# Centripetal/Gravitational Force

1. Nov 27, 2007

### bullardz

Orbiting Bodies Question

2. Two stars, A and B are in circular orbits of radii ra and rb, respectively, about their common center of mass at point P. Each star has the same period of revolution T.

Determine expressions for the following three quantities in terms of Ra, Rb, T, and fundamental constants.

a. The centripetal acceleration of star A
b. The mass Mb of star B

$$F_g=\frac{GM_1M_2}{r^2}$$, $$a_c=\frac{4pi ^2r}{T^2}$$

I solved for Part a and got [(4)(Ra)(pi)^2]/T^2. Part b has me stumped though. I think it has to do with the relationship between Fg and Fc and/or the fact that the periods of the two planets are equal. But when I try to solve for the mass, I keep cancelling out the mass variable. If someone could just steer me in the right direction, I would greatly appreciate it. Thanks.

Last edited: Nov 27, 2007
2. Nov 28, 2007

### Shooting Star

Equate the centripetal force on A to the force exerted on it by B.

3. Nov 28, 2007

### bullardz

Right, that makes sense... I don't know why I didn't think of that. Thanks!