How to use it
- Choose the primary body, or enter your own radius in km and density in g/cm³.
- Enter the density of the satellite: about 0.9 for ice, 3 for rock, 5 or more for iron-rich bodies.
- Optionally enter the orbit radius, measured from the primary’s centre, to see where it falls.
Formulas
- Rigid satellite: d = R × (2 × ρM ÷ ρm)^(1/3) ≈ 1.26 × R × (ρM ÷ ρm)^(1/3)
- Fluid satellite: d ≈ 2.44 × R × (ρM ÷ ρm)^(1/3)
R and ρM are the radius and density of the primary, ρm the density of the satellite. Only the ratio of densities matters, so the result in primary radii does not depend on the size of the primary.
| Primary | Mean radius, km | Mean density, g/cm³ |
|---|---|---|
| Sun | 695,700 | 1.408 |
| Earth | 6,371 | 5.514 |
| Mars | 3,389.5 | 3.934 |
| Jupiter | 69,911 | 1.326 |
| Saturn | 58,232 | 0.687 |
| Uranus | 25,362 | 1.27 |
| Neptune | 24,622 | 1.638 |
Worked example
A Moon-like satellite (3.344 g/cm³) around Earth (6371 km, 5.514 g/cm³): (5.514 ÷ 3.344)^(1/3) = 1.1814.
- rigid: 6371 × 2^(1/3) × 1.1814 = 6371 × 1.2599 × 1.1814 = 9,483 km (1.488 Earth radii)
- fluid: 2.44 × 6371 × 1.1814 = 18,365 km (2.883 Earth radii)
- the Moon’s orbit, 384,400 km, is 60.336 Earth radii away — far outside both
An icy body (0.92 g/cm³) around Saturn has limits of 66,562 km and 128,906 km; an orbit at 100,000 km lies between them, where Saturn’s main rings are.
Tips
- Denser satellites survive closer in. The limit shrinks with the cube root of the satellite’s density.
- Both formulas are idealised. The fluid coefficient 2.44 is the classic approximate value; real satellites with some internal strength survive somewhat closer than the fluid limit.
- Measure the orbit from the centre of the primary, not from its surface.