Enter the mass of the central object and the satellite density into the calculator to determine the Roche limit.

Roche Limit Formula

The following equation is used to calculate a Roche limit.

R = [ (100*M) / (9*pi*p) ] ^ 1/3

  • Where R is the Roch limit also known as the radius
  • M is the mass of the central object
  • p is the density of the satellite

Roche Limit Definition

Roche Limit is a gravitational boundary determining the minimum distance a celestial object can get to a larger celestial body before being torn apart by tidal forces. It is named after the French astronomer Édouard Roche, who first theorized its existence in the mid-19th century.

This phenomenon is important because it helps us understand the dynamics of celestial bodies, such as satellites, planets, and even galaxies.

The Roche Limit is particularly significant in understanding the formation and destruction of celestial objects, as well as the behavior of matter in extreme gravitational environments.

When a smaller object, like a moon or a satellite, approaches the Roche Limit of a larger object, the gravitational forces acting on it become significantly stronger on the side closest to the larger body compared to the farther side.

This difference in gravitational force across the object creates tidal forces that stretch and deform it. If the tidal forces exceed the object’s internal strength, it will disintegrate, forming a debris field or accreting onto the larger body.

Roche Limit Example

How to calculate the Roche Limit?

  1. First, determine the mass of the central object.

    Calculate the mass of the larger object.

  2. Next, determine the density of the satellite.

    Calculate the density of the orbiting object.

  3. Finally, calculate the Roche Limit

    Calculate the Roche Limit using the formula above.


What is the Roche limit?

The Roche limit is the distance at which an orbiting object or satellite will form rings around a larger body. This is also known as the point at which an object will be captured.

How is the Roche limit calculated?

The limit depends only on the mass of the central object and the density of the satellite.