A communication satellite of mass is initially in a circular orbit above Earth’s surface

PHYSICS · Subjective · A Level · Physics · Fields and their consequences · Fields and their consequences

Problem

A communication satellite of mass 500 kg500\,\text{kg} is initially in a circular orbit 600 km600\,\text{km} above Earth’s surface. It has to be placed in a new circular orbit 36 000 km36\,000\,\text{km} above the surface so that it can appear stationary with respect to an observer on Earth. Take RE=6.4×106 mR_E = 6.4\times10^{6}\,\text{m} for the radius of Earth and GME=3.986×1014 m3 s−2G M_E = 3.986\times10^{14}\,\text{m}^3\,\text{s}^{-2}. (a) Calculate the mechanical energy per unit mass of the satellite in the initial orbit. (b) Calculate the mechanical energy per unit mass in the final orbit. (c) Hence find the minimum work that must be done per kilogram of the satellite to accomplish this orbital change.

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