innermost stable circular orbit
/ ISCO, 'ISS-koh' /
Around an ordinary star or planet, you can in principle orbit at any distance you like, however close — just go faster the nearer you get. Around a black hole this stops being true. There is a critical distance, the innermost stable circular orbit (ISCO), inside which no stable circular orbit exists at all. Cross it, and you can no longer simply circle the black hole; you inevitably spiral inward and plunge across the event horizon. It is the last safe ledge before the fall.
Why does it exist? Near a black hole, gravity is so strong that Einstein's general relativity changes the rules — the effective pull rises so steeply that, inside the ISCO, any tiny nudge inward sends you plunging rather than settling into a new orbit. For a non-spinning black hole, the ISCO sits at three times the Schwarzschild radius (so about 90 km for a 10-solar-mass black hole). A spinning black hole drags space around and shrinks the ISCO if you orbit the same way it spins, letting matter circle even closer before falling in.
The ISCO is not an abstraction — it is the inner edge of an accretion disk. Gas orbiting a black hole can spiral inward, heating and glowing, only down to the ISCO; once there, it makes its final plunge. This means the ISCO sets how much energy infalling matter can release before disappearing, which is why spin matters so much for how brightly a black hole's disk shines: a fast-spinning black hole has a tighter ISCO, deeper infall, and a more efficient, brighter engine. Measuring where a disk's glow cuts off lets astronomers estimate a black hole's spin.
For a non-spinning 10-solar-mass black hole, the innermost stable orbit lies about 90 km out. Gas can circle and glow down to there, but once it drifts inside, no amount of orbiting can save it — it plunges across the horizon just a heartbeat later.
The ISCO is the last stable orbit; drift inside and the plunge is inevitable.
The ISCO sits well outside the event horizon, not at it. It is where stable orbits end, marking the inner edge of an accretion disk; the actual horizon lies still deeper in.