I “came up” with this problem already some time ago but it is today that I am going to solve it here.
When you draw satellite above Earth and draw the forces that act on it you will see that there is only one force there (only one really important). It is the gravitational force of Earth. Why does not this satellite fall back you ask?
Well this is actually very interesting. The thing here is called orbital velocity. This is the velocity you need to orbit around Earth at particular distance.
So such a satellite orbits around Earth and you need the speed to be so big that gravity wont just pull it back but not too big so it does not fly away. I read somewhere great analogy: orbiting is just a falling without the crash. Take ISS for example. Why are there astronauts in “zero G” when they still receive 96% of Earths gravity? This is because the ISS is actually falling, kind of. It is falling around the Earth.. AROUND so it actually misses all the time. With extremely small drag and friction the satellites slow down just a little bit so they orbit for tens of years. For example ISS has to use its motors to get back on her height from Earth because otherwise it would fall down in some time.
The closer you are to Earth, than the drag from atmosphere is greater so you must orbit at faster pace (+ the small amount of bigger gravity). Most satellites orbit in the low Earth orbit which is from 150-2000 kilometers or so.
Sometimes satellites need to be put away so they are moved on what is called satellite graveyard and they will orbit there for a long time. Or their path can be changed so they burn up in the atmosphere. The problem on Earths orbit is huge mess because of those years that we were just launching new and new satellites. This is a huge problem for the ones that are actually working and also for ISS because just a small piece of debris can do tremendous damage.