Question

An artificial satellite of mass $200$ kg revolves around the earth in an orbit of average radius $667$ km. Its total energy in the orbit is (Mass of the earth $=6.0\times {10}^{24}$kg and $G=6.67\times {10}^{11}N-m^2/k{g}^2$)

• A. $6.6\times {10}^9$ joule
• B. $-6.6\times {10}^9$ joule
• C. $6.6\times {10}^{-9}$joule
• D. $-6.6\times {10}^{-9}$ joule

Answer 1

The correct option is B $-6.6\times {10}^9$ joule

$K.E.=\frac{G{M}_{e}m}{2r}$

$=\frac{(6.67\times {10}^{-11})(6.0\times {10}^{24})\left(200\right)}{2\times (6670\times {10}^3)}$
$=6.0\times {10}^9$ joule.

Gravitation potential energy,
$U=\frac{G{M}_{e}m}{r}=-12.0\times {10}^9$ joule
$\therefore$ Total energy, $T=U+K=-6.6\times {10}^9$ joule.