Centripetal force

The centripetal force is the force that acts on an object to keep it moving in a circular path. The magnitude of the centripetal force for an object with mass m moving on a circular path (with radius r) at a constant tangential velocity v is given by F_c=mv²/r.

Figure 1: Schematic of circular movement of an object with mass m

It can be useful to write the centripetal force in terms of angular velocity ω, which is equal to velocity multiplied by the radius of the path, so that F_c=mrω². The orbital period is given by T= 2π/ω, so the centripetal force can be expressed as F_c=mr(2π/T)².
The centripetal acceleration (following Newton's second law of motion) is given by v²/r and radially directed towards the center of the circular path.
As follows from F_c=mr(2π/T)², the centripetal acceleration of e.g. a satellite can be calculated when the radius and the period T are given. Knowing the distance of the moon from the earth and the time it takes the moon for one round-trip, Newton calculated the centripetal acceleration of the moon from which he deduced the inverse square law of gravitation.