Roche Limit Calculator

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

• Escape Velocity Calculator
• Rocket Equation Calculator
• Orbital Speed Calculator
• Thrust Calculator

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

FAQ