"Centrifugal force" is a fictitious force. It's a mathematical construct due to the rotating reference frame.

Gravity is sort-of like an acceleration. When something undergoes a change in vector velocity (a change in speed or a change in direction), then it undergoes an acceleration. But things that are "not moving" are subject to gravity when they're not undergoing a change in vector velocity (i.e. acceleration).

So "centrifugal force" (the force required to bend an object's direction of motion into, e.g., a circle) can be determined using similar mathematics as calculating the force due to gravity, but they're not really "equivalent".

The details involve consideration of "inertial mass" and "gravitational mass" - http://en.wikipedia....ass#Inertial_mass

Clocks slowing down is usually thought of as being a consequence of their relative velocity, not their acceleration. But clocks in different gravity wells do read differently as a consequence of different curvatures of space-time. http://en.wikipedia....iki/Time_dilation

HTH a little.

Cheers,
Scott.