# Homework Help: Binary Star Analysis

1. Oct 5, 2009

### CaptainEvil

1. The problem statement, all variables and given/known data

We observe a binary system in which the two stars are 1 and 2 arc sec, respectively, from the center of mass. The system is 10pc from us. The period is 33 yr. What are the masses of the two stars, assuming that i=90 degrees?

2. Relevant equations

3. The attempt at a solution

I want to derive an equation for the masses based on what we know, so here goes.

Based on a simple sketch of the system, we know mara = mbrb.

We can label the distance between the two stars r = ra + rb

re-arranging and substituting yields mara = mb(r-ra)

Then ra = mbr/ma + mb = mbr/M where M = ma + mb

Now, force of Gravity must equal centripetal force in this binary system, so Gmamb/r2 = mava2/ra

since v = d/t, va = 2$$\pi$$ra/T where T is the period.

re-arranging once again yields ra = GmbT2/4r2$$\pi$$2

subbing in from our equation for ra yields M = 4r3$$\pi$$2/GT2

Now we have an equation for the total mass of the system, but I need individual masses.

Can anyone confirm my equation? Am I on the right track? Where does the inclination of the system come in? Is it just for an assumption? Likewise, where does the system distance d away from us come into play? Am I missing something here? Any help would be appreciated thanks.