Newton measures the speed of gravity

[bobsmith76]

Homework Statement

This doesn't come from a textbook but it's like a homework question so I thought it would be more appropriate here.

I'm trying to figure out what equation Newton used since the force of gravity or the mass of the Earth was not known until Cavendish. I'm looking for an equation that has the square of the distance or the radius, but all I can find is

(Gm₁m₂)/r^2 = (m₂v²)/r

But Newton couldn't have used that one because he didn't know G or the mass of the Earth. I also thought about a = (v^2)/r but Newton didn't know the acceleration.

 

[Andrew Mason]

In this case, you can calculate the acceleration of the moon from its angular speed and radius:

a = v^2/r = 4∏^2r/T^2

By measuring the acceleration of the moon and of an object on the surface of the earth, you get the 1/r^2 relationship.

AM