# Backward orbit of the planets

1. Jul 15, 2011

### Philosophaie

Backward "orbit" of the planets

How do you tell when a planet is going backwards in its "orbit" of the earth?

Do you have to plot a graph and pick out the points?

There must be an easier way!

2. Jul 15, 2011

### Drakkith

Staff Emeritus
Re: Backward "orbit" of the planets

The planets were observed over thousands of years through the skies. Over time it was realized that they made odd little "loops" backwards through the sky against the background starfield. This occured because the Earth is orbiting the Sun at a different rate than the other planets.

Now you can probably look it up online and find out when this will occur. I don't know if they have to calculate the orbits and all that or if it simply occurs on a repeating schedule over time.

3. Jul 16, 2011

### Filip Larsen

Re: Backward "orbit" of the planets

The phenomenon is called Apparent Retrograde motion [1].

Conceptually, I think the easiest method would be to do as you propose and simply plot the position of, say, Mars in the sky of Earth as a function of time and note when the motion becomes retrograde.

However, from the orbital elements of Earth and Mars it should be theoretically possible calculate the apparent rate of the geocentric ecliptic longitude of Mars and (numerically) solve for times when this rate is zero. If you want to be very accurate, such calculations will probably be very long winded and be something you'd want a computer to do for you.

If you only want a rough estimate for when the rate is zero, I guess it should be possible to simplify the problem assuming coplanar circular orbits, maybe even so much that an analytic solution is easy. Also, in this simple model the time between when the rate is going positive (prograde motion) or negative (retrograde motion) repeats itself with the synodic period [2]. For instance, for Mars retrograde motion repeats itself after about 2.1 year.