The satellite must mysteriously set itself up so that it is neither pulled back by gravity nor let loose into space.
It
is being pulled back by gravity, which is
why it's not let loose into space.
It must have that perfect balance between just enough gravity but not too much gravity.
"Must", you say? Did it not occur to you that before you announced what "must" be true about gravity, you should have studied the theory of gravity?
Its orbit is a "balance" (so to speak) between its velocity and its gravitational attraction to the earth. Now, orbits are
stable. That is to say, a change in the position or velocity or mass of the satelite would result in a change in its orbit, not in it stopping orbiting and crashing to earth or flying off into space.
If some sort of "perfect balance" of cosmic fine-tuning was required, as you seem to think, then we'd have futzed the solar system by landing spaceships on the moon and suchlike exploits.
Oh yes, and stay in orbit for MILLIONS OF YEARS.
Because as orbits are stable, it would take a miracle to knock it out of its orbit.
---
You can see some of the math, including a proof of the stability of orbits,
here.
Edited by Dr Adequate, : No reason given.
Edited by Dr Adequate, : No reason given.