Planet orbits: what's the difference between gravity and centripetal force?

Question

My physics teacher says that centripetal force is caused by gravity. I'm not entirely sure how this works? How can force cause another in space (ie where there's nothing). My astronomy teacher says that gravity is (note: not like) a 3D blanket and when you put mass on it, the mass causes a dip/dent in the blanket and so if you put another object with less mass it will roll down the dip onto the bigger mass. Is this true and is this what causes the centripetal force.

Answer 1

Since the planets move in near circular orbits, constantly changing direction there must be (by the 2nd law) a force causing the circular motion and it's the gravitational force

so we have, for planetary motion GMm/r² = mrω² so you could say gravity "causes" centripetal force but I think it would be clearer to say in order for a planet to move in a circular orbit centripetal force is necessary and in the case of planets gravitational attraction provides the force.

When you swing a bucket of water in a vertical plane you provide the centripetal force that keeps the water in the bucket.

Hope this is clear

Jim