when rockets are put in orbit, could they stay in orbit forever? if there was no one to man it, and it was not programmed to come back down, what would happen? would it stay up there, or would earth's gravity pull it back down?
There's the simplistic theory, and the more complicated practice.
In theory, yes, an object put in orbit would stay there forever. Earth's gravity pull keeps it in orbit, spinning it around the planet instead of flying off. It doesn't pull it back down, because the forces are already balanced.
However, in practice, there's other forces in play. Most importantly, on low Earth orbits, there's just a tiny bit of atmosphere leftovers slowing down the object. Depending on the altitude, it might take months, years, or decades, but eventually it will slow down enough to reenter. Also, there are minute forces from solar radiation and gravitational fields of other objects that might slow down the object (though that might take an awfully long time).