Challenging High School Planetary Mechanics Problem

[forcefrom]

Homework Statement

A certain binary star system consists of two stars of masses m and 3m respectively separated by a distance of 1.5 * 10^12 m measured between their centres. These stars revolve in sync with each other around their common centre of mass. If the smaller star has a mass of 1.0 * 10^30 kg, what is their common period of revolution?

r = 1.5 * 10^12 m
m1 = 1.0*10^30 kg
m2 = 3.0*10^30 kg

Homework Equations

Fg = Gmm/r^2
Fc = 4mpi^2r/T^2

The Attempt at a Solution

Initially, I thought I could do Fc = Fg and solve for period, but I'm not sure if that's the right way to do it and it doesn't sound right either.

 

[voko]

Your method is correct in principle. A slight complication is that the r's in both equations are different. One is measured from the center of revolution, another is the distance between the bodies. Which one is which and how are they related?

 

[forcefrom]

Oh, so the r in Fc is different. Center of revolution means I need to know my center of mass, right? Another problem I'm having is I'm not sure exactly how the sketch for this works, if that's needed at all?

 

[voko]

Yes, you need to find out the C. M. I am not sure what your problem with the sketch is.

 

[forcefrom]

Do I need a sketch (to know visualize/see the diagram of the problem) to find the C.M.? I'm not sure how to find it.

 

[voko]

What is the definition of the C. M.?