Physics

Problem

For certain space-based experiments a satellite must provide its occupants with an effective downward acceleration of only

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

while they remain in a circular orbit around the Earth. a. (a) Calculate the orbital radius (measured from the Earth’s centre) at which the centripetal acceleration of the satellite equals

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

. Use

M_{\rm E}=5.97\times10^{24}\,\text{kg}

and

G=6.67\times10^{-11}\,\text{N\,m}^2\!\text{/kg}^2

. b. (b) Hence find the altitude of this orbit above the Earth’s surface (

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

). c. (c) For an astronaut of mass

70\,\text{kg}

inside the satellite, calculate the gravitational force acting on the astronaut at that altitude and express it as a percentage of the astronaut’s weight at the Earth’s surface.

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