Mapping the Motion of a Planet in the Sky

The Wandering Stars

Summary: Track the position of one or several planets that is in the evening sky (could be Venus, Mars, Jupiter, or Saturn) against the starry background during the semester.

Needed Supplies: Logbook, pencils, crossbow and a blown up photocopy of the region of the star chart where the planet is located in the sky.

General Description:The word ``planet'' is derived from the Greek word for "wanderer,'' as ancient observers realized that several "stars'' moved against the background of "fixed'' stars. Because the planets orbit the Sun nearly all in the same plane (i.e. the solar system is "flat"), the planets always stay close to the ecliptic, something that you will observe for yourself. With the help of star charts and the crossbow, you will track the position of a planet among the fixed stars as it changes due to the orbital motion of both the Earth and the planet during a period of 2-3 months.

Procedure:

Note: The planets move relatively slowly in the sky; for some planets at some times, you may notice no positional change for several days or even weeks; for other planets or these same planets at different times, you may notice positional changes every day. For your chosen planet, note its position once every week (or more often if the planet moves rapidly, like Venus) throughout the entire semester. Start as soon as possible! These observations are simple and take little time once you know how to go about it. Do some observations outside of the lab period if the weather does not cooperate during scheduled labs.

1. Use a blown up photocopy of the star chart (200%) centered on the part of the sky where the planet is located. You will use this to chart its motion during the semester. Keep it in your logbook and always bring it with you at the lab!

2. Plot the position of the planet on the map AS ACCURATELY AS YOU CAN, based on several surrounding stars. Be careful in identifying the stars you see near the planet and those on the star chart. Note the date of each observation on the star chart as well as sky conditions and the visibility of stars near the planet (in your logbook).

If there are no stars near the planet to make an accurate assessment of its position in the sky, you can use the crossbow to make more precise measurements:

• Choose two suitable stars as fixed reference points (you can use 3 for more accuracy). Use the crossbow to measure the angular separation between the planet and each of the 2 (or 3) stars. Measure to the nearest 0.25^o (that's 1/8" on the crossbow scale). Note the date, sky conditions (such as visibility of stars near the planet), the names of the two stars you use as reference and the angular separations you have measured. You will need to establish the scale of the map to report your angular separation on it. This you can do using two fixed stars in the vicinity of the planet. Your measure of their angular separation and of their physical separation on the map (in mm) will give you the scale. You can now plot the position of the planet on the star chart. As a check on your work, compare the plotted position with what you see in the sky.

3. The ecliptic is shown on the star chart (wavy curve). Notice that it is marked with a scale in degrees and with the days of the year. The dates indicate the position of the Sun in the sky throughout the year. Use this to write down, for each day you measure the position of the planet, 1) The position of the planet along the ecliptic (in degrees) and 2) the position of the Sun. The difference between the two gives you the Sun-Earth-planet angle, as it would look it you were looking down on the solar system.

Example

Suppose that on April 20, 2001, you observed that the planet is located very near the star Regulus, in constellation Leo. Its position along the ecliptic (its ecliptic longitude) would be 150^o. On that date, the ecliptic longitude of the Sun is 30^o. The Sun-Earth-planet angle is 150^o-30^o=120^o.

Your report should consist of:

1. The star map with all recorded positions labeled by date.

2. An observation log showing dates, times, position measurements relative to stars, and personal comments as you see fit.

3. Make a table as follows:

   Date	Sun's Ecliptic Longitude	Planet's Ecliptic Longitude	Sun-Earth-Planet Angle	Earth's Ecliptic Longitude
   2001-Sep-11	168o	272o	104o	348o

   The S-E-P angle is given by the ecliptic longitude of the planet minus that of the Sun. The Earth's ecliptic longitude is opposite that of the Sun: E.E.L.=S.E.L. + 180^o.

4. Make a plot of the Sun-Earth-Planet angle as a function of the date (time in days).

5. Make a diagram of the solar system as seen from above, showing the orbit of the planet you have tracked during the semester as well as the orbit of the Earth. Your diagram must be drawn to scale. Assume that the orbits are circular and use the values given in the following table for the orbit dimensions. The semi-major axis is the radius of the orbit, given here in Astronomical Units (the Earth-Sun distance). Define a direction (from the Sun) to be 0^o of Ecliptic longitude. Using a protractor, plot the position of the Earth on its orbit (the Earth's ecliptic longitude) for each date of observation along its orbit (the ecliptic longitude increases counterclockwise). Then plot the position of the planet on its orbit for each date, using the Sun-Earth-Planet angle you have tabulated. Obviously, that last angle is centered on the Earth, not on the Sun. Note that in this diagram, planets orbit the Sun counterclockwise. The figure below shows an example using the entries for planet Mars in the table above.

Planet	Semi-Major Axis (A.U.)
Venus	0.72
Earth	1.00
Mars	1.52
Jupiter	5.20
Saturn	9.54






6. Answers to the following questions (HINT: Chapters 2 and 3 in the textbook may be useful in answering these questions):

   • a) In which direction is the planet moving against the background of stars?

   • b) Is the planet simply moving along one of the cardinal directions (say, east or west)? Explain why it is moving in the direction you observe.

   • c) Is there a relation between the direction of motion and the Sun-Earth-planet angle?

   • d) Do you notice any change in the motion (direction, speed) throughout the semester? If so, explain what is going on. Hint: use the plots you made in #4 and #5.

   • e) How does the planet's motion relate to the ecliptic? Is it above, below, moving closer or farther from the ecliptic. Explain what causes what you have observed.

   • f) If you observed more than one planet during the semester, compare their motions in light of your answers to the above questions. Which is moving faster? Why?

   • g) Using the diagram of the orbits (#5), determine the orbital period of the planet, i.e. how long it takes to complete one orbit around the Sun.