Physics

Problem

A communication satellite is to appear fixed over a point on the Earth’s equator. The mass of the Earth is

5.97\times10^{24}\,\text{kg}

and its radius is

6.37\times10^{6}\,\text{m}

. The universal gravitational constant is

6.67\times10^{-11}\,\text{N m}^{2}\text{kg}^{-2}

. (a) Determine the orbital radius from the centre of the Earth that will give the satellite a period of exactly

24\,\text{h}

. (b) Calculate the height of the satellite above the Earth’s surface. (c) For the radius found in part (a), find the magnitude of the satellite’s orbital speed.

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