Classical Dynamics of Particles and Systems · Problem 2-48

Oscillations — Marion & Thornton

Physics — Mechanics · binary-star-equal-mass-kepler-third-law

Problem

Two gravitationally bound stars with equal masses

m

, separated by a distance

d

, revolve about their center of mass in circular orbits. Show that the period

\tau

is proportional to

d^{3/2}

(Kepler's Third Law) and find the proportionality constant.