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What is the Escape Velocity?
Asked by preranapatil4360 | 25 Dec, 2021, 07:55: PM
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

Answered by Thiyagarajan K | 25 Dec, 2021, 09:54: PM
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