The most fuel$-$efficient to the hidden planet from earth is to travel via a Hohman ellipse : an elliptical orbit that has a perihelion at the orbit of one planet and an aphelion at the orbit of the other planet. Assuming that both planets have coplanar circular orbits in the solar system and that the period of the hidden planet is $4$ years, and that only Hohman transfer are allowed a$)$ determine the time it would take to travel to the hidden planet by Hohman transfer ellipse b$)$sketch the approximate location of position of earth and the hidden planet appropriate for the outbound journey and again for the inbound journey c$)$ what is the minimum amount of time to be spent on the hidden planet for this round trip