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# HW7 - n is the angular velocity of the nominal circular...

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MAE146: Astronautics – Homework #7 Assigned: Friday, February 29 th , 2008 Due date: Friday, March 7 th , 2008, (at 10 : 00 am, beginning of the discussion) Note: “Textbook” refers to Wiesel’s book, “Space±ight dynamics”. Please justify all of your answers. Problem 1 (20 pts): Olberth Maneuver Textbook, page 313, # 3 Problem 2 (30 pts): Sensitivity Analysis Textbook, page 314, # 5 Textbook, page 314, # 6 Problem 3 (20 pts): Planetary capture Textbook, page 314, # 7 Problem 4 (30 pts): Relative motion Recall that the in-plane solution to the linearization around a circular orbit (Clohessy-Whiltshire equations) is: x ( t ) = 4 x 0 + 2 ˙ y 0 n - p 2 ˙ y 0 n + 3 x 0 P cos ( nt ) + ˙ x 0 n sin ( nt ) y ( t ) = y 0 + 2 ˙ x 0 n (1 - cos ( nt )) - p 4 ˙ y 0 n + 6 x 0 P sin( nt ) + (6 nx 0 + 3 ˙ y 0 ) t where the x -axis is the pointing radially, y is along the orbit velocity and
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Unformatted text preview: n is the angular velocity of the nominal circular orbit (mean motion). Assume a satellite in a circular orbit around the Earth with altitude of 278 km and period T = 90 min. At an arbitrary time, a small free-±ying experiment package is ejected with a small Δ V from the satellite. What is the relative motion (i.e. the value of x/ Δ V and y/ Δ V as a function of time) in the following cases: 1. Δ V is applied in the direction of satellite motion 2. Δ V is applied radially outward. Then plot x/ Δ V vs. y/ Δ V for one period of the satellite orbit (90 min) for both cases. How far will the free ±yer be from the satellite after 90 min? 1...
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