Question

A satellite in a circular orbit around the earth has kinetic energy $E_K$ . Minimum amount of energy that has to be given to satellite so that it escapes from the earth’s gravitational influence, is

• A. $E_K$
• B. $\frac{E_K}{2}$
• C. $2E_K$
• D. $\frac{E_K}{4}$

Answer 1

The correct option is A $E_K$

Let a satellite of mass ‘m’ is revolving around the earth of mass ‘M’ in a circle of radius ‘r’(> radius of earth), then its total mechanical energy in the orbit is given by,
$T.E=P.E+K.E=-\frac{GMm}{r}+\frac{GMm}{2r}=-\frac{GMm}{2r}=-(K.E)$
So, $T.E=-E_K(GivenK.E=E_K)$
Let ‘x’ is the amount of energy supplied to the satellite in its orbit so that it goes to infinity where its total energy is zero.
Appling law of conservation of energy, x +T.E = 0
So, $x=-(T.E)=-(-E_K)=E_K$.