A satellite of mass mS orbits the Earth (with mass mE and radius RE) with a velocity v and an altitude h. The gravitational force FG and the centripetal force FC are given by: FG = G mS · mE (RE + h) 2 , FC = mS · v 2 RE + h , G = const. (a) Find an equation for the kinetic energy Ekin(h) of a satellite with an altitude h. (b) Based on the kinetic energy, how much liquid hydrogen (energy density: 106 J/Litre) is at least needed to bring a small 1 kg satellite in an orbit of 400 km. (Use literature to find mE, RE, G.)
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