What is the Escape Velocity?

 

 

 

Asked by preranapatil4360 | 25th Dec, 2021, 07:55: PM

Expert Answer:

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
 
begin mathsize 14px style v space equals space square root of 2 space G M over R space end root space equals space square root of 2 space open parentheses fraction numerator G M over denominator R squared end fraction close parentheses R end root space equals space square root of 2 space g space R end root end style
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
 
begin mathsize 14px style v space equals space square root of 2 space g space R end root space space equals space square root of 2 cross times 9.8 cross times 6378 cross times 1000 end root space space equals space 1.118 space cross times space 10 to the power of 4 space m divided by s end style
Hence escape velocity on earth's surface  = 11.18 km/s

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