Plaskett’s binary system consists of two stars that revolve in a circular orbit about the center of mass midway between them. This statement implies that the masses of the two stars are equal. Assume the orbital speed of each star is v=220 km/s and the orbital period of each is 14.4 days. Find the mass M of each star. (For comparison, the mass of our Sun is 1.99 x10^30kg).

Question

anonymous · Answer

I think i have a solution method, are you still working on this problem?

Do you have the main equation you need to solve this problem, ie. the gravitational force equation?

roadjester · Answer

The problem requires the use of Kepler's Laws but since it is two stars circling a CM and not the gravitational attraction of one object to another I'm not sure of the approach.

anonymous · Answer

Ah, I don't think I'm familiar with Keplers Law. If you have to use that, then I dont think I'm able to help :/

I was thinking you could use the equation

$$F _{grav} = \frac{ G*m _{1}*m _{2} }{ d ^{2} }$$
 with m1 = m2 = m
    you can determine d from the circumference from the planet's velocity and orbital period

and $$F _{grav} = m*a _{c} = m*centripetalforce = \frac{ mv ^{2} }{ r }$$

roadjester · Answer

Why square the diameter?

anonymous · Answer

err sorry I think that's supposed to be radius

anonymous · Answer

actually I think diameter is correct, the letter used is a bit confusing http://en.wikipedia.org/wiki/Newton's_law_of_universal_gravitation

anonymous · Answer

If you want more clarity, this guys seems to have a full explanation http://answers.yahoo.com/question/index?qid=20070113152923AAEsieP

roadjester · Answer

I don''t understand your confusion, that is the correct formula for Newton's law of universal gravitation. r is the radius because under normal circumstances, one of the two objects is "stationary". For example, between the sun and the earth, the sun is the stationary object, or a satellite, then the earth would be the stationary one (assuming that there are only two particles in the system).

roadjester · Answer

My confusion comes from the fact that both objects in this problem are moving.

anonymous · Answer

While they are moving, the equation should still hold since the planets are always directly across from each other, since they move at the same velocity along the same axis, in addition to the fact that their center of mass is always exactly between them

roadjester · Answer

In that case, should it be the radius from the center of mass to each object squared or the diameter squared? and in either case, how would I eliminate r through substitution? What do I substitute?

roadjester · Answer

hmm, gotta afk for about 20 min, bb after so if you don't hear from me, well, I'm afk. lol

anonymous · Answer

You don't eliminate r, you determine it by first finding the circumference of the orbit, then dividing by 2pi

|dw:1347342302235:dw|

circumference = velocity*orbital period
radius = circumference/2pi

ok np, I hope this clears it up, otherwise the yahoo link should help