Chapter 11, Problem 50P

Two stars of masses M and m, separated by a distance d, revolve in circular orbits about their center of mass (Fig. P11.50). Show that each star has a period given by

$T^2=\frac{4{\pi }^2{d}^3}{G(M+m)}$

Proceed as follows: Apply Newton’s second law to each star. Note that the center-of-mass condition requires that Mr₂ = mr₁, where r₁ + r₂ = d.