Satellites and Binding Energy EX 10

The distance between the Earth and the Sun is $1.5\times 10^{11}m$ and the masses of these objects are $6\times 10^{24}kg$ and $2\times 10^{30}kg$. The Earth is orbiting the Sun and therefore the energy of the system is

$E=\frac{1}{2}U=-\frac{1}{2}\frac{G{M}_S{M}_E}{r}=-\frac{1}{2}\frac{(6.67\times 10^{-11})(2\times 10^{30})(6\times 10^{24})}{1.5\times 10^{11}}=-5.3\times 10^{33}J$

The escape velocity at the distance $r=1.5\times 10^{11}m$ is given by

$v=\sqrt{\frac{2G{M}_S}{r}}=\sqrt{\frac{2(6.67\times 10^{-11})(2\times 10^{30})}{1.5\times 10^{11}}}=4.22\times 10^{4}m/s=42.2km/s$