# Gravitational Forces

## Homework Statement

So finals is coming up and I was reviewing my notes, when I read that according to Netwon's Third Law gravitational forces (Fg) should be equal between to objects like the sun and the Earth. So if the sun and earth have the same Fg toward each other, why doesn't the sun revolve around the Earth instead?

I looked at the Cavendish balance and it says the small object moves toward the bigger object even though they have the same Fg toward each other.

## The Attempt at a Solution

HallsofIvy
Homework Helper
Yes, for two bodies of masses m and M, the distance between their centers r, the gravitational force between them is
[tex] \frac{GmM}{r^2}[/math]

However, since force= mass times acceleration, acceleration= force/mass.

That is, the acceleration of the object of mass M is
$$\displaystyle \frac{GmM}{Mr^2}= \frac{Gm}{r^2}$$
while the acceleration of the object of mass m is
$$\displaystyle \frac{GmM}{mr^2}= \frac{GM}{r^2}$$

That is, if M is much larger than m (as for sun and earth) the lighter body will have a much greater acceleration.

Actually both bodies rotate around their mutual center of gravity. In the case of earth and sun, that center of gravity is well within the sun.