A satellite is to be raised from a low Earth orbit of altitude to a higher circular…

PHYSICS · Multi-part · CBSE · Physics · Gravitation · Gravitation

Problem

A 2000 kg2000\,\text{kg} satellite is to be raised from a low Earth orbit of altitude 300 km300\,\text{km} to a higher circular orbit of altitude 1200 km1200\,\text{km}. Take Earth’s mass ME=6.0×1024 kgM_E = 6.0 \times 10^{24}\,\text{kg}, radius RE=6.4×106 mR_E = 6.4 \times 10^{6}\,\text{m}, and the universal gravitational constant G=6.67×10−11 N m2 kg−2G = 6.67 \times 10^{-11}\,\text{N\,m}^2\,\text{kg}^{-2}. (i) Calculate the gravitational potential energy of the satellite in its initial orbit. (ii) Calculate the gravitational potential energy of the satellite in its final orbit. (iii) Hence determine the work that must be done against gravity to transfer the satellite from the lower to the higher orbit (neglect any change in the satellite’s kinetic energy due to burning of fuel).

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