Last updated: 2026-06-16

The Roche Limit

Gravity holds a moon together, but the same gravity from the planet it orbits tries to pull it apart. The near side of the moon feels a stronger pull than the far side, and this difference — the tidal force — stretches the moon. The Roche limit is the distance at which the tidal stretching finally overwhelms the moon's own self-gravity. Venture inside it, and a body held together only by gravity is torn into rubble.

For a rigid satellite, the limit is:

$d = R\left(\frac{2\rho_p}{\rho_s}\right)^{1/3}$

where $R$ is the radius of the primary (central) body, $\rho_p$ its density, and $\rho_s$ the density of the satellite. Remarkably, the satellite's size drops out entirely — only the densities and the primary's radius matter.

Worked Example

Take the Earth (radius 6,371 km, $\rho_p = 5{,}514\ \text{kg/m}^3$) and a Moon-like satellite ($\rho_s = 3{,}344\ \text{kg/m}^3$):

$d = 6{,}371 \times \left(\frac{2 \times 5{,}514}{3{,}344}\right)^{1/3} = 6{,}371 \times 1.49 \approx 9{,}480\ \text{km}$

The Moon orbits at about 384,000 km — roughly forty times farther out — so it is in no danger of being torn apart.

Rigid Versus Fluid Bodies

The formula above assumes the satellite stays rigid right up until it shatters. A real moon held together by gravity behaves more like a fluid: as it nears the planet it deforms into an elongated shape, which makes it even easier to disrupt. The fluid Roche limit is larger than the rigid one by a factor of about 1.9. The true breakup distance for a loosely bound body therefore lies somewhere between the rigid result and roughly twice it, depending on the body's strength and internal structure.

Rings, Not Moons

The Roche limit explains one of the Solar System's most beautiful features: planetary rings. The rings of Saturn, Jupiter, Uranus, and Neptune all lie inside their planets' Roche limits. Within this zone, tidal forces prevent the countless ice and rock particles from clumping into a single moon, so the debris stays spread out in a disc. Beyond the limit, the same material would gradually accrete into moons. A comet or asteroid that wanders too close — as comet Shoemaker–Levy 9 did at Jupiter in 1992 — can likewise be ripped into a string of fragments.