MAE146: Astronautics – HomeworkAssigned: Friday, February 5th,2010Due date: Wednesday , February 10th,2010,(at the beginning of the lecture)Please justify all of your answers. Write your answer cleanly with sentences and diagrams to explain. Don’t forgetto write your name on your copy to receive credit.Problem 1 (10pts): On derivativesCompute the following derivatives:1.∂∂vectorr1||vectorr||32.∂∂vectorr1||vectorr||n, n≥13.∂∂θ1(1+ecosθ)whereeis a constant.4.∂∂θ1(1+ecosθ)3whereeis a constant.Problem 2 (10pts): On numerical integrationSolve problem 2.5 of the textbook (p. 146 of current edition). In addition, please plot the resulting orbit segment ofthe 24hrperiod.The problem consists of numerically integrating the R2BP equations for a time span of 24hr, starting from thefollowing initial conditions (given in an ECI frame):•Position: (6600.0km,0.0km,0.0km).•Velocity: (0km/s,12.0km/s,0.0km/s).
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