# Sciency Words: Roche Limit

Sciency Words is a special series here on Planet Pailly celebrating the rich and colorful world of science and science-related terminology. Today, we’re looking at the term:

ROCHE LIMIT

Our yearlong voyage through the Solar System now brings us to Saturn, arguably the Solar System’s most beautiful planet.

Where did Saturn’s rings come from? That’s a subject of ongoing scientific debate, but whatever the explanation, it probably has something to do with the Roche limit.

First calculated in 1848 by French astronomer and mathematician Edouard Roche, the Roche limit describes the distance at which an object orbiting a larger object will be torn apart by the larger object’s gravity.

Gravity becomes exponentially weaker the farther you get from the source of that gravity. This is known as the inverse square law. What it means for a moon, especially a large moon, is that the gravitational pull on one side of the moon is stronger than on the other. Move that moon closer to its planet, and the discrepancy gets worse. Exponentially worse.

If our hypothetical moon strayed too close, the planet’s gravity could start pulling one side of the moon away from the other, causing the moon to crumble. The resulting debris field would tend to spread out, eventually creating planetary rings.

Calculating Roche limits can get complicated. The relative densities of the planet and moon matter a lot, since lower density objects (remember the rubble pile asteroids?) will fall apart much more easily. Molecular composition can also be a factor, as some molecular bonds are stronger than others and can do a better job holding a moon together.

But for a planet and moon of roughly the same density, the Roche limit equals about 2.5 times the planet’s radius (measured from the planet’s center). And it just so happens that Saturn’s rings extend to about that distance.

So thanks to the Roche limit, we can predict where planetary rings are likely to form, but not necessarily how. On Monday, we’ll look at four different ways that Saturn might have gotten its glorious rings.

The Roche Limit from Teach Astronomy.