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ASE 366K - First Exam Solutions

ASE 366K - First Exam Solutions - A SE 3 66K P reliminary E...

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ASE 366K Preliminary Exam #L Exam Date: October 8, 2009 Instructor: Dr. Humphreys Name: This test is open book and open notes. No devices capable of electronic communication are allowed during the test (e.g.,cell phones, computers). A pocket calculator is permitted. There are 3 problems on this exam. A total of 100 points is possible. The duration of the test is 90 minutes. Budget your time accordingly. Review the entire test package. If you have an incomplete package, see the instructor for a re- placement. Please use the space provided in the test package to derive solutions. Box all answers for clarity. Partial credit can only be awarded if the method of the solution is understandable. May your thoughts be clear.
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Problem 1 A probe in a "parking orbit" around Mars has a pericenter of 4000 km and a velocity at pericenter (relative to Mars) of 4.165 km/sec' The probe is commanded to transfer into another orbit by making a burn 10 minutes after passing pericenter. 1' (10 points) What is the mean anomaly at the time of the burn? Express your answer in radians to three significant digits. 2' (15 poi,nts) What is the eccentric anomaly at the time of the burn? Express your answer in radians to three significant digits. Note: If you need to solve Kepler's "qrrutiorr, solve it via the Newton-Raphson method. Set the problem up and solve for the first iteration only, assumingan initial guess of Eo : M. 3' (5 poi,nts) What is the true anomaly at the time of the burn, assuming the eccentric anomaly calculated above? Express your answer in radians to three significant digits.
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