What Keeps A Rocket From Falling To Earth Or Moving Off Into Space?

1st I need to say, I am NOT a Rocket Scientist!  :)

A rocket will and they do fall back to Earth!  They need to be travelling at about 17,000 mph to break into orbit. BUT while they are in orbit, they are falling back to Earth. They are usually high enough that they take a while to fall back. The air is SO thin that it doesn't affect the rocket very much. But as it gets lower, it will be affected more, and so will fall faster. Also, gravity will and does have a effect on the orbit as well. The ISS needs to be "pushed" to a higher orbit quite frequently to keep from falling back to Earth. As for moving out into space. They do as well. Many rockets have lifted satellites and probes into space to explore distant planets and such. They need to keep free of Earth's gravity. They can be sent far enough away that they will be affected by other planets gravity. They can also be steered by other Planets or even the Moon to direct them to different locations. And so, they can even leave our solar system. OR in other cases, they have been directed into the Sun.

I hope that answers your question.

Take care