Roche Limit Calculator
Roche Limit Calculator finds the minimum orbital distance for a satellite, with a plot of distance.
Formulas Used in Roche Limit Calculator
The calculator computes the Roche limit for a rigid satellite orbiting a primary body:
Roche Limit:
\\[ d = \left( \frac{2 M}{\rho_s} \right)^{1/3} \\]Where:
- \\(M\\): Mass of the primary body (kg)
- \\(\rho_s\\): Density of the satellite (kg/m³)
- \\(d\\): Roche limit distance (m)
Example Calculation
Example: Earth (\\(M = 5.972 \times 10^{24} \, \text{kg}, \rho_s = 2000 \, \text{kg/m}^3\\))
\\[
d = \left( \frac{2 \times 5.972 \times 10^{24}}{2000} \right)^{1/3} \approx 9.495 \times 10^6 \, \text{m} \approx 9495 \, \text{km} \approx 6.35 \times 10^{-5} \, \text{AU}
\\]