1. (40 pts.) You are designing a mission to Jupiter for NASA. You want to perform a Hohmann transfer from Earth using an Oberth departure (you may ignore Earth's rotation). NASA wants you to design the mission such that the spacecraft arrives at a distance d inside or outside of Jupiter's orbital path and applics a AV at the periapsis of your trajectory around Jupiter to circularize the orbit. NASA wants the resulting circular orbit to be clockwise (viewed from above the ecliptic as shown below) and have an altitude of 1000 n. m (1.84 x 10m). You may assume that Earth and Jupiter are both in circular orbits about the Sun and that the spacecraft's heliocentric velocity when it encounters Jupiter's sphere of influence is its aphelion velocity (regardless of the distance d). Determine the following mission characteristics a) Injection velocity b) Orientation of launch site in terms of ve[sce diagram below]) c) Distance d inside or outside of Jupiter's orbit (specify inside or outside) d) Total AV required e) Total time to transit from Earth to Jupiter View from above the Ecliptic (Earth's erhital plane) Earth's Orbit Jupiter's Orbit Transfer Orbit Earth V Launch Site (nu). Conceptual drawings ONLY not to scale