Question

A satellite of mass orbits the earth at a height h above the surface of the earth. How much energy must be expended to rocket the satellite out of earth’s gravitational influence ?

(where and be mass and radius of the earth respectively)

• A.
• B.
• C.
• D.

Answer 1

Answer: (B)

Answer 2

Total energy of orbiting satellite at a height h is

The total energy of the satellite at infinity is zero.

$\therefore$Energy expended to rocket the satellite out of the earth’s gravitational field is

$= 0 - \left( - \frac { \mathrm { GM } _ { \mathrm { E } } \mathrm { M } } { 2 \left( \mathrm { R } _ { \mathrm { E } } + \mathrm { h } \right) } \right) = \frac { \mathrm { GM } _ { \mathrm { E } } \mathrm { M } } { 2 \left( \mathrm { R } _ { \mathrm { E } } + \mathrm { h } \right) }$