Physics

Problem

The pull of gravity weakens with altitude. a. (a) Derive an expression for the acceleration due to gravity

g_{h}

at an altitude

h

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

g

and the Earth’s radius

R_{\oplus}

. b. (b) Using

g=9.80\,\text{m s}^{-2}

R_{\oplus}=6.37\times10^{6}\,\text{m}

and

h=35.8\times10^{6}\,\text{m}

, calculate

g_{h}

for a geostationary orbit. c. (c) Determine the apparent weight of a

70\,\text{kg}

astronaut inside a spacecraft in this orbit.