Planetary Motions

In Fall 2005 two planets -- Venus and Mars -- will outshine all others in the night sky. We will observe these planets and form a detailed picture of their -- and our -- orbital motion about the Sun.


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 because of our orbital motion, the Sun seems to move across the backdrop of distant stars.) The planets don't remain exactly on the ecliptic, but they always stay fairly close to it.

Unlike the Sun, however, the planets don't always make steady progress 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, including the Earth, move around the Sun in the same direction; retrograde motion is an illusion created when we observe other planets from the moving planet Earth.

It's easiest to understand the retrograde motion of the inner planets, Mercury and Venus. These 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 trundles 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 these planets moving in the same direction as the Sun, while at other times we see them moving in the opposite direction.

For the outer planets, Mars, Jupiter, Saturn, and so on, the explanation is a bit more subtle. These planets are further from the Sun than we are, and they orbit the Sun more slowly than we do. From time to time we pass one of these planets, and when that happens, the planet seems to be moving backwards because we're moving faster than it is. At such times we naturally see the Sun and the planet in opposite parts of the sky; the planet is said to be in opposition to the Sun. Opposition is a good time to observe an outer planet; it's above the horizon all night, and relatively close to the Earth.

An outer planet's apparent motion is always retrograde for a month or more before and after opposition. The duration of retrograde motion 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 instant the planet appears to be more or less stationary with respect to the stars. An outer planet always has one stationary point before opposition, and another stationary point after opposition.

Venus and Mars are the two planets that come nearest to the Earth. As all three planets orbit the Sun, the view of our neighbors will constantly change in various ways. By watching the apparent motion, change in distance, and change in phase of these two planets, we can see that many different effects are explained by the one basic idea that all planets orbit the Sun.

THE BIG PICTURE

Fig. 1 shows the orbits of Venus, Earth, and Mars and their positions in Fall 2005. From this diagram we can predict several interesting observational results.

  Positions of planets in Fall 2005.  

Fig. 1. Orbits of Venus, Earth, and Mars. This view looks `down' on the plane of Earth's orbit from the North, so all planets orbit counter-clockwise. Small filled circles show positions on 9/28; small open circles show positions 4 weeks earlier (8/31), 4 weeks later (10/26), and 4 weeks later (11/23).

 

Apparent Motions

Venus is catching up with Earth, but will not pass us before the end of the semester (see Fig. 2). For most of the semester, Venus is heading more or less toward us. As a result, it will appear in the roughly same position with respect to the Sun -- prominent in the West at sunset -- for several months. Venus appears to be moving along the ecliptic in the same direction as the Sun (West to East); this is called direct motion.

Earth-Venus-Sun triangles in Fall 2005.

Fig. 2. Triangles connecting Earth, Venus, and Sun on the dates indicated in Fall 2005. The line from Earth to Venus turns in the same direction (counter-clockwise) as the line from Earth to Sun, so Venus's motion is direct; also, the angle between Venus and the Sun as seen from Earth is roughly constant, so Venus will appear about the same distance above the horizon each night. The distance between Venus to the Earth steadily decreases, so Venus will appear larger and larger. At the same time, the angle of sunlight falling on Venus changes; by the end of the semester Venus will appear as a crescent.

Earth is overtaking Mars on the inside, passing between Mars and the Sun in early November (see Fig. 3). When we overtake an outer planet like Mars, that planet appears to move in a backwards or retrograde direction with respect to the stars -- East to West instead of West to East. This year, Mars begins retrograde motion on 10/01 and resumes normal motion on 12/11.

Earth-Mars-Sun triangles in Fall 2005.

Fig. 3. Triangles connecting Earth, Mars, and Sun on the dates indicated in Fall 2005. The line of sight from Earth to Mars turns in a clockwise direction, so Mars's motion is retrograde. The distance between Mars to Earth first decreases and then increases again, but the variation is not that large. The side of Mars we see will be almost completely illuminated by sunlight, so Mars will always appear nearly full.

Distances

The distance between the Earth and Venus will steadily decrease throughout the semester. Closer objects look bigger; consequently, Venus will appear to grow steadily, more than doubling in apparent size by the end of the semester.

The distance between Earth and Mars will gradually decrease from now until late October, with closest approach occurring on 10/30; after that, the distance will gradually increase again. As a result, Mars will appear largest in late October, but its apparent size won't change very much.

Phases

Venus will be passing between the Earth and the Sun, and as it does so the side we can see will be less and less illuminated by the Sun. At the start of the semester, Venus appears gibbous, or just slightly less than full, but by the end of the semester Venus will appear as a crescent lit from behind.

Since we are observing Mars near opposition, when Mars and the Sun are on opposite sides of the Earth, the face of Mars turned toward us will be almost completely illuminated by the Sun, and Mars will appear nearly full the entire time we can observe it.

OBSERVATIONS

Apparent Motions

We will follow the motions of Venus and Mars along the ecliptic by plotting their positions on star charts. While Venus appears in about the same place in the sky each evening, its motion with respect to the distant stars is quite rapid; we will use a circular all-sky chart. The main problem will be seeing the stars behind Venus; luckily, Venus will pass by some rather bright stars, so it should be possible to chart its motion fairly well.

Mars will cover a much smaller distance across the sky, so a rectangular star chart will be adequate to plot its motion. Binoculars will be needed to plot its position since many of the stars we will use as `landmarks' are rather faint. Depending on when we first sight Mars, we may or may not be able to observe it turn around and begin retrograde motion.

Distances

The variation in distance for both planets will be studied in the same way we study the variation in the Moon's distance: by measuring the apparent size of the planet using an eyepiece with a built-in scale. Since the sizes change gradually, we don't need to make a measurement every night; a few observations over the rest of the semester will suffice.

Phases

The phases of Venus and Mars can be seen directly when these planets are viewed through a telescope. Mars will appear nearly full at all times, but the phase of Venus will change dramatically. We will sketch both planets at various times through the semester.

WEB RESOURCES

REVIEW QUESTIONS

LAB REPORT

Once your observations of Venus and Mars are complete, please write a lab report on this project. If you cannot make enough observations because of bad weather, you can at least use the "planetarium" software to find the position of a planet at any time. Or, in the case of Mars, you can use the maps given in the book "Stars and Planets". Your report should contain an introduction to the problem of planetary motion, a brief section on equipment used, a description of your observations collecting all relevant measurements and plots, and a section describing your conclusions. In this last section, you should compare the predicted behavior of Venus and Mars with your actual observations; do they agree?


Roberto H. Méndez (mendez@ifa.hawaii.edu)
Last modified: October 20, 2005
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