Expert: Jayendra Upadhye - 7/15/2009

Question
Hi! I've finished 12th standard. Earth is revolving around the sun in an elliptical orbit and the moon is revolving around the earth in an elliptical orbit. In order to revolve in an elliptical orbit, you must have two focus. If earth is considered, sun is one foci and what is the other? The same question to the moon also by replacing sun to earth. Please, explain me. (mathematical proof if you wish)

Answer
Hi,
I am terrible at maths!
So bear with me. :)
1 - Sun Earth system.
The sun has a dia of more than a million km.
It is terribly more massive.
In such systems, one focii and the center of mass lies within the body of the sun (or star), the other focus lies in the center of the planet on the major axis of the orbit.

2 - Earth moon case.
One focus inside the earth's surface, other at the center the moon on the major axis of the orbit.

As the focus is not smack on the CG of the sun nor of earth in the cases above, a sort of precession about the center of mass happens.
As it flings the planets around, the sun itself wobbles a bit around the center of mass.

Because of Jupiter, the center of mass of the solar system is not deep inside the sun, but has an offset. It is thought that every 11 years jupe approaches closer to the sun, and that causes the sun spot cycle.
All the while onw must remember that for convinience we tend to focus always on the heacier body and hold it steady and see how the ligher body moves.
Actuall both bodies move, but the more massive a bosy the lesser is the degree of its movement.

Distant planets have been found due to the tell tale wobbles of stars.

If you send me a mail at jupadhye_99@yahoo.com, I will mail to you a program that actually plots the paths of multiple bodies as they go around each other in stable orbits.
There you will see the exact motions.

I have a 21 star cluster orbiting each other all working under the inverse square law!
regards
Jayen