General Relativity: An Introduction for Physicists · Problem 9.15

The Schwarzschild geometry — Hobson, Efstathiou & Lasenby

Physics · circular-orbit-angular-velocity

Problem

For a particle in a circular orbit of radius

r

in the Schwarzschild geometry, use the alternative form (9.28) of the geodesic equations to show that

\frac{d\phi}{dt} = \sqrt{\frac{GM}{r^3}}.