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 3 (This question is long and difficult) (a) [ 4 marks ] A spacecraft is launched from Earth with a v, of 8.941 km/s and a flight path angle of zero degrees. Does it reach Saturn? Determine the apoapsis distance of the spacecraft's orbit. (b) [ 4 marks | The spacecraft encounters Jupiter near its apoapsis, what is the v, of the encounter? (c) [ 4 marks | During its Jupiter encounter, the spacecraft performs a flyby with a perijove of 1.80 x 10 km. Is this inside the sphere of influence of Jupiter? (d) [ 4 marks | What are the eccentricity of the hyperbolic encounter and the deflection angle of the hyperbola? (e) [ 5 marks | What then would be the heliocentric outgoing velocity after departing Jupiter? And the new flight path angle? (f) [ 4 marks | What is the semimajor axis and eccentricity of the new orbit? Does it reach Saturn's orbit? (g) | 5 marks | How much Av would a spacecraft save by flying to Saturn via the trajectory we just computed? Consider the same departure conditions at Earth as in the previous question.