Constants: For all questions, use the following constants (remember that M = GM so you can use u instead of M when calculating rsor): . Ro = 6, 378 km . MOD = 3.986 x 105 km3 /s2 . am = 1.496 x 108 km = 1 AU . My = 1.267 x 108 km3 /s2 . ax = 7.785 x 108 km . Mn = 3.793 x 107 km3 /s2 . an = 1.4334 x 109 km . Mo = 1.327 x 10ll km3 /s2 Note: I am using standard astronomical symbols: @ = Earth, 2 = Jupiter, h = Saturn, O = Sun.Question 1 A satellite is in a geocentric orbit with the following orbital parameters: a =15,000km, e = 0.5, i = 45, Q = 250, and w = 90. At midnight on June 7** 2023 (Day Number 158.0), calculate the eclipse of the orbit in order to answer the following questions: (a) [ 4 marks | What are the true anomalies (fst4r and 60epng) of the start and end of the eclipse (to the nearest degree)? (b) [ 4 marks | What times past perigee do these correspond to? (c) [ 2 marks | What time fraction of the orbit is this eclipse? Question 2 (a) [ 3 marks | What is the minimum v, required to reach Saturn? (b) [ 3 marks | What is the minimum Aw required if the spacecraft departs from a circular orbit at 250 km altitude? (c) [ 3 marks | What is the flight path angle of our trajectory to Saturn when reaching Jupiter orbit? (d) [ 3 marks | How long would it take for the spacecraft to reach Jupiter? And Saturn? (e) [ 3 marks | In the patched conic approximation, at what distance from Saturn can we consider that the spacecraft follows a Keplerian orbit about Saturn?