# Escape Speed

Physics

## definition

### Define Escape Velocity

Escape Velocity:
The minimum velocity with which a body should be projected from the surface of the earth so that it escapes from the earth's gravitational field, is called the escape velocity of the body.

## example

### Find the variation of escape velocity

Escape velocity is a function of radius and gravitational field of the planet. Its value varies from planet to planet as radius and gravity changes.

Example:
The ratio of the radius of a planet A to that of planet B is . The ratio of accelerations due to gravity for the two planets is . Find the ratio of the escape velocities from the two planets?

Solution:
Escape Velocity is given by
Given  and
Taking ratio of the escape velocities of the 2 planets,

## formula

### Expression for Escape velocity

Consider a satellite of mass m, stationary on the surface of earth, then binding of the satellite on the surface of earth is given by

R - radius of earth
To escape from the surface of earth, the Kinetic energy of satellite equivalent to binding energy.
K.E. = B.E.

..........(1)
We know that

hence,
..........(2)