(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 1.80 106 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.