In 1992, Comet Shoemaker-Levy 9 wandered too close to Jupiter and, without touching anything, was torn into a string of fragments that later slammed into the planet in spectacular explosions. It had crossed the Roche limit, an invisible boundary calculated with pen and paper in 1848 by French astronomer Edouard Roche. This episode explains the physics of that line: the distance at which a primary body's tidal forces, the differential pull between the near and far side of a satellite, overwhelm the satellite's own self-gravitation, shredding it into rings rather than letting it coalesce into a moon.

We cover why the limit only applies to bodies held together by gravity alone, so a spaceship survives but a loose wrench on its hull would drift away, and why density and rigidity matter, with fluid or rubble-pile bodies stretching into a cigar-s ...