A spacecraft is in a circular orbit above the Earth’s surface

PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences

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

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

. (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) State whether the astronaut is in true weightlessness or apparent weightlessness, giving one reason for your choice.

Related theory

Mass, Weight & Apparent Weight
Gravitation
Satellites & Orbital Motion
Orbital velocity and period
Earth satellites

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