Kepler's 3rd Law as a result of Newton's Laws

1. Sep 6, 2011

takbq2

thanks in advance for any and all help!

The question is to show that Kepler's 3rd Law holds when you assume circular orbit with TWO gravitating bodies both orbiting around the center of mass. (by equating gravitational and centripetal forces and finding the constant of proportionality which includes the masses of the gravitating bodies).

my attempt at a solution:

I already have shown it when assuming just one mass. I'm having a very hard time differentiating between the two situations.

I know I need to start by using Newton's 3rd law to get a relationship between r1 and a (where a is the distance between the two masses) and eliminate r2 or vice versa (r1 is the distance from m1 to the center of mass, and r2 is the distance from m2 to the center of mass)

2. Sep 6, 2011

3. Sep 6, 2011

Janus

Staff Emeritus
What do you think the ratio of r1 to r2 would be as compared to the ratio of m1 to m2?

4. Sep 6, 2011

takbq2

bigger m1 means smaller r1.. which would in turn mean smaller m2 and larger r2

5. Sep 7, 2011

Janus

Staff Emeritus
Alright, what is the ratio of r1 to r2 if m1=m2.

What happens to the ratio of r1:r2 if you now double the mass of m2?