🕳 Schwarzschild Geodesics — Black Hole Orbits & General Relativity

It's the radius rs = 2GM/c² at which the escape velocity from a non-rotating mass equals the speed of light, defining the event horizon of a Schwarzschild black hole. Nothing, not even light, can escape from inside r = rs once it crosses.

The photon sphere sits at r = 1.5 rs, where light itself can, in principle, orbit the black hole in an unstable circular path. Any perturbation sends a photon either spiraling in or escaping outward, which is why it appears as a sharp dashed ring in the simulation rather than a place you can safely park an orbit.

ISCO stands for innermost stable circular orbit, located at r = 3 rs for a Schwarzschild black hole. Inside this radius, circular orbits become dynamically unstable and any inward perturbation causes the orbiting body to spiral into the horizon — which is why accretion disks around real black holes have an inner edge near this radius.

In Newtonian gravity a bound orbit is a fixed ellipse that never rotates. General relativity adds an extra 1/r³ term to the effective potential, so each orbit's perihelion advances by a small angle every revolution — the "Precessing Ellipse" preset makes this rosette pattern easy to see.

The Plunging preset starts a particle with too little angular momentum to resist gravity at its radius, so it spirals inward and crosses the event horizon at r = rs. The Escape preset gives the particle enough energy (Ẽ ≥ 1) to overcome the black hole's pull entirely and fly off to large r, never to return.