Answer: Escape velocity is the minimum velocity with which a body must be projected from a planet’s surface so that it never returns; for the earth it is 11.2 km/s.
- When a body is thrown upwards, it goes up to a certain height and falls back because the earth’s gravity pulls it down. If it is thrown with a large enough velocity, it can go so far that the earth’s gravitational pull becomes negligible and it does not return.
- Escape velocity is that minimum velocity. Equating the kinetic energy given to the body with the work needed against gravity gives \(v_{esc} = \sqrt{\dfrac{2GM}{R}} = \sqrt{2gR}\), where M and R are the mass and radius of the planet.
- For the earth, \(v_{esc} = \sqrt{2 \times 9.8 \times 6.4 \times 10^6} \approx 11.2\) km/s. It does not depend on the mass or the direction of projection of the body, only on the planet. For the moon it is about 2.4 km/s, which is why the moon has no atmosphere — gas molecules could escape.