Question

A satellite orbits the earth at a height of $400km$ above the surface. How much energy must be expended to rocket the satellite out of the earth’s gravitational influence? Mass of the satellite is $200kg$; mass of the earth is $6.0\times {10}^{24}kg;$ radius of the earth is $6.4\times {10}^{6}m;G=6.67\times {10}^{-11}N{m}^{2}k{g}^{-2}$ .

Answer 1

Total energy of an orbiting satellite.

Total energy of the satellite orbiting at a height from the surface.
Total Energy = Kinetic Energy + Potential Energy

$=\frac{GmM}{2(R+h)}+(-\frac{GmM}{(R+h)})$
$=-\frac{GmM}{2(R+h)}$


Energy expended to rocket the satellite

Net energy expended to rocket the satellite outside the earth’s gravitational field
= − (Total energy of the satellite)
$=\frac{GmM}{2(R+h)}=\frac{(6.67\times {10}^{-11})\times 200\times (6\times {10}^{24})}{2\times (6.4\times {10}^6+4\times {10}^5)}$
$=5.9\times {10}^{9}J$