Find the escape velocity of a planet, moon, star or black hole from its mass and radius using v = √(2GM/r) — the minimum speed needed to break free of gravity without further propulsion.
Escape velocity is the minimum speed an object needs to permanently escape a body's gravity, with no further thrust. It comes from setting kinetic energy equal to the gravitational potential energy binding the object: ½ m v² = GMm/r, which rearranges to v = √(2GM/r).
Notice the escaping object's own mass cancels out — a pebble and a spaceship need the same escape speed. Escape velocity depends only on the mass and radius of the body you are leaving. For a black hole, the radius at which this speed equals the speed of light is the Schwarzschild radius.
About 11.2 km/s (11,186 m/s, or roughly 25,000 mph). This is the speed needed to leave Earth's gravity without further propulsion, ignoring air resistance.
Use v = √(2GM/r), where G is the gravitational constant (6.674×10⁻¹¹), M is the body's mass in kilograms and r is its radius in metres. Enter M and r above to get v.
No. The escaping object's mass cancels out of the equation, so a small probe and a large spacecraft have the same escape velocity from a given body.
At the event horizon (the Schwarzschild radius), the escape velocity equals the speed of light, which is why not even light can escape from inside it.