Paths of the Planets

This Fall (2009) we will be able to observe just one bright planets. Jupiter is well-placed for viewing in the evening sky throughout the semester.

Background Reading: Stars & Planets, p. 298 to 301 (The Solar System)

As seen from the Earth, the Sun, Moon, and planets all appear to move along the ecliptic. More precisely, the ecliptic is the Sun's apparent path among the stars over the course of a year. (Of course, it's actually the Earth that moves about the Sun, and not the other way around, but the result of our orbital motion is that the Sun seems to move against the stellar backdrop.) The planets don't remain exactly on the ecliptic, but they stay pretty close to it at all times.

Unlike the Sun, however, the planets don't always move in the same direction along the ecliptic. They usually move in the same direction as the Sun, but from time to time they seem to slow down, stop, and reverse direction! This retrograde motion was a great puzzle to ancient astronomers. Copernicus gave the correct explanation: all planets move around the Sun in the same direction, and retrograde motion is an illusion created when we observe the other planets from our moving point of view, the planet Earth.

It's easiest to understand the retrograde motion of Mercury and Venus. These inner planets are closer to the Sun than we are, and they orbit the Sun faster than we do. From our point of view, the Sun moves slowly along the ecliptic (due, of course, to our orbital motion), while Mercury and Venus run rings around the Sun. So at some times we see them moving in the same direction as the Sun, while at other times we see them moving in the opposite direction. For Mars, Jupiter, Saturn, Uranus, Neptune, and Pluto the explanation is a bit more subtle. These outer planets are further from the Sun than we are, and they orbit the Sun more slowly than we do. When the Earth passes between one of these planets and the Sun, we see it going backwards because we're moving faster than it is.

When the Earth passes between one of the outer planets and the Sun, we see the Sun and the planet in opposite parts of the sky; the planet will rise about the time the Sun sets, remain visible all night, and set about the time the Sun rises. At this time, the planet is said to be in opposition to the Sun. Opposition is a good time to observe an outer planet; it's visible all night, and relatively close to the Earth.

An outer planet's apparent motion is always retrograde for a month or two before and after opposition. The length of time when a planet appears retrograde depends on the planet; it's shortest for Mars, and generally longest for Pluto. The moment when a planet's apparent motion changes direction is called a stationary point, because at that exact instant the planet appears to be stationary with respect to the stars. An outer planet always has one stationary point before opposition, and another stationary point after opposition.

As it turns out, both Jupiter and Saturn will be in retrograde motion at the start of the semester, and both will have turned around and gone back to normal motion by the end of the semester. Some positions of Jupiter and Saturn are shown in the star charts on the next page. In both charts, the ecliptic is shown as a slanting line; the normal direction of planetary motion is West to East, parallel to the ecliptic.

Positions of Jupiter. The first stationary point is on 12/04/02, opposition is on 02/02/03, and the second stationary point is on 04/04/03; during this entire period, Jupiter's motion with respect to the stars is East to West (retrograde). The stars labeled with Greek letters are Gamma and Delta Cancri, and Lambda Leonis.

Positions of Saturn. The first stationary point is on 10/11/02, opposition is on 12/17/02, and the second stationary point is on 02/22/03; during this entire period, Saturn's motion with respect to the stars is East to West (retrograde). The stars labeled with Greek letters are Beta and Zeta Tauri.

TRACKING PLANETARY POSITIONS

The two charts handed out in class on Feb. 4th should be used to plot the positions of Jupiter and Saturn. (You can get fresh copies by following the links below.) These charts show more stars than you can see with your naked eyes, but under typical urban conditions most of these stars will be visible with binoculars. Each chart has a scale of 2 cm per degree; thus, two stars separated by 0.5° in the sky appear 1 cm apart on these charts. At the top of each chart is an arrow pointing toward the North celestial pole. Finally, the three small crosses on each chart show the positions of Jupiter and Saturn during the first three classes of this semester.

Your assignment is to plot Jupiter and Saturn on these charts every time we observe. This should be pretty routine after a few weeks, and a reasonably complete set of plotted positions will nicely show the tracks of both planets as they end their retrograde phases and resume normal (West to East) motion along the ecliptic. Here's how to plot planetary positions:

Align the chart with the sky by holding it up next to the planet and turning it until the arrow points toward Polaris.
Center your binoculars on the planet and look at the surrounding stars. Carefully match the stars you see in your binoculars with the ones shown on the chart. (Note: the transparent overlay handed out with the planet charts shows the field of view of the binoculars - you can use it to help match stars on the chart with those in the sky.)
Look for patterns of stars which include the planet's present position. For example, you might notice that the planet is on a line between two stars, or that the planet and two stars form an equilateral triangle. You'll get better results if you find two or more different patterns; each helps you check the other.
After you've matched the stars on the chart with those in the sky, and found some patterns including the planet, you are ready to plot the planet's position on your chart. Use a pencil to mark its position, and compare your chart with the sky a few times to make sure everything's in the right place.
Once you are satisfied with the position you've plotted, mark the planet's position with ink. Write the date next to the mark you've made. (Note: when the planets are near their stationary points they don't seem to move much, and you may have trouble indicating which date goes with which mark. One solution is to use different colors for different observations.)

The point of this exercise is to track the planets over the entire semester as they switch back from retrograde to normal motion. Don't worry if we miss a few observations due to bad weather; we can just pick up again when the weather improves. If you want, you can make additional observations whenever you have the chance. For example, if we miss an observation due to bad weather on Tuesday, you can go out the next clear night and fill in the gap (of course, always write the current date next to your mark).

REPORT: PATHS OF THE PLANETS

Make the observations described in the section on TRACKING PLANETARY POSITIONS, and write a report on your results. This report is due on May 6th (the last class of the semester); if the weather is good that night, we won't collect the reports until you've had a chance to make one final observation. Your report should include, in order,

an introduction explaining the purpose of the observations,
a description of the observing sites and equipment you used,
a summary of your observational results, and
the conclusions you have reached.

In more detail, here are several things you should be sure to do in your lab report:

Explain retrograde motion in your own terms, and discuss its significance for early astronomers.
Note any weeks when you found the observations particularly easy (for example, due to bright stars near a planet's position) or difficult (due to a lack of bright stars or whatever).
List the last week when each planet was definitely West of the previous position, and the first week when it was definitely East of its previous position.
Try to estimate the accuracy of your positions. This is a bit subjective, but you will probably develop some feeling for your margin of error as you gain experience. For example, if you think the positions you plot on these charts are off by less than 0.5 cm, your measurements have an accuracy of 0.25° (since these charts have a scale of 2 cm per degree).

WEB RESOURCES

Chart for Jupiter: GIF file or Postscript.
Chart for Saturn: GIF file or Postscript.

These charts show 12.7° by 9.5° regions of the sky. If printed at a resolution of 100 dpi, the GIF images have an scale of 2 cm per degree; the Postscript plots should automatically print at this scale. The faintest stars shown are magnitude 8.5, which is about the limit for our binoculars from Kapiolani park.

REVIEW QUESTIONS

At which time would you expect Venus to show retrograde motion - when it's between the Earth and the Sun, or when it's on the far side of the Sun as seen from Earth?
Suppose that we (on Earth) see Mars moving in a retrograde direction. How would Earth's motion look to an observer on Mars?
It takes Jupiter almost exactly 12 years to complete one orbit around the Sun. How many times in that 12-year period will an observer on Earth see Jupiter moving in a retrograde direction?