University Physics with Modern Physics (14th Edition)

Published by Pearson
ISBN 10: 0321973615
ISBN 13: 978-0-32197-361-0

Chapter 13 - Gravitation - Problems - Exercises - Page 426: 13.23

Answer

The speed of the second satellite is 7330 m/s.

Work Step by Step

Let $M$ be the mass of the planet. We can write an expression for the speed of the first satellite. $v_1 = \sqrt{\frac{G~M}{R_1}}$ We can write an expression for the speed of the second satellite. $v_2 = \sqrt{\frac{G~M}{R_2}}$ We can divide $v_2$ by $v_1$. $\frac{v_2}{v_1} = \sqrt{\frac{R_1}{R_2}}$ $v_2 = v_1~\sqrt{\frac{R_1}{R_2}}$ $v_2 = (4800~m/s)~\sqrt{\frac{7.00\times 10^7~m}{3.00\times 10^7~m}}$ $v_2 = 7330~m/s$ The speed of the second satellite is 7330 m/s.
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