Escape Velocity
Escape Velocity
Escape velocity is the speed at which kinetic energy just balances the gravitational potential well — enough to leave without further thrust.
The escape velocity is v = √(2·G·M/r). where G is the gravitational constant, M the planet mass and r the radius.
Inputs
G := 6.674e-11 N·m^2/kg^2=6.67e-11 m^3/kg/s^2
M := 5.972e24 kg=5.97e+24 kg
r := 6.371e6 m=6.37e+06 m
Set kinetic energy equal to the gravitational well depth.
v := sqrt(2·G·M/r)=11185.73 m/s
Results
Earth’s escape velocity is about 11.2 km/s — exactly √2 times the circular orbital speed at the same radius. It is independent of the escaping object’s mass.
Assumptions & limitations
- Ignores atmospheric drag.
- Non-rotating planet.
- Radial escape from the surface.