Escape Velocity of Earth

escape velocity

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,

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M is the mass of the celestial object whose gravitational pull has to be superseded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

From this relation it is obvious that escape velocities for larger planets (or celestial bodies) is greater since it will have a larger mass compared to smaller planets with a lower mass (having less gravity in comparison).
On earth, the escape velocity is around 40,270 kmph, which is around 11,186 m/s. For example, when a spacecraft is launched into outer space, the velocity attained by this should be greater than the escape velocity so that the rocket doesn’t fall back onto earth. And guess what, the escape velocity is different at the poles of the earth compared to that from the equator because the radius is slightly more at the equator.
It is said that it is impossible to escape a black hole because the gravitational field inside the event horizon is so huge that the calculated velocity is greater than the speed of light!
Check out this video to visualize how escape velocity works:

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Practise This Question

A particle on earth's surface is given a velocity equal to its escape velocity.  Its total mechanical energy will be