APAS Laboratory 1 Planetary Motions PLANETARY MOTIONS
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1 APAS Laboratory 1 Planetary Motions PLANETARY MOTIONS SYNOPSIS This computer exercise is intended not only to help you understand the motions of the planets around the Sun, but also to appreciate why our ancestors were confused by the manner in which they wander across the sky. EQUIPMENT: Macintosh computer, Voyager II program, Planetary Motions folder. You will be using the Voyager II planetarium program on a Macintosh computer If you are already familiar with Macs, operation of the program should be straightforward and intuitive. If you re accustomed to PCs and Windows, there are only a few subtle differences between the way Windows and Macintosh controls behave. And if you ve never used computer programs before, now is a great time to learn! Although you may struggle for awhile, don t worry - the use of mouse clicks, menu bars, and dialog boxes will soon become second nature. Part I. Introduction The behavior of planetary motions confounded humanity for over two thousand years, simply because it was believed that the Earth was the center of the universe (the geocentric view). Not until the 16th century was a heliocentric (Sun-centered) hypothesis proposed by Copernicus, with details refined by Kepler (including elliptical rather than circular orbits), and ultimately explained by a few physical laws devised by Newton. Our problem today is just the reverse: we were all taught the right answer in grade school - that the planets orbit the Sun - and were (hopefully!) made to memorize the order in which they do so: Mercury, Venus, Earth, Mars, etc. Few people, however, ever take the time to actually watch a planet move across the sky, much less try to explain that motion in terms of what we supposedly know to be true. As a result, we are amused and amazed at our ancestors seemingly ridiculous ideas about planets attached to spheres rolling on spheres, small circles (epicycles) attached to large circles (deferents) pivoting on off-center axles (equants). By the time you ve finished this exercise, you ll have gained a little more respect for your elders! Starting the Program - On the computer screen, find the folder icon labelled Planetary Motions. Position the cursor over the icon, and double-click the mouse button (depress and release it rapidly twice in succession) to open the folder as a window showing its contents. Then double-click the icon labelled Here and Now, and confirm that it is OK to proceed. The Voyager II program will load, and present you with a screen showing the current view of the western sky as seen from Sommers-Bauch Observatory - except that the stars remain visible in the daylight, constellation stick-figures really only exist in our imagination, and planets don t actually come with labels! You can use the scroll-bars at the bottom and right sides of the screen to observe in other directions - just click on the corner arrows - or alternatively, position the cursor on a slider, hold down the mouse button, and drag the slider along its rail. Take a look around, and find answers to the following questions:
2 APAS Laboratory 2 Planetary Motions I.1 Name an object (constellation, star, planet) currently setting behind the mountains. I.2 Name an object (constellation, star, planet) currently rising above the Eastern horizon. I.3 Name one object that is close to the zenith (the point straight overhead). I.4 If the Big Dipper in the constellation of Ursa Major were a real dipper, could it hold water right now, or would it spill out? I.5 What constellation is the Sun in, or near? I.6 What planets are above the horizon? (Hint: look along the dashed-line of the ecliptic, the path along which the Sun appears to travel around the sky once each year.) I.7 Is the Moon up? If so, what phase is it in, and where is it located? You can now access additional settings, or viewing circumstances, that have been preprogrammed to re-create interesting sky situations from the past, present, or future. From these starting points, you can turn on or off items such as planets, stars, trails, constellation figures, coordinate lines, labels, etc. You can select and follow objects of interest, or gaze at a fixed location in space. Time can run fast, slow, or even backwards. It s possible to travel to other locations on the Earth, hop to another planet, or even float around in interplanetary space. Loading a Setting - To open a setting, do the following: use the mouse to position the cursor over the word File in the Menu Bar across the top of the screen, and then hold down the mouse button. A drop-down sub-menu appears. Without releasing the mouse button (those accustomed to Windows will find this unusual), slide the cursor downward to the words Open Setting..., which will darken. Release the mouse button, and the option has been selected. Any menu item followed by... implies that a dialog box will appear giving you further selections. In this case, the box offers you a choice of settings from the Planetary Motions folder. Now click the mouse on the words Lion Tracks (the selection will darken), and then click the button marked Open. The computer will automatically load the settings and configure the planetarium display accordingly. In the future, whenever we say open setting Such-and-Such, we ll mean to repeat the above procedure: bring down the File sub-menu, select the Open Settings option, and then select and open Such-and-Such. In shorthand notation: {File Open Settings Such-and-Such}. Part II - Lion Tracks Take a moment to get oriented to the new scene presented to you. The constellation of Leo the Lion is centered in the view. Directions are as you would expect: North is up, South is down, West is to the right, East to the left. There s also a couple of boxes floating in space.
3 APAS Laboratory 3 Planetary Motions The Control Panel box gives you date and time information, and allows you to manipulate time itself. If the box is in the way, it can be moved to another part of the screen by positioning the cursor on the name bar at the top, depressing the mouse button, and dragging the box to a new location. II.1 What date and time we are starting with? The Step Forward button instructs the computer to calculate and display the next time-step interval and then stop. Click it now. II.2 How much time did you advance? The Run Forward button causes the computer to calculate and display successive time increments as fast as computations allow. The cursor changes to a spinning globe to remind you that time is passing. Click the Run Forward button to start the simulation. For some time, not much happens, except that the control panel keeps track of the changing time. That s because none of the objects selected by the Planet Panel to be shown (Mars, Jupiter, and Saturn) have yet to appear. Note that with the computer, it is possible for us to keep a constant year-round watch on Leo - we have eliminated bothersome details such as mountains blocking our view, rotating skies, or getting drowned out by bright sunlight. But be ready! After about a year goes by, the red planet Mars suddenly streaks into view. When this happens, click the mouse button (anywhere on the screen) to halt time. Note that the planet s name appears whenever the simulation is stopped, and that its path against the stars is shown since the Paths button in the planet panel has been set. Start up the simulation again by clicking the Run button. A second planet appears shortly, then a third. You can start and stop the simulation as many times as you wish, back time up (by using the corresponding - Step and Run buttons), or repeat the entire scenario as many times as you wish by re-loading the setting {File Open Settings Lion Tracks}. The whole scene eventually plays out by the end of Now you can appreciate what ancient astronomers were attempting to understand and explain - and perhaps you ve concluded that they really weren t crazy after all! But let s look at the motions of the planets more closely, and see if we can find any patterns. II.3 II.4 Overall, do the planets meander everywhere, or do they tend to stay within a fairly narrow band running across the sky (the Zodiac, centered on the ecliptic)? Generally, do the planets move, with respect to the stars, from East to West, or West to East (called prograde motion)?
4 APAS Laboratory 4 Planetary Motions Occasionally, the planets exhibit a bizarre behavior: they appear to stop dead in their tracks, and then reverse direction for awhile - called retrograde motion. Some of the resultant loops are somewhat circular or open, while others appear to be zig-zags, like a circle seen edge-on. II.5 II.6 II.7 II.8 II.9 Which of the three planets moves most rapidly across the sky? Which is the slowest? Which of the three planets throws the biggest loop? Which makes the smallest? Which of the three planets has the longest time between the start of one retrograde loop and its next? Which has the shortest interval between loops? (You ll probably need to run the simulation at least once again and keep a close watch on the time.) Which of the three planets, according to what you have you been taught in school, actually orbits closest to the Sun and the Earth? Which is furthest away? Summarize any correlation that might exist between your answers to questions II.5, through II.8. Part III - Apparent Motion of a Superior Planet: Mars To help you make sense of these apparent motions of the planets in the sky, open the setting Mars (Superior Planet) - remember: {File Open Settings Mars}. Mars is called a superior planet, which simply means that its orbit lies farther from the Sun than the Earth. The time is right now, and the view is from a point floating in space, far above the North pole of the Sun, looking back down at the solar system. For simplicity, the scene excluded everything except the Sun, Earth, and Mars. No human being, or even spacecraft for that matter, has actually witnessed this view - it exists only in our mind s eye (and of course, on the computer display) as a reconstruction of what astronomers have deduced about how the Sun and planets are arranged. Start time by clicking the Run Forward button, and take a minute to watch how the planets move. III.1 III.2 As seen from our view looking down from the North, which direction, clockwise or counter-clockwise, do the planets orbit around the Sun? Which planet, Earth or Mars, moves faster through space in its orbit? In addition, which has the shorter distance to travel? As a result, which planet completes a full lap sooner (i.e., which has the shorter year)? There are two arrangements where the two planets line up in a straight line with the Sun: in the order Mars-Sun-Earth (called a conjunction, since from Earth, both Mars and the Sun lie in the same direction in space); and Sun-Earth-Mars, called opposition, since we on Earth would have to look in a direction directly opposite the Sun to view Mars. The motions appear to be straightforward, since we are keeping our gaze fixed on the Sun. But we really ride on the Earth, so let s shift our attention to it. First, click anywhere to stop the simulation, and then double-click the green Earth symbol (it looks like ) on the Planets Panel. the display will then indicate that our view is now locked (centered) on the Earth. Next, click the Clear button on the panel, which erases the old planet paths. Now continue to Run the simulation. Note that the planetary motion is exactly the same as before. Although the Sun and Mars now appear to move around the Earth, the paths of the planets prove otherwise.
5 APAS Laboratory 5 Planetary Motions III.3 III.4 When (at opposition or at conjunction) is Mars closest to the Earth? When is it most distant? In which case (opposition or conjunction) is Mars most easily visible to us on the Earth? Explain your reason(s). Continue to run the simulation until the Earth lies directly in a straight line between the Sun and Mars at opposition; then halt the motion. Now let s make the full leap to the Earth s point of view: instead of floating above the Sun, we will switch to a vantage point that is always directly over, and moves with, the Earth. Under the menu item Control, select the sub-menu item Observe from Planet.... Click on the box labelled Sun, slide the mouse down the new menu to the word Earth, and then release - in shorthand, {Control Observe From Planet... observe from: Earth}. Click OK to close the box. Once again, the arrangement is exactly as it was before - the date is the same, with Mars in opposition - but watch what happens when you click the Run button! Now, the paths show how Mars and the Sun appear to move, for observers attached to a stationary Earth. III.5 At which configuration (conjunction, opposition) does a superior planet appear to undergo retrograde motion? III.6 Imagine that the planets are on a racetrack around the Sun. Explain the statement: retrograde motion occurs each time the innermost, or inferior, planet overtakes or gains a lap, on the outer (superior) planet. Part IV - Apparent Motion of an Inferior Planet: Venus Now open the setting Venus (Inferior Planet). As before, first watch how the planets actually move, from a vantage point above the Sun. IV.1 Why doesn t the planet Venus ever get into an opposition configuration (Sun-Earth- Venus)? You ll notice, however, that there are two configurations in which the planets and the Sun do line up: Sun-Venus-Earth (called inferior conjunction), and Venus-Sun-Earth (called superior conjunction). IV.2 At either of these conjunctions, would it be easy to observe Venus while standing on the Earth? Why or why not? Now lock onto the Earth (double-click the Earth symbol in the Planets Panel), clear the planet trails, and observe the motion. IV.3 At which of the two conjunctions is Venus physically closest to the Earth? Finally, switch your viewing platform again so that it is attached to the Earth: {Control Observe From Planet... observe from: Earth}. IV.4 IV.5 At which of the two conjunctions does retrograde motion occur for an inferior planet? Does the statement made in III.6 still hold true?
6 APAS Laboratory 6 Planetary Motions Part V - The Solar System By now you ve begun to understand why planetary motions appear so confusing when observed from a moving platform such as the Earth. Just to experience the full effect, open the setting The Solar System, which includes all of the planets. First, observe the regular motion as seen with the Sun stationary. You may wish to zoom out to the outer parts of the solar system by clicking on the - Zoom button in the lower-left corner of the screen, and then return to the inner solar system using the + Zoom button. V.1 Do all planets orbit the Sun in the same direction? V.2 Do inner planets always move faster than outer planets? Now use the Observe From Planet option to watch the motions from a viewpoint fixed above the Earth. V.3 Which solar system object comes closest to the Earth at some point in time or another? V.4 Zoom out until you can see the outermost planets. Formulate an explanation for why the loops for Uranus, Neptune, and Pluto all appear to be about the same-sized circles. (Hint: remember it is the motion of the Earth that creates the appearance of the loops.) You may have realized that aliens living on other planets would experience the same phenomenon as we do: no matter which planet you observe from, all others will appear to undergo retrograde motion. To see this for yourself, view the solar system from above Mercury {Control Observe From Planet... observe from: Mercury}, and see how the solar system appears to move with time. Then then switch to a similar vantage point above Jupiter. V.5 In your opinion, who would have the easiest time figuring out that planets really orbit around the Sun: Mercurians, Earthlings, or residents of Jupiter? Defend your answer. Part VI - Lion Tracks Revisited Finally, load and run the setting Lion Tracks (Revisited), for one last look at the planets - this time with our feet back on the Earth, and including all of the planets passing through Leo, not just a select few. Just to show you re paying attention: VI.1 VI.2 VI.3 Name the two constellations of the Zodiac on either side of Leo (remember, the ecliptic, or path of the Sun, and most of the planets pass through the Zodiac constellations). Name the one lonely little planet whose motion is not confined to the Zodiac band. Explain why the size of that planet s retrograde loops appear smaller than those of the other planets. When you re done, please close up the program. First, click anywhere on the screen to stop the simulation. Then terminate the program using the bottom option, Quit, under the File menu: {File Quit }. And finally, close up the Planetary Motions folder by clicking on the button in the upper left corner of the window.
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