General Relativity: An Introduction for Physicists · Problem 9.18
The Schwarzschild geometry — Hobson, Efstathiou & Lasenby
Physics · innermost-stable-circular-orbit
Problem
Show that a massive particle moving in the innermost stable circular orbit in the Schwarzschild geometry has speed c/2 as measured by a stationary observer at this radius. Hence calculate the period of the orbit as measured by the local observer. What is the period of the orbit as measured by a stationary observer at infinity?