(40 Pts) This past summer, the New Horizons spacecraft made its closest approach (periapsis) to Pluto at 13,695 km from the planet's center. At closest approach, its speed was 13.78 km/sec with respect to Pluto (hint: this approach is hyperbolic about Pluto!). a) (10 Pts) If NASA had attempted to inject New Horizons into a circular orbit about Pluto with a single impulsive AV when the spacecraft reached periapsis, what would the required magnitude and direction of the AV have been? b) (10 Pts) The mass of the spacecraft was approximately 450 kg at the flyby, and onboard thrusters have an Isp of no more than 250 seconds. With that Isp, how much additional propellant would New Horizons had to have stored on board to perform the AV found in part (a)? Briefly comment on the feasibility of this option. c) (20 Pts) If this AV was postponed and instead executed when 30,000 km from Pluto's center (and still to circularize the orbit, now with a 30,000 km radius), what would the magnitude and direction of the maneuver have been? Would this have presented a feasible option? (40 Pts) This past summer, the New Horizons spacecraft made its closest approach (periapsis) to Pluto at 13,695 km from the planet's center. At closest approach, its speed was 13.78 km/sec with respect to Pluto (hint: this approach is hyperbolic about Pluto!). a) (10 Pts) If NASA had attempted to inject New Horizons into a circular orbit about Pluto with a single impulsive AV when the spacecraft reached periapsis, what would the required magnitude and direction of the AV have been? b) (10 Pts) The mass of the spacecraft was approximately 450 kg at the flyby, and onboard thrusters have an Isp of no more than 250 seconds. With that Isp, how much additional propellant would New Horizons had to have stored on board to perform the AV found in part (a)? Briefly comment on the feasibility of this option. c) (20 Pts) If this AV was postponed and instead executed when 30,000 km from Pluto's center (and still to circularize the orbit, now with a 30,000 km radius), what would the magnitude and direction of the maneuver have been? Would this have presented a feasible option