Innermost stable circular orbit

Summary

The innermost stable circular orbit, or ISCO, of a compact mass is the smallest circular orbit on which a test particle can move stably. For the Schwarzschild metric of mass $M$ it lies at $r = 6GM/c^2$, three times the Schwarzschild radius. In Newtonian gravity every radius allows a stable circular orbit, so the ISCO is a purely relativistic effect. It marks the inner edge of thin accretion discs and the end of the slow inspiral of a small body into a black hole.