# What is Escape Velocity? | Definition, Derivation, Formula – Gravitation

Escape Velocity Definition Physics:
Escape velocity on earth is the minimum velocity with which a body has to be projected vertically upwards from the earth’s surface, so that it just crosses the earth’s gravitational field and never returns.

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## What is Escape Velocity? | Definition, Derivation, Formula – Gravitation

Escape Velocity Formula:

ve = $$\sqrt{\frac{2 G M}{R}}=\sqrt{2 g R}=\sqrt{\frac{8 \pi \rho G R^{2}}{3}}=R \sqrt{\frac{8}{3} \pi G P}$$

Escape velocity does not depend upon the mass or shape or size of the body as well as the direction of projection of the body. Escape Velocity of a body from earth is 11.2 km/s

Some Important Escape Velocities

 Heavenly body Escape Velocity Moon 2.3 km/s Mercury 4.28 km/s Earth 11.2 km/s Jupiter 60 km/s Sun 618 km/s Neutron star 2 x 105 km/s

Relation between escape velocity and orbital velocity of the satellite

ve = $$\sqrt{2}$$v0

A missile is launched with a velocity less than the escape velocity. The sum of its kinetic energy and potential energy is negative.

Maximum Height Attained by a Particle
When projected vertically upwards from the earth’s surface,

h = $$\frac{v^{2}}{2 g-v^{2} / R}$$

(i) If velocity of projection v is equal the escape velocity (v = ve), then v < ve, the body will attain maximum height and then may move around the planet or may fall down back to the planet.

(ii) If velocity of projection v of satellite is greater than the escape velocity (v > ve), then the satellite will escape away following a hyperbolic path.

(iii) If v < ve, the body will attain maximum height and then may move around the planet or may fall down back tothe planet.

Gravitation:
Have you ever thought, when we throw a ball above the ground level, why it returns back to the ground. It’s because of gravity. When a ball is thrown above the ground in the opposite direction, a gravitational force acts on it which pulls it downwards and makes it fall. This phenomena is called gravitation.

Learn relation between gravitational field and potential field, Kepler’s law of planetary, weightlessness of objects in absence of gravitation, etc.