Escape velocity
● VERBATIM — examined word-for-wordEscape velocity is the minimum velocity at which a mass must be projected from a planet's surface in order to reach infinity, that is, to completely escape the planet's gravitational field.
v_esc = √(2GM/r) = √(2gr) ≈ 11 km s⁻¹ for EarthWhat this actually means
The word doing the work is MINIMUM. Escape means arriving at infinity with exactly zero kinetic energy left, nothing to spare. Anything faster also escapes, so the definition has to pin down the smallest speed that does.
Say 'to reach infinity' or 'to escape the gravitational field completely'. Vague phrases like 'to leave the Earth' are not enough, because a ball thrown upwards also leaves the ground and comes straight back.
It is independent of the mass of the escaping object, because m cancels in ½mv² = GMm/r, and independent of launch direction, because energy is a scalar and does not care which way you point. Both facts are separately creditable.
For Earth it is about 1.1 × 10⁴ m s⁻¹, roughly 11 km s⁻¹, and it is √2 times the speed of a circular orbit at that same radius. A neat check on any answer you produce.
The name is a historical misnomer: it is a speed, not a velocity, precisely because direction is irrelevant. Examiners still use the term, so use it too, but if asked to comment, that is the comment they want.
Leaving out 'minimum', or claiming escape velocity depends on the projectile's mass or direction.
Prove it — watch it be true
- Open the escape-velocity launcher and set the launch speed just below the quoted escape value.
- Watch the outcome readout show fall back or orbit, not escape.
- Nudge the launch speed up to the escape value and confirm the outcome flips to escape, with the projectile coasting away and its speed tending to zero.