What escape velocity means
Escape velocity is the minimum speed an object needs, without further propulsion and ignoring air resistance, to break free of a body’s gravity and never fall back:
v = √(2GM ÷ r)
- G: gravitational constant, 6.674 × 10⁻¹¹ N·m²/kg²
- M: mass of the planet, moon or star
- r: distance from its center (radius plus altitude)
It does not depend on the mass of the escaping object: a pebble and a spacecraft need the same speed.
Worked example
From the surface of the Earth (mass 5.972 × 10²⁴ kg, radius 6,371 km):
- v = √(2 × 6.674 × 10⁻¹¹ × 5.972 × 10²⁴ ÷ 6,371,000) = 11.19 km/s.
- That is about 25,000 mph.
- The speed for a circular orbit at the surface would be 7.91 km/s.
- Surface gravity: 9.82 m/s².
Escape velocities in the solar system
| Body | Escape velocity | Surface gravity |
|---|---|---|
| Moon | 2.38 km/s | 1.62 m/s² |
| Mars | 5.03 km/s | 3.73 m/s² |
| Earth | 11.19 km/s | 9.82 m/s² |
| Jupiter | 60.2 km/s | 25.9 m/s² |
| Sun | 617.7 km/s | 274 m/s² |
Escape velocity versus orbital velocity
At any distance r, the speed for a circular orbit is √(GM ÷ r). Escape velocity is √2 ≈ 1.41 times larger. Between the two, an object follows an elliptical orbit; above escape velocity, it follows a hyperbolic path and leaves for good.
Altitude
Escape velocity decreases with distance. At the altitude of the International Space Station, about 250 miles, it is 10.9 km/s; at the Moon’s distance from Earth, only 1.4 km/s.
Rockets
Rockets do not need to reach escape velocity all at once: they burn engines for minutes and gain speed gradually. Reaching low Earth orbit requires about 7.8 km/s plus losses to gravity and drag, which is why launches use about 9 to 10 km/s of total velocity change. Missions to the Moon and Mars then add a burn that brings them close to escape velocity.
Black holes
If a body is compact enough that its escape velocity exceeds the speed of light, nothing can escape. The radius at which this happens is the Schwarzschild radius, r = 2GM ÷ c², about 9 mm for the mass of the Earth.