Question

A geostationary satellite orbits the earth at a height of nearly $36000km$ from the surface of the earth. If the magnitude of potential due to earth's gravity at the site of the satellite is $(x\times {10}^6)Jkg$, then find the $x$.[Mass of the earth $=6\times {10}^{24}kg$ and radius $=6400km$ (approximately)]

Answer 1

Given, mass of earth,$M=6\times {10}^{\left(24\right)}kg$,
Radius of the earth,$R=6400km$,
Height of the satellite from surface of earth,$h=36000km$
Height of the satellite from centre of earth,
$r=R=h$
$r=6400+36000$

$=42400km$

$=4.24\times {10}^{7}m$
Gravitational potential,
$V=-\frac{GM}{r}$

$V=-\frac{6.67\times {10}^{-11}\times 6\times {10}^{24}}{4.24\times {10}^7}$

$V=-9.43\times {10}^{6}Jkg$

Compare it with$(x\times {10}^6)Jkg,$
$x=-9.43$

Final answer:$-9.43$