A weather satellite is in an elliptical orbit around Earth with initial perigee…

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

Problem

A weather satellite is in an elliptical orbit around Earth with initial perigee distance

r_{p0} = 7.2\times 10^6\,\text{m}

and apogee distance

r_{a0} = 3.0\times 10^7\,\text{m}

. At apogee the satellite briefly fires a retro-thruster that reduces its speed by

5.0\%

. Ignore the satellite’s mass compared to Earth’s. (a) Determine the satellite’s speed

v_{a0}

just before the burn. (b) Using the value from part (a), calculate the new apogee speed

v_{a1}

immediately after the burn. (c) Derive an expression for the new perigee distance

r_{p1}

in terms of

v_{a1}

r_{a0}

, and known constants, then compute its numerical value. (d) Discuss whether the satellite’s orbital period increases, decreases, or remains the same after the burn, and explain your reasoning.

Related theory

Conservation of Angular Momentum
Angular Momentum
Satellites & Orbital Motion
Gravitation
Orbital velocity and period
Energy of an orbiting satellite

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