A satellite of mass moves in a circular orbit around an unknown

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

Problem

A satellite of mass

450\,\text{kg}

moves in a circular orbit around an unknown, isolated planet. The radius of the orbit (measured from the planet’s center to the satellite’s center) is

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

, and the orbital period is

2.7\,\text{h}

. Throughout this problem you may treat the satellite–planet interaction as an isolated two-body system and neglect all other forces. Take

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

. (a) Calculate the magnitude of the satellite’s orbital speed. (b) Using the orbital information, determine the mass of the planet. (c) The planet’s radius is

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

. Determine the magnitude of the gravitational field strength at the planet’s surface and compare it to the value near Earth’s surface (

\approx9.8\,\text{N/kg}

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