lL-llT--------T-----------------------T---------------T-------T-------T-----TrRr
>ABOUT PLANET TRACKER

 Planet tracker requires MS-DOS 3.0 or higher, a VGA or EGA monitor, and 512K
 RAM. A hard disk and math coprocessor are suggested but not required.

 An earlier version of this program was called "Planets in the Classroom." This
 greatly enhanced version was written by David Chandler in collaboration with
 Michael Zeilik for use in astronomy classes to accompany CONCEPTUAL ASTRONOMY
 (by M. Zeilik, 1st edition, 1993), ASTRONOMY: THE EVOLVING UNIVERSE (by M.
 Zeilik, 7th edition, 1994), and ASTRONOMY: THE COSMIC PERSPECTIVE (by M.
 Zeilik and J. Gaustad, 2nd edition, 1990)--all published by John Wiley & Sons.
 Teachers using other textbooks will find the program useful as well.

 Planet Tracker is distributed in the form of a self-extracting archive file
 compressed using the LHA utility Copyright (c) Haruyasu Yoshizaki, 1988-91.

>PROGRAM OVERVIEW

 Planet Tracker is the result of a collaboration between David Chandler and
 Michael Zeilik, both authors and teachers of astronomy. "Planet Tracker" was
 designed primarily with students in mind, but amateur astronomers and others
 will also find it useful as a planet calendar and self-teaching aid.

 "Planet Tracker" is a tool to investigate the laws of planetary motion and
 create printed planet charts and worksheets in a variety of useful formats.
 The program is sharply focused on concepts of planetary motion that most
 students find difficult to grasp from textbooks and chalkboard lectures alone.

 You can think of the program as a simulation of the "raw" data from which
 models of planetary motion were derived. The key to the program's usefulness,
 however, is the way it displays this information. It allows us to see
 planetary motion from vantage points that were available to Copernicus and
 Kepler only in their imaginations. You and your students will find this
 program is very easy to learn as we have been selective in its capabilities.
 All screens have instructions at the bottom. You can leave any screen by
 hitting the <Esc> key.

>ACTIVITY/LAB MANUAL

 A collection of exercises and activities is provided in a separate ASCII file
 (ACTIVITY.TXT) to suggest a few of the many possible uses in the classroom.
 You may print out ACTIVITY.TXT by typing:  PRINT ACTIVITY.TXT  at the DOS
 prompt. You are encouraged to import ACTIVITY.TXT into a word processor and
 modify it to meet your own needs. The exercises are divided into two
 categories: those using printouts only and those requiring direct student
 access to computers. There is much that can be done with printed activity
 sheets alone, but of course direct student access is preferable if possible.
 Please obtain a site license from David Chandler Co. if the program is to be
 used on multiple machines at one time or placed on a local area network (LAN).

>HOW TO GET THE MOST OUT OF PLANET TRACKER

 PLAY!
 Explore the various displays freely. In each display try the default options
 first, then experiment with variations. Watch them run. Try all combinations
 of split-screen displays. Stop and single-step the displays with the
 <Spacebar>. Type <R> to try the "Rays" option in the split-screen displays.
 Compare similarities and differences in the various viewpoints. Leave trails
 with the <T> key. Identify the planets with the <N> key. Make use of the Dates
 and Julian Day numbers to time cycles and explore the regularities (and
 irregularities) of planetary motion. Use Planet Tracker to find the planets in
 the sky at night and follow their motions. Make it a habit to look up at
+night. Predict conjunctions between the planets and alignments with bright
 stars. Print out a Zodiac Time Line and use it as a planet calendar. Peruse
 the notes given here and use your own observations as a point of departure for
 further study.

>CONFIGURATION

 The "Modify Configuration" option at the main menu allows you to select your
 printer type, and to choose the default time interval between calculations,
 and the display speed. If your computer is slow you can speed up the display
 by choosing a larger interval between calculations: 5 day jumps, for instance,
 rather than one day jumps. If your computer display is too fast for your taste
 you can limit the display speed. Either of these can be modified for
 individual runs at run time. The settings here simply modify the default
 values. Note: 0 delay means the calculations will proceed as fast as your
 computer allows.

 I you are using Planet Tracker on a monochrome VGA screen (such as a laptop
 LCD display) choosing the Monochrome option will show the planets in high
 contrast, which may increase their visibility.  It also removes their color-
 coding, so they cannot easily be recognized except by noting the characteris-
 tics of their motions or by using the naming function (the <N> key).  Even
 with a color monitor it may be a good exercise to switch to monochrome mode,
 occasionally, to practice recognizing the planets from their motions alone!

>MENUS & DATA ENTRY

 When presented with a list of options (such as the main menu), you can select
 an option using the <Arrow> keys, the first letter of the menu items, <PgUp>,
 <PgDn>, <Home>, or <End>. The <Enter> key activates the selection and the
 <Esc> key exits from the menu.

 When presented with a page of entry boxes, each box will contain a default
 entry. You can choose the default entry by typing the <Enter> key. If you want
 to enter a different value, simply start typing and the default entry will
 disappear. If you want to modify an existing value without having to re-type
 the whole thing, the first keystroke must be <Home>, <End>, <Arrow>, or
 <BkSp>.

 "Toggle" entries (such as the individual planet selections) are turned on or
 off with the <Spacebar>. When selected, a check mark will appear. When "de-
 selected" the space will be blank.

 If you want to accept all of the default entries you can jump to the bottom of
 the page with the <PgDn> key.

>DATES / JULIAN DAYS

 All the planet computations in this program give actual positions on actual
 dates. This makes the program useful both for studying the patterns of
 planetary motion and for finding planets in the sky.

 Dates are given in the Julian Calendar through October 4, 1582 and in the
 Gregorian Calendar after that date. In 1582 the day following October 4 is
 October 15.

 Julian Days (no relation to the Julian Calendar!) count consecutive days from
 a point in the distant past. Julian Day numbers are useful primarily for
 finding time intervals. To find the time between two events, simply note the
+starting and ending Julian Day numbers and subtract.

>NAMES, TRAILS, STEPS, & RAYS

 Some or all of these options are listed at the bottom of the screen while the
 animations are running. Type the indicated letter to activate the option.

 Names--The planets are color coded: Sun=Yellow, Mercury=Blue-green, Venus=
   Light Blue, Earth=Dark Blue, Mars=Red, Jupiter=Purple, Saturn=Orange.
   You can stop the action and identify each planet with the <N> key. Type <N>
   repeatedly to cycle through each name. To exit, type <Esc> or <Enter>.

 Trails--Several of the displays allow the planets to leave trails. To activate
   this feature type <T>. To turn the trails off, type <T> again.

 Steps--To freeze an animation at any point, type <Spacebar>. To step through
   an animation one increment at a time, type <Spacebar> repeatedly. Continue
   full speed animation by typing <Enter>.

 Rays--The split-screen animations allow rays to be drawn from the earth to the
   sun and planets by typing <R>. This allows for comparison of the angular
   relationships from the various points of view. To step through the animation
   with the rays active, type <R> repeatedly. Exit by typing <Esc>, leaving the
-  action stopped, or <Enter> to allow the action to resume.

 [Note: Most of the screen drawing is done in what is known in computer jargon
 as "XOR" mode. This means if a mark is drawn twice with the same color in the
 same place it will cancel itself out. That is how animation is accomplished in
 this program. The current position is canceled, then the new position is
 marked. One side-effect is sometimes the rays will partially overlap leaving a
 blank or partially blanked line. Another side-effect is that when colored dots
 overlap, the "cancellation" results in a seemingly unrelated color. These
 problems are not "bugs", per se, but rather limitations of the method.]

>ACCURACY

 Planet Tracker uses a low precision algorithm for planetary motion: mean
 orbital elements as presented in Astronomical Algorithms, by Jean Meeus. This
 method is fast and quite adequate for the purposes of the program: finding the
 bright planets visible to the naked eye in the sky within the lifetime of the
 current generation, and studying the regularities of planetary motion.
 (Uranus, Neptune, and Pluto are omitted because finding them with a telescope
 requires high resolution finder charts. Deep Space 3-D, another program by the
 same author, can be used to plot finder charts with much higher resolution.)
 The accuracy of the calculations degrades slowly as you move further from the
 present era. The algorithms lose all validity and will produce bizarre results
 at extremely remote times in the past or future.

>TERMINOLOGY ILLUSTRATED

 Inferior Planet--a planet inside the earth's orbit: Mercury and Venus. The
   apparent motions of the inferior planets are quite distinctive. Run the
   Ecliptic Motion display and notice that two of the planets always stay near
   the sun, whereas the other planets circle the entire sky. Display the names
   with the <N> option to see that those two planets are Mercury and Venus. In
   the split-screen displays, choose the heliocentric option to show the orbits
   of Mercury and Venus as seen from above. Note that the inferior planets move
+  faster than the earth.

 Superior Planet--a planet outside the earth's orbit: Mars, Jupiter, and Saturn
   are included here. Uranus, Neptune, and Pluto are also superior planets, but
   Planet Tracker focuses on the bright naked-eye planets. Note the distinctive
   motion of the superior planets in the Ecliptic Motion display. In the split-
   screen Heliocentric display Mars is the only superior planet shown with the
   inner planet option. Select the outer planets to view the orbits of Earth,
   Mars, Jupiter and Saturn. Note that the superior planets orbit the sun more
   slowly than the earth, with the speed decreasing with greater distance from
-  the sun.

 Conjunction--when two objects appear together in the sky (although they may be
   at very different distances in space). Two planets may be in conjunction.
   When only one planet is named, it is assumed to mean that planet is in
   conjunction with the sun. Run the Ecliptic Motion display to see many
   examples of planets in conjunction with each other and with the sun. Run the
   split-screen Heliocentric display along with the Sky Dome to see where two
   planets are in space when they are together in the sky. Type <R> to show
   rays to highlight the moment of conjunction. When two rays lie on top of
   each other they will "cancel" or partially cancel. In the Zodiac Time Line
   graph conjunctions occur when two paths cross. Since the bright planets are
   very bright compared to the stars, a conjunction in the sky can be quite an
   interesting event. Not only will there be two bright star-like objects near
   each other, their relative motion from one night to the next can be very
-  apparent.

 Superior Conjunction--when any planet lines up behind the sun. The superior
   planets only line up with the sun when they are behind the sun. The inferior
   planets can line up either in front of or behind the sun. Superior planets
   cross through superior conjunction moving from left to right (east to west).
   Inferior planets go through superior conjunction when they cross the sun
   from right to left (west to east). Notice that all planets appear to move
   slowest during superior conjunction because they are farthest from the earth
   at that time. Run the split-screen Heliocentric option along with the Sky
   Dome option to see examples from two points of view. Planets are not visible
   in the sky when they are in conjunction with the sun because of the glare of
   the sun. It is a non-event as far as observers are concerned.

 Inferior Conjunction--when any planet lines up between the earth and the sun.
   Note that all planets go through superior conjunction, but only the inferior
   planets can go through inferior conjunction. Inferior conjunction occurs
   when an inferior planet crosses from left to right (east to west) across the
   sun. Run the split-screen Heliocentric option along with the Sky Dome option
   to see examples from two points of view. (See the notes on the Motions of
-  Mercury and Venus for a discussion of transits.)

 Opposition--when a planet is opposite the sun as seen from the earth. When a
   planet is at opposition it is closest to the earth, so it is brightest and
   largest in a telescope at that time. Only the superior planets go through
   opposition. On the top frame of the ecliptic motion display the superior
   planets go through opposition when they leave the screen and re-appear on
   the other side. (Think of the screen as wrapping around behind us with the
   earth in the middle.)  The Zodiac option in the split-screen displays works
   the same way, except the display wraps around already. Note that the
   retrograde motion of the superior planets occurs as they are passing through
   opposition. The Zodiac Time Line display shows the opposition point as a
+  heavy dashed line running parallel to the path of the sun 180 degrees away.

 Elongation--the angle between the sun and the planet as seen from the earth.
   To visualize the elongation in the split-screen displays, type <R> to show
   the rays, and notice the angle between the sun ray and the planet ray.

 Greatest Elongation--the maximum angle between the sun and one of the inferior
   planets as seen from the earth. Since the planets are best seen against a
   dark sky the angle of elongation is critical to observability. Mercury can
   only be observed near greatest elongation. Even then it will be low on the
-  horizon and may be difficult to see because of twilight.

 Quadrature--when a superior planet appears at right angles to the sun from the
   earth's perspective. Roughly speaking, a planet at eastern quadrature would
   be overhead at sunset and at western quadrature would be overhead at
   sunrise. (The word "overhead" is used very loosely here. Planet Tracker does
   not take account of the observer's latitude or seasonal effects.) Run the
   split-screen display of the Sky Dome and the Heliocentric view and note
   where the superior planets are in the solar system when they are at right
   angles to the sun as seen in the sky.

>ECLIPTIC MOTION

 Run the Ecliptic Motion option and note that the sun traces a smooth
 repeatable path through the stars. This path is called the ecliptic. The
 apparent motion of the sun is caused by the actual motion of the earth around
 the sun. The regularity of the motion is an indication of the regularity of
 the earth's motion in its nearly circular orbit. The sun travels eastward once
 around the sky, relative to the background stars, in one year. We can't see
 the stars in the daytime, because of the sun's great brilliance, but we do see
 that the stars shift slightly westward in the sky from one night to the next.

 Note that the planets all follow the ecliptic, more or less. This is an
 indication of the flatness of the solar system. The orbital planes of the
 planets are all fairly close to the orbital plane of the earth. They are not
 exactly coplanar with the earth's orbit, however. The deviations can be
 magnified and studied in more detail by using a vertical exaggeration factor
-greater than 1.

 The planets can be displayed one at a time or all together. Try it both ways.
 You will find it instructive to select the sun and one planet at a time and
 let the display run for many years. Compare the patterns, for instance, of
 Mercury and Venus to those of Jupiter and Saturn. Try setting the vertical
 exaggeration to 5 or more to bring out the details of the retrograde loops.
 You may want to increase the calculation interval to speed up the display.
 Trails can be turned on or off using the <T> key.

 The diagram above the ecliptic star chart shows motions identical to those
 below, except the sun is held fixed rather than the stars. This display
 highlights the symmetry of planetary motion relative to the sun. The inner
 planets oscillate back and forth never straying far from the sun. The outer
 planets circle the whole sky, but their motions are also "centered" on the
 sun, in a sense. They move slowly past the sun and speed up as they approach
 opposition (180 degrees from the sun--the outer edges of the screen). The
 outer planets do not backtrack from this perspective, but when the whole
 pattern is slewed past the stars, as in the lower display, the changes in
 speed of the outer planets, relative to the sun, causes their direction of
-motion to alternate relative to the stars.

 Note what happens in the Ecliptic Motion animation when you use a calculation
 interval of 365 days. Step repeatedly one year at a time. Note that the sun
 doesn't quite complete its cycle in 365 days. Try 365.25 days. Try 365.26
 days. One year as measured by the motion of the sun against the background of
 the stars is called a Sidereal Year: 365.2564 days. The year length that keeps
 the seasons constant (the basis for calendar leap-year systems) is 365.2422
 days, called the Tropical Year. The difference between the tropical and
 sidereal years is caused by precession, a wobble in the earth's axis that
 takes about 26,000 years to go full cycle.

>SPLIT-SCREEN ANIMATIONS

 Planetary motion can be described from many points of view. The usual view
 with the planets going around the sun is simple in concept, but we can't see
 this happening directly in the sky. It corresponds to the point of view of an
 imaginary observer far out in space looking down on the solar system. This
 viewpoint is useful but an abstraction for earth-bound observers. Planetary
 motion is more complex as seen from earth because the earth itself is a moving
 observing platform. Not only are we moving around the sun, we are spinning as
 well. To describe any motion we need to define a frame of reference. To say
 something is moving we need to define what we consider to be fixed. The usual
 approach is to hold the stars fixed. The physics of orbital motion is simplest
 in this frame of reference. Thinking of the sun as fixed highlights its
 dominant role in the motion of the planets. Our senses say the earth is fixed.
 This was the accepted world view some centuries ago. It can also be useful to
 hold both the earth and sun fixed. In this case the observer rotates at one
 turn per year to "freeze" the motion of the earth. This corresponds to our
 view of the sky if we go out and look up briefly each night at the same time.
 We perceive the earth to be fixed under our feet and the sun fixed at the same
 position below the horizon from one night to the next. The split-screen
 animations allow comparisons between these various viewpoints.

>THE APPARENT DOME OF THE SKY

 There is no sky!  The sky is an illusion due to the limitations of our depth
 perception. The large apparent dome of the sky in the first split-screen
 display represents the illusion of the sky as we directly perceive it. The
 point of view is that of a person viewing the sky relative to his or her
 horizons briefly each night at the same time...a sort of "stroboscopic" view 
 that eliminates the earth's rotation. The user can choose to observe at one of 
 four primary times: sunset, midnight, sunrise, or noon. The rotating circle of 
 tiny dots surrounding the diagram represents the background of stars, moving 
 westward from night to night. (Details such as the tilt of the earth are 
 ignored.) 

 Each of the display options has a small "sky dome" attached to the earth which
 rotates to maintain its orientation relative to the sun. Its orientation
 depends on whether the viewing is at sunset, midnight, sunrise, or noon. If
 the large sky dome is paired with any of the other views and the "rays" are
 turned on (by typing <R>), the planets can be seen to project onto the small
 sky domes just as they appear on the large dome.

 The "sky dome" views are simplifications. They show the view of an observer at
 the equator on an earth without a tilted axis. Despite this simplification it
+is a useful visualization aid.

>SKY DOME VS. ZODIAC

 The Zodiac display is a wrap-around version of the Ecliptic Motion display.
 One significant difference, however, is the presence of the earth in the
 center with its mini sky dome. The presence of the dome indicates what part of
 the sky would be visible for the given day and time. Running the Sky Dome /
 Zodiac pair highlights a significant fact: planets to the left of the sun are
 visible in the evening sky and planets to the right of the sun are visible in
 the morning sky. This is a good way to see why Mercury and Venus alternately
 appear as morning and evening "stars". Set the time for midnight and notice
 that Mercury and Venus never rise to the horizon. Notice that although the
 outer planets go through retrograde motion relative to the stars, they never
 backtrack relative to the horizons. Instead, they speed up and slow down as
 they circle around the sky. Compare the speed of Mars, for instance, relative
 to the circle of stars in the sky dome view. It moves very slowly when it is
 near the sun so the stars pass it by. When Mars is opposite the sun it is
 moving rapidly, so it passes the stars in their constantly westward motion.
 Its motion appears to reverse in a frame of reference where the stars are held
 fixed.

>SKY DOME VS. HELIOCENTRIC VIEW

 Pairing the sky dome with the heliocentric viewpoint brings the heliocentric
 system down to earth. Set the planets moving and let them run. Notice how the
 position of a planet right or left of the sun as seen from the earth
 determines whether it will be visible in the morning or evening sky. Notice
 also that the speed of the planets across the sky dome is determined by
 whether the planet is on the near side or far side of the sun. This is
 particularly apparent in the cases of Venus and Mars: the planets whose
 distances from the earth vary the most. Display one planet at a time to
 highlight its characteristic motions.

 For each of the orbital views the user may select the inner or the outer
 planets. The outer planets are so far apart that it would be hard to fit all
 the planets on one display. The inner selection includes Mercury through Mars
 and the outer selection includes Earth through Saturn.

>HELIOCENTRIC VS. GEOCENTRIC VIEWS

 Select these two displays and let them run for a few minutes noticing their
 similarity. They differ only in which point is held fixed (sun or earth). Now
 type <T> to leave trails. Notice how different the paths appear from these two
 points of view. Notice the conspicuous looping motions explained by ancient
 astronomers as movement along epicycles. The geocentric view shown here
 actually corresponds to Tycho Brahe's modification of the Ptolemaic system.
 Display rays occasionally with the <R> key to remind yourself that the motions
 in both cases are really identical. Be sure to run this combination for both
 inner and outer planets. The geocentric paths for the inner planets overlap.
 To reduce the clutter it is helpful to select one planet at a time. Run Mars
 alone. Note that the dips toward the earth in the geocentric view correlate
 with opposition when the earth comes closest to Mars. Run Venus Alone. Note
 the dips toward earth in the geocentric view correlate with inferior
+conjunction when Venus comes closest to earth.

>HELIOCENTRIC VS. EARTH & SUN FIXED

 Select these views and let them run noticing the similarities of the two
 displays. Freeze the motion occasionally with the <Spacebar> and notice that
 the fixed earth display is simply a rotated view of the other. The rotation of
 the reference frame is matched to the orbital motion of the earth, causing it
 to freeze. The observer looking down on the solar system rotates to keep the
 earth to the left of the sun at all times. Now leave trails. Type <T> to leave
 trails. Notice that as we rotate with the earth, we are rotating faster than
 Mars and the other outer planets, so their direction of motion is reversed.
 Mercury and Venus still orbit the sun in the same direction, but slower than
 before. Note that with the earth and sun held fixed, planetary orbits do not
 close neatly on themselves. That is because they are elipses being viewed from
 a rotating frame of reference.

>SKY DOME VS. EARTH & SUN FIXED

 Watch them run. Display the rays frequently with the <R> key and notice the
 close correspondence between these two views. If you have a reasonably fast
 computer holding the <R> key down is an effective way to view this pair. The
 Earth & Sun Fixed display is the same as the sky dome except depth is added.
 Notice how the variable distances of the planets translate to variable speed
 on the sky. The closer a planet is to the earth, the more its apparent speed
 is amplified from our point of view. In a telescope, the changing distance
 translates to a changing apparent size and phase of the planets. When Venus,
 for instance, comes between the earth and the sun it looks larger in a
 telescope, and since it is backlit by the sun, it appears in crescent phase.
 When it is on the far side of the sun, it is smaller. The direction of
 lighting from the sun is more similar to our own line of sight, so it appears
 gibbous or nearly full. The reference frame holding the earth and sun fixed is
 very useful for interpreting the motions of the planets on the sky as they are
 seen from the earth.

>USING PLANET TRACKER AS A PLANET FINDER

 Several displays are quite useful for the would-be observer. The ecliptic
 motion display shows where to find the bright planets against the background
 of the constellations on any day. Furthermore, whether the planets are to the
 left or the right of the sun indicates when they will be visible: evening or
 morning. The sky dome view in the split-screen options also gives a quick
 overview of where to look for the planets. Since the planets are generally the
 brightest star-like objects in the sky (except for airplane landing lights),
 the general direction to look may be all you need to find them. Jupiter and
 Venus are always brighter than any star. Mars can be even brighter than
 Jupiter when it is near the earth at opposition or as faint as a second
 magnitude star when it is on the far side of its orbit. Saturn and Mercury are
 about as bright as the brightest stars. Mercury, however, is usually seen in
 twilight so it may be difficult to see despite its brightness.

 Probably the most useful feature for planet finding is the Zodiac Time Line.
 This display can be printed out to serve as a year-long planet calendar
 showing planet positions both relative to the background constellations and
+relative to the sun.

>ZODIAC TIME LINE

 The Zodiac Time Line is a display format designed primarily for print-outs. It
 presents in graphical form the same information shown in the Ecliptic Motion
 animation. It is most useful as a planet calendar, showing the background
 constellations for the planets and their relation to the sun for any date
 during the year. To locate a planet among the stars, find the position of the
 planet on the desired date and trace straight up to the ecliptic (the center
 line of the zodiac chart). Where a planet is in relation to the sun is
 critical to its observability. Planets to the left of the sun are visible in
 the evening sky; planets to the right of the sun are visible in the morning
 sky. The diagonal lines running down the page parallel to the sun indicate
 positions 90 and 180 degrees from the sun (quadrature and opposition,
 respectively). Planets near opposition are high in the sky around midnight.

 On screen the chart is combined with animation to clarify the meaning of the
 graph. The animation can be stopped and single stepped by typing <Spacebar>
 and full animation can be resumed by typing <Enter>.

 The tracks for the different planets are identified by the heavy dot on the
 track near the top of the page. Read directly across from the dot to see the
 name of the planet.

>SOLAR TIME LINE

 What if the solar system were surrounded by fog so that only the sun and
 planets were visible with no stars as reference points in the sky? The angle
 from the sun (the elongation angle) would be the most obvious way to describe
 the motion of the planets. The Solar Time Line plots elongation vs. time,
 highlighting the dominant role of the sun in planetary motion. It looks very
 much like the Zodiac Time Line (which plots ecliptic longitude vs. time)
 except the sun now runs down the center of the page. The solar time line
 presents in graphical form the same information shown in the top frame of the
 Ecliptic Motion animation.

 Note that Mercury and Venus immediately appear to orbit the sun! We can
 clearly discern their motions to be orbits around the sun because we on earth
 lie outside their orbits. The outer planets also appear to orbit the sun, in a
 sense, but they orbit in reverse direction and wrap around the whole sky going
 behind us, because the earth lies inside their orbits. They appear to move
 backward because the earth orbits faster than the outer planets do, constantly
-passing them by.

 Of the outer planets Mars travels fastest, so the Earth takes longer to
 overtake it. Therefore Mars has the longest "period" in this view. (The period
 of an orbit relative to the sun is called the "synodic period.")  Jupiter and
 Saturn are progressively easier to overtake, so their synodic periods are
 shorter.

 The Solar Time Line divides easily into evening and morning sky: the left half
 of the page is visible at sunset and the right half of the page is visible at
+sunrise.

>ORBIT DIAGRAMS--HELIOCENTRIC

 (The orbit diagrams are intended primarily for printouts to be used as
 classroom exercises. See the activity file (ACTIVITY.TXT) for suggested uses.)

 The heliocentric orbit diagrams show complete orbits (once counterclockwise
 around the sun) for either Mercury, Venus, Earth, and Mars, or at a smaller
 scale, Earth, Mars, Jupiter, and Saturn. Large dots indicate the positions of
 the planets for the chosen starting date and small dots indicate the positions
 for successive dates based on the chosen calculation interval. These diagrams
 are the basis for many of the exercises in the activity file.

 The heliocentric perspective has become standard for "scientific" descriptions
 of the solar system because the orbits and laws of motion are described most
 simply from this point of view. Unfortunately this is not the view of the
 solar system we see from our moving platform, Earth. It is important for
 students to connect the simplicity of the heliocentric perspective to the
 directness of our observations in the sky if astronomy is not to become a
 detached abstraction. It is the desire to make this connection that has
 motivated most of the features of the program and the accompanying exercises.

>ORBIT DIAGRAMS--GEOCENTRIC

 (The orbit diagrams are intended primarily for printouts to be used as
 classroom exercises. See the activity file (ACTIVITY.TXT) for suggested uses.)

 The geocentric orbit diagrams show approximately complete orbits (once
 counterclockwise around the earth) for either the Sun, Mercury, Venus, and
 Mars, or at a smaller scale, the Sun, Mars, Jupiter, and Saturn. (We say
 approximately complete, because in this system the orbits are not closed
 curves.) Large dots indicate the positions of the planets for the chosen
 starting date and small dots indicate the positions for successive dates based
 on the chosen calculation interval. These diagrams are the basis for some of
 the exercises in the activity file.

 The geocentric model shows how the sun and planets appear to move against the
 starry background as seen from earth. The earth appears fixed in the center,
 just as it is perceived by earth-based observers. The motions are rather
 complex loops with a westward drift on the average (counterclockwise as seen
 from above). Of course we can't discern the depth dimension directly; we see
-all of this complexity projected onto the dome of the sky.

 At first, we may see the geocentric perspective as introducing needless
 complexity into the picture. But in reality it is this view that is closest to
 our sense perceptions. Historically this was the starting point. The challenge
 was to bring order out of chaos. The most notable early synthesis was
 Ptolemy's model, which was developed around 140 A.D., and persisted into the
 Middle Ages. Ptolemy accepted the apparent looping motion as real. He
 visualized the planets moving on circles called epicycles that moved along
 other circles called deferents that in turn circled the earth.

 The amazing thing is that the geocentric description of the solar system is a
+perfectly valid point of view that can be correlated with the heliocentric
 description. If matching geocentric and heliocentric charts are held one
 behind the other, or overlaid as transparencies on an overhead projector, they
 can be seen to correspond. Simply shift the central earth of the geocentric
 plot to line up with the marker for the earth on the heliocentric plot. The
 sun and all the other planet markers should line up simultaneously. If you
 count forward along each planet's path the same number of steps on both charts
 and mark the endpoints with large dots, the charts can again be made to line
-up exactly.

 The geocentric orbits for the outer planets are well separated and work best
 for a classroom introduction to geocentric motion. The situation looks more
 complicated for the inner solar system. The paths of the inner planets badly
 overlap. Ptolemy didn't want the planets to intertwine (after all, how could
 crystal spheres pass through each other?), so he scaled each orbit separately
 so the orbits appeared stacked inside each other and filled all of the space.
 Since Ptolemy did not know the distances to the planets anyway, this was a
 satisfactory solution at the time. Tycho Brahe altered the distance scale so
 Mercury and Venus orbited the sun. The geocentric orbits represented here
 resemble Tycho Brahe's version of the Ptolemaic model.

>THE MOTION OF MERCURY

 Display the sun and Mercury alone on the Ecliptic Motion display with some
 vertical exaggeration. The retrograde motion is not simply back and forth: it
 produces loops. The orientation of the loops depends on the orientation of
 Mercury's orbital plane relative to the earth at that time of year. Sometimes
 we are looking at Mercury's orbit from above, sometimes from below, and
 sometimes edge-on.

 Display the inner planets in the Heliocentric split-screen display along with
 the Sky Dome view. Notice that Mercury, in particular, has a decidedly
 lopsided orbit. Notice the effect this has on the greatest elongations of
 Mercury. Some greatest elongations are greater than others. This effect is
 also noticeable in the time line displays. Mercury's greatest elongations can
-vary from 18 to 28 degrees.

 A transit is when an inferior planet crosses the disk of the sun. All transits
 occur at inferior conjunction, but not all inferior conjunctions result in
 transits. Usually when Mercury or Venus cross "in front of" the sun they do
 not actually cross the sun's disk. They pass above or below the disk of the
 sun because of the inclination of their orbital planes. An exact alignment can
 occur at the two points of the orbit where the planet crosses the ecliptic
 plane, the plane of the earth's orbit. These times are in May and November, in
 the case of Mercury. Transits of Mercury are relatively rare. The next few
 transits of Mercury are Nov. 6, 1993, Nov. 15, 1999, May 7, 2003, and Nov. 8,
 2006. Transits are observable only from places in the world where the sun is
 up while the transit occurs. Run the Ecliptic Motion display with vertical
 exaggeration to compare transits with non-transit inferior conjunctions. The
 dot representing the sun is not to scale, and the precision of the
 calculations is not sufficient to predict transits exactly, but the great
 variation in center-to-center distance between the sun and Mercury from one
+inferior conjunction to the next is easy to observe.

>THE MOTION OF VENUS

 Display the sun and Venus alone on the Ecliptic Motion display with some
 vertical exaggeration. Venus presents a particularly interesting pattern. Let
 it run for many cycles and notice where the retrograde loops occur against the
 background of stars. The repetition you see is called a resonance. It is
 caused by a gravitational linkage between Venus and the earth. Venus is our
 closest neighbor. When Venus passes the earth the two planets interact in such
 a way as to synchronize their orbital periods. The effect is quite striking.
 Select Venus to run in the various split-screen displays (especially the
 Geocentric view) and look for similar effects. Run other planets to verify
 that the repetitious pattern is unique to Venus.

 Venus occasionally transits the sun's disk at inferior conjunction. See the
 discussion of Mercury's motion for an introduction to transits. Transits of
 Venus can occur when inferior conjunction occurs in late May/early June, or in
 December. Transits of Venus are even more rare than transits of Mercury. The
 last transits of Venus were Dec. 9, 1874 and Dec. 6, 1882. The next transits
 of Venus are June 8, 2004, June 6, 2012, Dec. 11, 2117, and Dec. 8, 2125. They
 usually come in June or December pairs. As with Mercury, run the Ecliptic
 Motion display with vertical exaggeration to compare transits with non-transit
 inferior conjunctions. Remember, the dot representing the sun is not to scale,
 so the representation of transits is qualitative, not quantitative.

>THE MOTION OF MARS

 Notice that the distance from earth to Mars varies more than for any other
 planet. This can be seen in several of the split-screen displays including the
 heliocentric and geocentric views. Because of the large distance variation the
 brightness of Mars and its apparent size in a telescope vary tremendously.
 Mars can appear brighter than Jupiter at opposition or as faint as a second
 magnitude star when it is on the far side of the sun.

 Not all oppositions of Mars are created equal. Run the geocentric split-screen
 display for Mars with a 10 or 20 day calculation interval for hundreds of
 years. What time of year do the "Most Favorable" oppositions of Mars occur?
 When will the next opposition of Mars occur?  Plan to observe it. When will
 the most favorable opposition occur within your expected lifetime?

>THE MOTIONS OF JUPITER AND SATURN

 Run the Ecliptic Motion display with each planet alone. For the inner planets,
 the average motion is along the ecliptic (a projection of the earth's orbit)
 and the loops are inclined depending on the tilt of the inner planet's orbit.
 For the outer planets, however, the average motion is along a curve determined
 by the tilt of the outer planet's orbit and the individual loops are parallel
 to the ecliptic. Imagine trading places with observers on other planets. If
 you were on an outer planet viewing earth it would behave like the inner
 planets behave from earth's point of view. If you were on an inner planet
 viewing earth, it would behave like the outer planets from earth's point of
 view. The average motion is dominated by the more distant, slower moving
 planet. In the case of Mercury, the more distant planet of the pair is Earth.
+Thus the average motion is along Earth's orbital plane: the ecliptic. In the
 case of Saturn, the more distant planet is Saturn itself, so the average
 motion is along Saturn's orbital plane. The looping motion is dominated by the
 closer, faster moving planet. In the case of Mercury, the looping is
 determined by Mercury's orbital plane. In the case of Saturn, the looping is
-determined by Earth's orbital plane, the ecliptic plane.

 As planets recede into the distance the size of the retrograde loops
 diminishes. This is best understood by reversing the line of sight. The
 retrograde loop of the earth as seen from Saturn is simply the orbit of the
 earth around the sun as the sun slowly drifts among the stars. The retrograde
 loop of Saturn as seen from the earth is a mirror image of the motion of earth
 from Saturn's point of view. The more distant the planet, the smaller the
 earth's orbit appears, so the smaller that planet's retrograde loops will
 appear from earth.
>

