Escape Velocity
Find the minimum speed needed to escape the gravity of a planet, star or any mass — from its surface or from any altitude above it. Also gives the circular orbit speed and surface gravity.
What is Escape Velocity?
Throw a ball up and gravity pulls it back. Throw it faster and it goes higher. At the escape velocity it never comes back: its kinetic energy exactly matches the energy needed to climb out of the gravitational well to infinity.
Remarkably, the escape velocity does not depend on the mass of the object you launch — a pebble and a rocket need the same speed. The launch direction does not matter either (as long as you don’t aim at the ground). The formula ignores air resistance, and real rockets accelerate gradually instead of starting at full speed.
Live Graph
EarthEscape Velocities
from the surface| Body | Surface gravity | vesc |
|---|---|---|
| Moon | 1.62 m/s² | 2.38 km/s |
| Mars | 3.73 m/s² | 5.03 km/s |
| Earth | 9.82 m/s² | 11.19 km/s |
| Jupiter | 25.9 m/s² | 60.2 km/s |
| Sun | 274 m/s² | 617.7 km/s |
| Neutron star | ~1012 m/s² | ~0.6 c |
Key Ideas
Escaping means reaching infinity with zero speed left over: total energy (kinetic + gravitational potential) equals exactly zero. The launched mass m cancels out.
A circular orbit needs about 71% of the escape speed. That is why getting into low Earth orbit (7.8 km/s) is most of the work of leaving Earth altogether.
Squeeze a mass inside this radius and not even light can escape. The Newtonian formula happens to give exactly the correct general-relativistic result.
Sources & Verification
- D. Halliday, R. Resnick & J. Walker, Fundamentals of Physics, 10th ed., Wiley, 2014 — Ch. 13 (Gravitation).
- H. D. Curtis, Orbital Mechanics for Engineering Students, 3rd ed., Butterworth-Heinemann, 2014 — Ch. 2 (The Two-Body Problem).
- E. Tiesinga, P. J. Mohr, D. B. Newell & B. N. Taylor, “CODATA recommended values of the fundamental physical constants: 2018”, Reviews of Modern Physics 93, 025010 (2021) — values of the constants used.