Mechanics
Escape velocity from mass and radius
The original form, useful when the mass is known but the surface gravity is not.
The Formula
v = sqrt(2 x G x M / r)
The original form, useful when the mass is known but the surface gravity is not.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| v | Escape velocity | metres per second | Required speed at the surface. |
| G | Gravitational constant | newton metre squared per kilogram squared | Universal constant, about 6.6743e-11. |
| M | Body mass | kilograms | Total mass of the body. |
| r | Radius | metres | Distance from the centre to the surface. |
What Each Symbol Means
vmetres per second
Escape velocity
Required speed at the surface.
Gnewton metre squared per kilogram squared
Gravitational constant
Universal constant, about 6.6743e-11.
Mkilograms
Body mass
Total mass of the body.
rmetres
Radius
Distance from the centre to the surface.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate an escape velocity page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Calculate An Escape Velocity, filed under Science. Every number the guide produces comes from substituting into this one line.