# Geosynchronous Orbits

1. Oct 21, 2009

### Charlie G

I was having trouble making sense of the geosynchronous orbits from a relativistic point of view. Correct me if I am wrong, but in a geosynchronous orbit the object appears to hover over a certain place on the Earth, from the point of view of the Earth, which can be said to be at rest according to the principle of relativity, the object is at rest above the Earth.
Therefore, should the general pinciple of relativity hold true, the object should begin to fall towards the Earth in a straight line relative to an observer on the Earth's surface.

This obviously doesn't happen, but I have good faith that there exist a solution somewhere in the theory, which is why I have addressed my troubles here.

Thank-you.

2. Oct 21, 2009

### Integral

Staff Emeritus
Just what is it in the Special Relativity that makes you think this is true?

3. Oct 22, 2009

### A.T.

The principle of relativity applies to inertial frames. A frame attached to "a certain place on the Earth", where the geosynchronous satellite is at rest, is an rotating frame of reference. In rotating frames of reference you have centrifugal forces:
http://en.wikipedia.org/wiki/Centrifugal_force_(rotating_reference_frame)

4. Oct 22, 2009

### HallsofIvy

Staff Emeritus
Yes, that is correct.

How does that follow?

5. Oct 22, 2009

### Charlie G

Thanks for the replies. I suppose my troubles only lied in my confusion about relativity, I had assumed tht the general principle applied to all frames of reference, even non-inertial frames, so that even an observer in one could call himself at rest and attribute inertial forces to a gravitating body. I must read my book for a second time for I seem to have misunderstood.

6. Oct 22, 2009

### mikeph

This sounds fine to me... I don't get why you think the satellite will fall though? It is in an orbit with no resistance, the gravitational field provides the acceleration required for circular motion, don't you think it would stay where it is?

7. Oct 23, 2009

### A.T.

Not in a co-rotating frame of reference where the satellite is at rest. There you need to introduce the centrifugal force to keep it from falling. That's what the OP forgot.

8. Oct 23, 2009