Physics Assignment Help With Escape Velocity

6.5 Escape Velocity

It is the minimum velocity with which a body should be projected from the surface of a planet so as to reach infinity. It can be calculated using conservation of energy. If a body of mass m is projected with velocity v from the surface of a planet of mass M and radius R, then

Einitial = (on the surface of planet) and at the total energy i.e.Efinal = 0

Hence using conservation of energy Einitial = Efinal

Hence = 0

[as g = GM/R2]

From the above result we can conclude that

(1) Escape velocity is independent of the mass and direction of projection of the body.

(2) If v > ve, i.e. if a body is projected with velocity greater than escape velocity, then by be conservation of energy



i.e.

i.e.

(3) A given reference body (planet) will have atmosphere if the velocity of molecules in its atmosphere [which according to kinetic theory of gases is given by ] is lesser than escape velocity. This is why earth has atmosphere [(as at earth uRMS < ve) while moon has no atmosphere (as at moon vRMS > ve)]

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