Step 1: If an object is moving in a circular path of radius **R**
with velocity **v**, some force must be pushing
or pulling it towards the center of the circle.
How large must that centripetal force be?

Step 2: In the case of a planet (mass **m**)
moving around the Sun (mass **M**),
gravity provides this force. How strong is the
force of gravity in this case?

Step 3: Setting these two forces equal to each other gives
us a relationship between the square of the velocity **v**
and the radius **R**.

Step 4: If a planet moves around a circle of radius **R** with
speed **v**, can you express the velocity in terms
of the period **P**?

Step 5: Take this expression for velocity and square it.

Step 6: Almost there! Just re-arrange things so that all the
terms with **P** go on the left, and all the terms
with **R** to on the right.
What do you get?