The formula
v = √(2 · G · M / r)
| Symbol | Quantity | Unit |
|---|---|---|
| v | Escape velocity | m/s |
| M | Mass of the body | kg |
| r | Radius of the body | m |
What it means
Escape velocity is the speed at which kinetic energy exactly matches the gravitational potential energy binding an object. Reach it and the object never returns, however slowly it ends up travelling.
How to work it out by hand
- Multiply 2 by the gravitational constant and the body's mass
- Divide by the radius
- Take the square root
What is worth knowing
Escape velocity does not depend on the escaping object's mass, which surprises people: a marble and a spacecraft need the same 11.2 km/s. Note too that it is a speed, not a direction — anything at that speed escapes, whichever way it points, as long as nothing is in the way. In practice rockets never actually reach it, because they accelerate continuously rather than being fired ballistically, and a sustained thrust can leave at any speed. The concept also gives the definition of a black hole: a body whose escape velocity exceeds the speed of light.