Physics

Problem

A spacecraft is in a circular orbit

400\,\text{km}

above the Earth’s surface. Take Earth’s radius

R_{\rm E}=6.40\times10^{6}\,\text{m}

, Earth’s mass

M_{\rm E}=6.0\times10^{24}\,\text{kg}

and the universal gravitational constant

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

. a. (a) Calculate the orbital speed of the spacecraft. b. (b) Determine the centripetal acceleration of the spacecraft and express it as a fraction of

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

. c. (c) An astronaut of mass

80\,\text{kg}

is inside the spacecraft. Compute the reading that a spring balance would show if the astronaut were attached to it. d. (d) State whether the astronaut is in true weightlessness or apparent weightlessness, giving one reason for your choice.

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