Question

A satellite is in a circular orbit around the earth has kinetic energy $E_k$ . Minimum amount of energy that is added so that it escapes the earth's gravitational field is:

• A. $E_k$
• B. $E_k$ /2
• C. $E_k$ /4
• D. 2 $E_k$

Answer 1

The correct option is D 2 $E_k$

$T.E$ at circular orbit,

$T.E=K.E+P.E$

$=E_k-\frac{GMm}{r}$

But $E_k=\frac{1}{2}m{v}^2=\frac{1}{2}m(\frac{GM}{r}{)}^2=\frac{GMm}{2r}$

$T.E=\frac{GMm}{2r]}\frac{GMm}{r}=-\frac{GMm}{r}$

To escapre the orbit, an energy of $\frac{GMm}{r}$ should be given.

$=2E_k$