Roche limit
The closest a moon held together by its own gravity can orbit a planet before tides tear it apart, about two and a half planet radii.
A moon feels a planet's gravity more strongly on its near side than on its far side. This difference, the tidal force, tries to stretch the moon along the line to the planet. Far away the stretching is gentle and the moon's own gravity easily holds it together. Closer in the stretching grows rapidly, and at a certain distance it wins. That distance is the Roche limit, named after the French astronomer Édouard Roche, who calculated it in the 19th century.
For a large moon and a planet of similar composition, the Roche limit is about two and a half times the planet's radius. A moon that drifts inside it, or a comet that passes through, can be pulled apart into fragments, which then spread out into a ring.
The rings of Saturn lie inside its Roche limit, which is why they remain countless separate pieces of ice and rock rather than clumping into a moon. They may even be the remains of a moon that strayed too close.
The limit applies to bodies held together mainly by their own gravity, such as large moons and loose rubble-pile asteroids. Small, solid objects held together by the strength of their material can survive much closer. That is why artificial satellites and astronauts are not torn apart in low orbit: they are far too small for tidal stresses to matter.