What is the Escape Velocity?

 

 

 

Escape velocity is defined as minimum velocity required for a particle at the surface of planet

so that the particle reaches a far point away from planet where the gravitational force of attraction

acting on the particle  is zero .

 

Let us consider the escape velocity requirement of a particle on earth's surface

 

On surface of earth , let us consider the particle is projected with speed v upwards.

 

Total energy on surface of earth = Kinetic energy + Potential energy

 

Total energy on surface of earth = (1/2) m v²  - ( G M m ) / R   ....................................(1)

 

where m is mass of particle. Second term in above expression is potential energy ,

where G is universal gravitational constant ,M is mass of earth and R is radius of earth .

 

At far away point ( at infinity ) , potential energy is zero and let us consider the speed is negligible

compare to initial speed at earth's surface

 

Hence at infinity , total energy is zero

 

Hence by conservation of energy , (1/2) m v²  - ( G M m ) / R  = 0

 

After simplification , above expression becomes

 

Where g = G M / R²  , is the acceleration due to gravity on earth surface

 

if we substitute R = 6378 km in above expression , we get

 

Hence escape velocity on earth's surface  = 11.18 km/s