Roche Limit Calculator

Calculate the Roche Limit, which is the minimum distance at which a celestial body, due to tidal forces, will disintegrate due to the gravity of another body.

Input Parameters

Calculation Results

Roche Limit Calculation

Roche Limit (d) = (2/3) * (ρ₁/ρ₂)^(1/3) * (R₁/R₂) * (M₂/M₁)^(1/3) * R₁

Where:
M₁ = Mass of Body 1
M₂ = Mass of Body 2
ρ₁ = Density of Body 1
ρ₂ = Density of Body 2
R₁ = Radius of Body 1
R₂ = Radius of Body 2

Roche Limit (d): N/A meters

Roche Limit Calculator Calculator Usage Guide

Learn how to use the Roche Limit Calculator calculator and its working principles

What is the Roche Limit?

The Roche Limit is the minimum distance at which a celestial body, due to tidal forces, will disintegrate due to the gravity of another body. This concept is crucial in understanding the dynamics of celestial bodies and their interactions.

How to Use the Calculator

  1. Enter the mass of Body 1 (M₁) in kilograms.
  2. Enter the mass of Body 2 (M₂) in kilograms.
  3. Enter the density of Body 1 (ρ₁) in kilograms per cubic meter.
  4. Click the "Calculate" button to compute the Roche Limit.
  5. The result will be displayed in meters.

Formula Explanation

The Roche Limit (d) is calculated using the formula:

d = (2/3) * (ρ₁/ρ₂)^(1/3) * (R₁/R₂) * (M₂/M₁)^(1/3) * R₁

Where:

  • d = Roche Limit
  • ρ₁ = Density of Body 1
  • ρ₂ = Density of Body 2 (default is 1000 kg/m³ for water)
  • R₁ = Radius of Body 1 (default is 6371 km for Earth)
  • R₂ = Radius of Body 2 (default is 1737 km for Moon)
  • M₁ = Mass of Body 1
  • M₂ = Mass of Body 2

Practical Applications

The Roche Limit has several practical applications, including:

  • Understanding the tidal forces that can break apart celestial bodies.
  • Explaining the formation of rings around planets.
  • Assessing the stability of artificial satellites.