Calculateur de Vitesse de Libération Gratuit
Calculez la vitesse de libération d'une planète ou d'un corps céleste.
Vitesse de libération
11,185.73 m/s
Escape Velocity vs Body Mass
Formule
## Deriving Escape Velocity Escape velocity is the minimum launch speed at the surface for an object to reach infinity without further propulsion. ### Formula **v_esc = √(2 G M / r)** This is exactly √2 times the circular orbital velocity at the same radius. It comes from setting kinetic energy equal to gravitational potential energy: 1/2 m v² = G M m / r.
Exemple Résolu
Find Earth's escape velocity (M = 5.972e24 kg, r = 6 371 km).
- 01v_esc = √(2 G M / r)
- 022 G M = 2 × 6.674e-11 × 5.972e24 = 7.972e14
- 037.972e14 / 6.371e6 = 1.251e8
- 04v_esc = √(1.251e8) ≈ 11 186 m/s ≈ 11.19 km/s
Questions Fréquentes
Does escape velocity depend on the escaping object's mass?
No. The mass cancels out in the energy balance. A pebble and a spacecraft need the same speed.
Why is escape velocity √2 times orbital velocity?
Orbital velocity balances gravity for a circle. Escape requires enough extra kinetic energy to overcome the remaining potential, which works out to a factor of √2.
What is the escape velocity of the Moon?
About 2.38 km/s, much lower than Earth's because the Moon is less massive and smaller.