How do satellites maintain altitude in space?
First, let’s look at what a satellite in orbit is doing. A satellite is being pulled constantly toward the Earth. It’s falling toward the Earth. However the satellite is traveling so fast, horizontally, that by the time it would have hit the Earth it’s on the other side of the earth. Here is a great illustration:
Second, the atmosphere gets thinner as we increase altitude, very slowly tapering off to zero. From this chart you can see that it’s pretty much non-existent by about 37km shown here:
However, It’s not truly zero, and so we have drag. There are very small amounts of gas particles at high altitudes, Drag decreases the horizontal velocity. If we do nothing, eventually we hit thicker atmosphere, and burn up.
Finally, a satellite maintains it’s altitude by maintaining it’s horizontal velocity by firing it’s rockets in the prograde direction (direction of positive velocity tangent to it’s orbit). This is done periodically with hot or cold gas until fuel runs out, then eventually the satellite re-enters the atmosphere.
Bonus Giz Tip: Learn more about Lagrange points. Basically a Lagrange point is a location where the pull of gravity between two bodies (say the Earth and Moon) is nearly equal, resulting in a very stable orbit. Maintenance is still required, just less.
TL;DR: They are constantly falling towards the earth but their forward momentum makes them miss the planet and keep going around it.