Escape Velocity of Earth

When you throw a ball up into the air, why doesn’t it fly through the atmosphere and escape into outer space? This is because gravity pulls it back down. Then how does a rocket fly into outer space? It can fly into outer space because it is travelling with a very high velocity. This velocity is called escape velocity. The escape velocity of celestial bodies like planets and their natural satellites (the moon for us) is the minimum velocity that has to be achieved by an object, to escape the gravitational sphere of influence (pull or force or attraction) of the celestial body. At this velocity, the sum of the gravitational potential energy and kinetic energy of the system will be equal to zero.

\( v_c = \sqrt {\frac {2GM}{r}}\),

where,

v_c is the escape velocity

G is the universal gravitational constant

M is the mass of the celestial object whose gravitational pull has to be superseded

r is the distance from the object to the centre of mass of the body to be escaped

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