General Relativity: An Introduction for Physicists · Problem 11.20

Schwarzschild black holes — Hobson, Efstathiou & Lasenby

Physics · binary-mass-function

Problem

From observations of a compact binary system, one may calculate the mass function

f(M) = \frac{PK^3}{2\pi G},

where

P

is the orbital period and

K

is the radial velocity amplitude. From Kepler's laws in Newtonian gravity, show that

f(M)

is related to the masses

M_1

and

M_2

of the compact object and the companion star and the inclination angle

i

of the orbit to the plane of the sky by

f(M) = \frac{M_1^3\sin^3 i}{(M_1+M_2)^2}.