Question

As you have learnt in the text, a geostationary satellite orbits the earth at a height of nearly 36,000 km from the surface of the earth. What is the potential due to earth's gravity at the site of this satellite ? (Take the potential energy at infinity to be zero). Mass of the earth = $6.0\times {10}^{24}kg$, radius = 6400 km.

Answer 1

Mass of the Earth,$M=6.0\times {10}^{24}kg$
Radius of the Earth, $R=6400km=6.4\times {10}^{6}m$
Height of a geostationary satellite from the surface of the Earth, $h=36000km=3.6\times {10}^{7}m$
Gravitational potential due to Earth's gravity at height h

$V=-\frac{GM}{R+h}$

$=-\frac{6.67\times {10}^{-11}\times 6\times {10}^{24}}{3.6\times {10}^7+0.64\times {10}^7}$

$=-9.4\times {10}^{6}J/kg$