Engineering Mechanics: Statics & Dynamics (14th Edition)

Published by Pearson
ISBN 10: 0133915425
ISBN 13: 978-0-13391-542-6

Chapter 13 - Kinetics of a Particle: Force and Acceleration - Section 13.7 - Central-Force Motion and Space Mechanics - Problems - Page 171: 116



Work Step by Step

We can determine the required minimum increment in speed as follows: $v_c=\sqrt{\frac{GM_e}{h+r_e}}$ We plug in the known values to obtain: $v_c=\sqrt{\frac{66.73(10^{-12})\times 5.976(10^{24})}{20(10^6)+6.378\times 10^6}}$ This simplifies to: $v_c=3888.17m/s$ and $v_e=\sqrt{2\frac{GM_e}{h+r_e}}$ We plug in the known values to obtain: $v_e=\sqrt{2\frac{66.73(10^{-12})\times 5.97(10^{24})}{20(10^6)+6.378(10^6)}}$ This simplifies to: $v_e=5498.7m/s$ Now $\Delta v=v_e-v_c$ $\implies \Delta v=5498.7-3888.17=1610.53m/s=1.6~km/s$
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