How to use it
- Choose a body from the list, or Custom mass and radius.
- For a custom body, enter the mass (in kg, Earth masses or solar masses) and the radius.
- Optionally enter an altitude above the surface in kilometres.
- Read the escape velocity and the orbit speed and gravity at that distance.
Formula and data
vₑ = √(2GM ÷ r), with r = radius + altitude. The circular orbit speed is √(GM ÷ r) and the gravitational acceleration GM ÷ r².
| Body | GM, m³/s² | Mean radius, km | Escape velocity, km/s |
|---|---|---|---|
| Sun | 1.32712440018 × 10²⁰ | 695,700 | 617.675 |
| Mercury | 2.2032 × 10¹³ | 2,439.7 | 4.25 |
| Venus | 3.24859 × 10¹⁴ | 6,051.8 | 10.361 |
| Earth | 3.986004418 × 10¹⁴ | 6,371 | 11.186 |
| Moon | 4.9048695 × 10¹² | 1,737.4 | 2.376 |
| Mars | 4.282837 × 10¹³ | 3,389.5 | 5.027 |
| Jupiter | 1.26686534 × 10¹⁷ | 69,911 | 60.202 |
| Saturn | 3.7931187 × 10¹⁶ | 58,232 | 36.094 |
| Uranus | 5.793939 × 10¹⁵ | 25,362 | 21.375 |
| Neptune | 6.836529 × 10¹⁵ | 24,622 | 23.565 |
| Pluto | 8.71 × 10¹¹ | 1,188.3 | 1.211 |
A custom body uses G = 6.6743 × 10⁻¹¹ m³/(kg·s²), 1 Earth mass = 5.9722 × 10²⁴ kg, 1 solar mass = 1.98847 × 10³⁰ kg and 1 Earth radius = 6371 km.
Worked example
From Earth’s surface: v = √(2 × 3.986004418 × 10¹⁴ ÷ 6,371,000) = 11,186 m/s, that is 11.186 km/s or 40,270 km/h. From 400 km up (r = 6,771 km) it drops to 10.851 km/s, while a circular orbit there needs 7.673 km/s.
Tips
- Escape velocity is not the speed rockets fly at. A rocket that keeps firing its engines can leave slowly; the figure is for a single push with no further thrust.
- Twice the mass and twice the radius gives the same escape velocity, because only M ÷ r matters.
- Gas giants have no solid surface; their radius is the mean radius at the 1-bar level.