LearnMechanics & orbitsSome maths
Escape velocity
The speed at which an object's kinetic energy exactly cancels the gravitational well it sits in, so it can leave and never return.
Why it matters
It sets which worlds can hold an atmosphere. Titan keeps a thick one at 2.6 km/s because it is cold; Mercury loses everything at 4.3 km/s because it is hot.
The maths, in layers
1 · Intuition
Set kinetic energy equal to the depth of the gravitational well and solve for v.
2 · The equation
v_esc = √(2·G·M / r)
- M
- mass of the body
- r
- distance from its centre — the surface, usually
What people usually get wrong
You must reach escape velocity to leave a planet.
Only if you are coasting unpowered. A rocket that keeps thrusting can leave at any speed — escape velocity is about ballistic trajectories, not propulsion.
Leads to
Nothing here builds on it yet.