Question

ENERGY OF AN ORBITING SATELLITE
A satellite of mass m 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 $M_E$ and $R_E$ be mass and radius of the earth respectively)

• A. $\frac{G{M}_{E}m}{4(R_E+h)}$
• B. $\frac{G{M}_{E}m}{2(R_E+h)}$
• C. $\frac{G{M}_{E}m}{(R_E+h)}$
• D. $\frac{2G{M}_{E}m}{(R_E+h)}$

Answer 1

Answer: (B)

$\frac{G{M}_{E}m}{2(R_E+h)}$

Total energy of orbiting satellite at a height h is $E=\frac{G{M}_{E}m}{2(R_E+h)}$
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 $\Delta E=E_{\infty }-E$
$=0-(-\frac{G{M}_{E}m}{2(R_E+h)})=\frac{G{M}_{E}m}{2(R_E+h)}$