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.

Venus and Mars are the two planets nearest to the Earth this semester. 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.


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.


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.


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.


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.


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.


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.




Once your observations of Venus and Mars are complete, please write a lab report on this project. 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?

Joshua E. Barnes (
Last modified: September 27, 2005
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