Is centripetal force relative based on location in space time?

Would an object rotating in orbit 2,000 miles above the Earth be expected to generate the exact same centripetal force as an identical object with identical spin velocity in orbit 20,000 miles above Earth or an identical object with identical spin velocity in deep space? Does being closer to or further away from very massive objects in space time impact centripetal force the way it does gravity? Related question, would identical objects with identical spin velocity, but traveling at materially different velocities through space time, generate the exact same centripetal force?