[wasyoungonce (Brendan)]

It is classic circular motion. It is motion is the sum of it's velocity vectors one at a tangent to the motion and the other towards the earth.

Vector addition shows that the change in velocity is always at an angle to it's motion. The change in velocity is acceleration thus it is constantly accelerating at an angle to it's motion.

If it alters motion and moves away from earth it does work against gravity (a change in radius from earth means work is done against gravity by the body and thus the body looses some energy...some velocity, ek (energy kinetic)= 1/2mv^2 thus reduce Ek you must reduce Velocity (V), mass is constant) which will slow the body down altering it's velocity vectors making it move back in towards the earth. edit: errrr actually it will slow down and assume a new (slower) equilibrium of motion (velocity vectors).

If it alters it's motion and moves in it towards earth will gain energy (a change in radius from earth inwards means the body gains some potential energy (from gravity) and thus the body gains some velocity)) and speed up. The energy it had and the potential energy it gained equals new energy level for the body thus new velocity vectors. This again alters it's velocity vectors making it move back out again. edit: errrr actually it will speed up and assume a new equilibrium of motion (velocity vectors).

Thus it is maintaining equilibrium of it's motion.

edit:

edited for clarity.

This is a good question. In fact it's a similar one I posed to a yr 12 Physics teacher...whom couldn't answer it. I asked why a satellite cannot be at any velocity and also be geostationary orbit. In other words why cannot it be at a lower orbit and faster velocity but still be geostationary.

The answer is that at a faster velocity it's vector components will make it move at a tangent to it's current orbit (it has too much energy to remain geostationary). It will move outwards doing work against gravity (loosing energy) until such time as the energy of the satellite equals the energy of it's motion (eK=1/2mv^2)=(Ug=mv^2/R).

In other words the body (bodies) maintain an energy balance between themselves. Any movement of either body will alter this balance and the system bodies will move and re-balance energies. Thus equilibrium!

Hope this helps.