p0420

# p0420 - 4.20 CHAPTER 4 PROBLEM 20 293 4.20 Chapter 4...

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4.20. CHAPTER 4, PROBLEM 20 293 4.20 Chapter 4, Problem 20 Problem: A vehicle is in a circular orbit of radius r A about the moon. To transfer to an orbit of larger radius r B , the vehicle is first placed on a Hohmann transfer orbit from Point A to Point B by firing its rocket momentarily at Point A and then again at Point B. Determine the changes in velocity, v A and v B , as functions of r A , r B , the mass of the moon, M ,andthe Universal Constant of Gravitation , G . Compute v A and v B for r A = 1200 mi, r B = 1800 mi, and M =5 . 04 zettaslugs. B A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...... •• Solution: After the rocket has finished firing, denote the vehicle’s velocity at Point A by ˜ v A . Similarly, denote the vehicle’s velocity prior to firing the rocket by ˜ v B . Since angular momentum is conserved on the transfer orbit, we know that H o = mr A ˜ v A = mr B ˜ v B Therefore, the velocities are related by ˜ v A = r B r A ˜ v B Because total energy is also conserved, we have 1 2 m ˜ v 2 B GMm r B = 1 2 m ˜ v 2 A r A Substituting for ˜ v A , this equation simplifies as follows.

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p0420 - 4.20 CHAPTER 4 PROBLEM 20 293 4.20 Chapter 4...

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