Physics

Problem

An astronaut has a mass of

70\,\text{kg}

on the Earth’s surface where the acceleration due to gravity is

9.8\,\text{m s}^{-2}

and the Earth’s radius is

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

. (i) Derive an expression for the astronaut’s weight

W(h)

at an altitude

h

above the Earth’s surface in terms of the surface weight

W_0

. (ii) Determine the altitude (to the nearest kilometre) at which the astronaut’s weight becomes one-sixteenth of the surface value. (iii) Comment briefly on how this altitude compares with the typical heights of low-Earth-orbit satellites.

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