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# HW9 - MAE146 Astronautics Homework Assigned Friday February...

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MAE146: Astronautics – Homework Assigned: Friday, February 5 th , 2010 Due date: Wednesday , February 10 th , 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 forget to write your name on your copy to receive credit. Problem 1 (10pts): On derivatives Compute the following derivatives: 1. ∂vector r 1 || vector r || 3 2. ∂vector r 1 || vector r || n , n 1 3. ∂θ 1 (1+ e cos θ ) where e is a constant. 4. ∂θ 1 (1+ e cos θ ) 3 where e is a constant. Problem 2 (10pts): On numerical integration Solve problem 2.5 of the textbook (p. 146 of current edition). In addition, please plot the resulting orbit segment of the 24 hr period. The problem consists of numerically integrating the R2BP equations for a time span of 24 hr , starting from the following initial conditions (given in an ECI frame): Position: (6600 . 0 km, 0 . 0 km, 0 . 0 km ). Velocity: (0 km/s, 12 . 0 km/s, 0 . 0 km/s ).
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