💫 Escape Velocity

Written and maintained by the PhDino author · Last reviewed 21 September 2026 · Checked against 2 independent reference calculations · how PhDino checks its numbers

The speed needed to break free of a body's gravity entirely, never to fall back.

Escape velocity is the speed at which an object has exactly enough kinetic energy to overcome a body's gravitational pull all the way to infinity, arriving there with (in the idealized case) zero velocity left over. Anything launched faster than this, in any direction, will never fall back — anything launched slower eventually will (assuming no further propulsion).

Escape velocity is exactly the circular orbital velocity at the same radius multiplied by √2 — not a coincidence, but a direct consequence of how gravitational potential and kinetic energy trade off, and a handy way to sanity-check either calculation against the other.

Key formula

v_escape = √(2μ ÷ r)

Notes & limitations

• This is a launch-speed concept, not a statement about how a real spacecraft leaves a planet — actual spacecraft don't reach escape velocity in one instant burn from the surface; they typically accelerate gradually while already well clear of the dense lower atmosphere.
• Escape velocity decreases with altitude, same as orbital velocity does — this is why it's always specified relative to a particular starting distance from the central body, not as one single number for a planet.