Measuring the centripetal acceleration of an orbiting object is rather difficult, so an alternative approach is to use the period of the orbiting object. find an expression for the gravitational constant in terms of the distance between the gravitating objects rm, the mass of the larger body (the earth) me, and the period of the orbiting body t.

Explanation:

We write the force of gravity a body of mass experiments by being at a distance from a larger body (the earth) of mass using Newton's law of universal gravitation:

Since this force is the centripetal force that keeps the object on orbit, and the velocity of the orbiting body will be given by the relation between the circumference and the period of the orbit, we can write:

Which means:

or:

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