A Earth–orbiting satellite moves in a circular orbit of radius measured from Earth’s…

PHYSICS · Multi-part · CBSE · Physics · Gravitation · Gravitation

Problem

600\,\text{kg}

Earth–orbiting satellite moves in a circular orbit of radius

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

measured from Earth’s center. At point A the satellite’s thrusters fire for a very short time, imparting a purely radial inward impulse that instantaneously places the satellite at a new distance of

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

from Earth’s center. Neglect the mass of expelled propellant and assume

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

and

M_E=6.0\times10^{24}\,\text{kg}

. (a) Calculate the satellite’s speed

v_0

just before the impulse while it was in its original circular orbit. (b) Determine the satellite’s speed

v_1

immediately after the impulse at the new distance of

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

, assuming no external torque acted during the impulse. (c) Based on your result in part (b), state whether the satellite’s new path is circular or elliptical and provide a qualitative justification.

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