In order to maintain any probe, satellite, space station....and the moon itself in an orbit around the Earth, the "trick" is calculate the velocity of the orbit keeping in mind the distance of the orbit you want the object to be positioned away from our planet.
Any object that would be thrust with a higher speed than it should at a certain altitude will make it escape from Earth. The opposite is if the object slows down more than it should at that height, it will fall on Earth. So this means that each "orbit distance" has its own "orbit speed".
Wanting to keep the satellites at a geostationary orbit (facing the same side of the Earth), the speed and the altitude these satellites have allows them to obtain their purpose.
The moon, as well as with the other objects I have mentioned, is always in a free fall onto Earth. The point is, its speed will not let it "reach" the ground because the fall is compensated by the moons speed that can't find the ground beneath it (the horizon keeps moving away). If the moon should slow down for one reason or another, then the Earth would be hit by it.
To obtain those satellites you mentioned facing the same side of our planet, the height of the orbit AND the correct speed determine the success of their missions.