Why don't satellites in orbit fall to the ground? Why don't they fly off into space?
The fact that a satellite is in orbit means that it will neither fall to the ground or fly off into space.
When a satellite is in orbit there is a relationship between the orbital period
The closer a satellite orbits the planet, the shorter its period must be to keep it in orbit and the faster it is travelling.
If a satellite fires a rocket engine and slows down, its orbital period increases and it is no longer in orbit and it starts to fall. As it falls under gravity it speeds up. When the orbital period and distance are again in balance, the satellite will assume a lower orbit with a shorter period.
If the satellite falls low enough and at a steep enough angle, the atmosphere will continue to slow it down and it will fall to the ground. This is how orbiting space craft are landed.
If a satellite fires a rocket engine and speeds up, then its orbital period reduces and it starts to fly off into space. As it gets higher, gravity slows it down. When the orbital period and distance are again in balance, the satellite will assume a higher orbit with a longer period.
If the satellite fires its rocket for long enough it will be travelling to fast for gravity to slow it into an orbit. In this case it will fly off into space. This is how we get space craft to the Moon and other planets.
This is a interactive webpage for the experimentation of satellite's orbit.