Answer to Question #303749 in Mechanics | Relativity for Mrinmoy kranjilal

Question

a satellite of mass 200kg is displaced by a distance of 2re from a point on the earths surface,whwre re is the radius of the earth. calculate the work done on the satellite by the force of gravitation. take the valus of the constants in your calculation from the astrophysical data given in the course

Answer 1

The work is equal to difference between the potential energies at the large and at the small distances with minus sign. The height increases, so the work done by the gravitational force is negative:

$A = - \Delta U = - \left(-\dfrac{GM_{\oplus}m}{3R_{\oplus}} +\dfrac{GM_{\oplus}m}{R_{\oplus}} \right), \\ A = \dfrac{GM_{\oplus}m}{3R_{\oplus}} - \dfrac{GM_{\oplus}m}{R_{\oplus}} = -\dfrac{2}{3}\cdot \dfrac{GM_{\oplus}m}{R_{\oplus}},\\ A = -\dfrac{2}{3}\cdot \dfrac{6.67\cdot10^{-11}\,\mathrm{N\cdot m^2/kg^2}\cdot6\cdot10^{24}\,\mathrm{kg}\cdot200\,\mathrm{kg}}{6.4\cdot10^6\,\mathrm{m}},\\ A = -8.34\cdot10^9\,\mathrm{J}.$