How exactly does gravity act on bodies moving in uniform circular motion?

If a satelite is in a circular orbit, its speed is constant. Therefore its kinetic energy is constant.

This means tha although some energy is needed to get the satellite up and orbitting,from then on no further energy has to be supplied. The satellite will keep going forever (assuming no friction/air resistance).

However, the satellite *is* accelerating while in orbit!. In physics, acceleration means speed and or direction are changing. Technically acceleration is a vector and is the rate of change on the velocity vector.

So although the satellite's speed is constant (so no more energy is need to make it go faster) its *direction* is constantly changing. So we say it is acceleratating.

This type of acceleration has a special name - centripetal acceleration.

There is loads about this if interrested. E.g. see link.

I'm gonna have to let you down here because nobody knows where gravity comes from.

However it's an innate property of mass. Whenever there is mass, there is attraction. It is for now actually more accurately explained as the curvature of space, but for most purposes it can just be thought of as just a force that depends on the two masses.

So when you have two bodies orbiting around one another, they both attract each other with the same amount of force. Hence both objects will move in circular paths around a common center, which is very often inside the larger body.

For such a large difference in size as with Earth and man-made satellite, this motion of Earth can be absolutely neglected, but for similar sized things they do noticeably orbit one another (google Pluto and Charon).

Thing is, there is no net energy release or buildup connected with an orbit. The satellite always moves at same speed and the force acts perpendicular to its line of motion at all points. Being that nothing happens to its energy, the acceleration only changes direction and it's a free ride.

If it's more of an elliptical orbit, the satellite gets a boost at one portion and a slow down at another, but the net effect is still zip. Only if the orbit becomes unstable and it hits the ground, or if it escapes Earth's grip does there exist a change in mechanical energy.

"could somehow that energy be used to generate clean energy for human use?"

Hmm... I would hope so otherwise this is all a hoax:

https://www.youtube.com/results?search_query=hydro...

That is technically not infinitely reusable either. All of that enormous lake first has to get there. This is done by the Sun (rain etc), and even Sun doesn't have infinite energy to keep doing it forever.

We need to define "clean energy" though. Building&running a dam requires massive resources and displacing of wildlife and population. It doesn't pollute as much as coal, and doesn't blow up as readily as nuclear but still...

There are also places that harness energy of tides. This is pretty clean, but it doesn't pay off as much. Let's just stick to wind :)

There really isn't any energy expended in keeping an object in orbit, at least from the gravitational side. The object stays at the same potential energy. It is inertia which keeps the object moving.

If you add up (integrate) the acceleration for a full orbit, the net acceleration is 0. The object returns to where it once was. No net displacement, no net energy dispensed.

There is energy lost in the process, but it is due to friction. That results in a change in velocity (or unit speed) of the object, which also causes a slight change in its orbit.

Gravity is not the only force involved.