What Are the Linear Speeds of Binary Stars?

[Gunman]

Homework Statement

A binary star consists of two stars of mass 5.0 * 10 ^ 30 kg each and separated by a distance of 2.0 * 10 ^ 11 m . The stars rotate about their common center of mass. Determine their linear speeds.

Homework Equations

F = GMm/r2
F = mv2/r

Well I’m confused on what is the r value. How is the object able to move in a circular motion when the point at which its spinning about isn’t the center of the circle?
And secondly when I’m using the formulae F = GMm/r2, is the r value 2.0 * 10 ^ 11 ?

Hmm. Would appreciate any help given to solve this problem. Thanks in advance.

 

[turdferguson]

The two objects rotate around the center of mass of the system. In this case, the objects have the same mass so the COM is at the geometric center of the system. r doesn't equal the separation distance, but the distance from the center of mass of the system

 

[Gunman]

Thanks for the help turdferfuson. =)

So it can be formulated that :

GMM/r2 = Mv2/r(Gravitational force = centripetal acceleration * M)
GM/r = v2 ( I cancel out the common mass M and bring over the r)
(GM/r) ^ (1/2) = v (I square root the equation to attain v)

Then I get the answer of 5.78 * 10 ^ 4 m/s. Its incorrect.
Any reason why I'm wrong ?
Thanks again. =)

 

[turdferguson]

Are you using one mass or the combined mass?

 

[Gunman]

I'm using one mass which is 5.0 * 10 ^ 30.

 

[Doc Al]

So it can be formulated that :

GMM/r2 = Mv2/r(Gravitational force = centripetal acceleration * M)

Careful here. What does "r" represent? In the formula for gravitational force, r is the distance between the masses; but in the formula for centripetal force, r is the radius of the circular path. Those aren't the same!

 

[Gunman]

Thanks al. =) That solved the problem..=) haha