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

$E={\frac {1}{2}}U=-{\frac {1}{2}}{GM_{S}M_{E} \over r}=-{\frac {1}{2}}{(6.67\times 10^{-11})(2\times 10^{30})(6\times 10^{24}) \over 1.5\times 10^{11}}=-5.3\times 10^{33}J$

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

$v={\sqrt {2GM_{S} \over r}}={\sqrt {2(6.67\times 10^{-11})(2\times 10^{30}) \over 1.5\times 10^{11}}}=4.22\times 10^{4}m/s=42.2km/s$