HELP!! need it by tomorrow!

[yayforyeh]

Plaskett's binary system consists of two stars that revolve in a circular orbit about a center of mass midway between them. This means that the masses of the two stars are equal. If the orbital velocity of each star is 220 km/s and the orbital period of each is 14.4 days, find the mass M of each star.

Comments

[mjhamilton]

Think about the centripetal force and the gravitational force.

[yayforyeh]

yes. but the masses cancel out!

(GMm)/r^2 = (Mv^2)/r

so i found the mass of the thing it's rotating around...but if you plug that in..the Ms (which you need to find) go away

[cthulhu_dream]

No, just solve for m.

[mjhamilton]

m = M

[cthulhu_dream]

Start with Newton's universal law of gravitation, aka F(grav) = G*M*m/R^2
In this case, M = m, G you can look up, and R is the distance between M and m.

Remember also that F(centripetal) = mv^2/r
Here r is the distance to the center of mass of the binary system.

You are given the period, so you can easily work out r using v = r*omega where omega is the radial frequency of rotation. You are given the period of rotation, so finding omega is easy.