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  4. A satellite is revolving around the earth with a kinetic energy E . The minimum addition of kinetic energy needed to make it escape from its orbit is

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Q. A satellite is revolving around the earth with a kinetic energy $ E $ . The minimum addition of kinetic energy needed to make it escape from its orbit is

KEAMKEAM 2008Gravitation

Solution:

Kinetic energy of satellite in its orbit
$ E=\frac{1}{2}mv_{o}^{2} $
Or $ E=\frac{1}{2}m\left( \frac{GM}{r} \right)=\frac{GMm}{2r} $
Kinetic energy at escape velocity
$ E=\frac{1}{2}mv_{e}^{2} $
$ =\frac{1}{2}m\left( \frac{2GM}{r} \right)=\frac{GMm}{r} $
$ =2E $
Therefore, additional kinetic energy required
$ =2E-E=E $