Physics (10th Edition)

Published by Wiley
ISBN 10: 1118486897
ISBN 13: 978-1-11848-689-4

Chapter 5 - Dynamics of Uniform Circular Motion - Focus On Concepts - Page 137: 11

Answer

(e) is correct.

Work Step by Step

In a satellite orbital, gravity provides the centripetal force for the satellites. $$F_c=G\frac{mM_{earth}}{r^2}$$ 2 satellites have similar mass $m$. The one in the large orbit has twice the radius of orbit than the other one $(r_l=2r_s)$ If we take the centripetal force of the satellite in the large orbit to be $F_l$, and the centripetal force of the other one $F_s$, we have $$\frac{F_l}{F_s}=\frac{G\frac{mM_{earth}}{r_l^2}}{G\frac{mM_{earth}}{r_s^2}}=\frac{r^2_s}{r^2_l}=\frac{1}{4}$$ So $F_l$ is one-fourth as great as $F_s$.
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