. It is a simple but prefound prediction of the Copernican picture of planetary motion, that Mars should transit in the middle of the night when it is moving retrograde. EXERCISE 14. What s the best date to see Vega at 9 pm? Vega at 5 am? Goals: to review basic use of the planisphere, and to review seasonal changes (now that the seasons have changed!) This should be an easy review exercise for you to do on your own! The best viewing of a star or planet is when it is high in the sky (transiting), but the time of night when this happens depends on the calendar date. Your planisphere lets you figure this out. EXERCISE 15. To enjoy the Lyrid meteor shower in April, should I look in the evening or in the morning? Goal: to get thinking about actually looking for yourself, and to see that the planisphere can be used for planning observations! A few meteor showers are listed on the table of Astronomical Phenomena; Table 4.3 in C&M gives a longer list. Most showers are named after the constellation from which the meteors (or shooting stars ) appear to radiate. The Lyrids have their radiant point in Lyra. Find this constellation, and consider spending an hour or so watching Nature put on a show!