how do jupiter's moons stay in orbit around jupiter
They rotate around jupiter. If you rotate around an object you are accelerating toward it, even though the distance can stay the same. This so-called centripetal acceleration multiplied by the mass must equal the gravitational force on the moon by Newton's second law.
well, moons just stay in an orbit. if they stray off they will turn into asteroids and either go towards another planet or they would plunge right towards the earth.
because of gravity
I do not know
the stay in orbit because of the gravitational pull from Jupiter!