Roche Limit Calculator

Why planetary rings exist where they do

The Roche limit marks the distance within which a body held together only by self-gravity (rather than structural strength) will be torn apart by tidal forces from a larger body it orbits - this is precisely why planetary rings form just inside many gas giants' Roche limits.

Worked example

For an Earth-sized primary body (radius 6,371 km, density 5,514 kg/m³) and a rocky satellite (density 3,340 kg/m³, similar to the Moon):

d = 6371 x (2 x 5514/3340)^(1/3) = 9,486.9 km

Frequently asked questions

Why do rings form instead of a moon inside the Roche limit? Any moon-sized body that formed or wandered within the Roche limit gets pulled apart into countless smaller fragments by differential tidal forces, which then spread into an orbiting ring rather than remaining a single intact satellite.

Does the Moon orbit inside or outside Earth's Roche limit? The Moon orbits at roughly 384,400 km, comfortably outside Earth's Roche limit calculated here - which is exactly why the Moon remains a single intact satellite rather than a ring system.