Escape Velocity

Definition

The minimum speed an object needs to break free from a planet's gravity forever, without further propulsion.

$v_{esc} = \sqrt{\frac{2GM}{R}}$

Symbol: $v_esc$ · Unit: m/s

Technical definition

Derived from energy conservation (KE + PE = 0 at infinity): v_esc = √(2GM/R), where M is the planet's mass and R its radius. Notably independent of the escaping object's mass. Earth's escape velocity is about 11.2 km/s.

Example

Earth's escape velocity is 11.2 km/s (about 40,000 km/h) — which is why rockets need multiple stages. The Moon's is only 2.38 km/s.

Common confusion

Escape velocity is about speed, not sustained thrust. A rocket does not need to reach 11.2 km/s instantly — it can climb slowly on continuous thrust. Escape velocity is the speed needed for a single unpowered ‘throw’ to never fall back.