Problem 3 (30 points): Two satellites are flying in formation in LEQ. The chief is in a circular orbit with altitude of 600 km. At #; the deputyv''s LVLH coordinates relative to the chief are z, = 69.78 km, , = 139.56 km, z, = 139.56 km, y;, = 151.116 m/s, .'f = 2'(; =1 lf.':'. (a) Based on the initial relative state, would you expect a drift in the relative orbit? Explain your reasoning, (b) Using the closed-form CW state transition matrix (STM) propagate the relative motion for 2 orbital periods. Plot the relative trajectory in a 3-D plot and comment on the results, (c) Propagate the same relative motion by numerically integrating the CW equations (e.g., use ode45 in MATLAB). Compare the numerically integrated solution to the closed- form solution obtained via the ST Problem 4 (25 points): A satellite in geostationary orbit is unexpectedly struck by orbit- ing debris. The satellite is found 2 hrs later and has drifted to position p = [-10, 10, 0] km relative to its initial position. (Hint: This problem can be solved using CW targeting and the answers should be vectors, the components of Av are important) (a) Calculate the effective impulsive Av imparted on the satellite when it was impacted by the debris. (b) It is determined that the satellite's status allows for a maneuver to return to mission. Calculate the two impulsive burns required to maneuver the satellite back to its original position in 6 hrs