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## Homework Statement

How do I show that for a binary star system, if one star has mass ##M_s##, speed ##V_s##, period ##P##, the mass of the other star is given by: ##M_P^3 \approx \frac{V_s^3}{2\pi G} PM_s^2##?

## Homework Equations

## The Attempt at a Solution

[tex]\frac{GM_pM_s}{(a_p+a_s)^2} = \frac{M_s v_s^2}{a_s}[/tex]

Substituting in ##PV_s=2\pi a_s##:

[tex]M_p = \frac{2\pi(a_p+a_s)^2V_s}{PG}[/tex]

Using kepler's second law: ## P^2 = \frac{(a_p+a_s)^3(2\pi)^2}{G(M_p+M_s)} ##:

[tex]M_p^3 = \frac{V_s^3}{2\pi G} P (M_p+M_s)^2[/tex]