Here is a tricky Orbital Mechanics (spacecraft and space not atomic orbits) problem. i will give a fanatstic rating!

2) Assume you're participating in a Space Tournament in the Interstellar Medium (ISM) where you are far far away from any gravity field. There are five teams and you are one of them. This year, what is required from the teams is to design a gravitational space boomerang. In this gravity free medium, the only objects available to the teams are, 1) five small spacecrafts, and 2) five big spherical mass with GM=u=62.4 Each Team is given a specific orbit eccentricity (Team 1: e,=0, Team 2: e>=0.2, Team 3: e;=0.5, Team 4: e4=0.7, Team 5: es#0.9). All teams need to dispatch their identical spacecrafts at the same time and have their spacecrafts return to the exact same point where they were dispatched from at the same time after 22 hours. How would you do that? Explain in details and step by step. What can you tell about the kinetic and potential energy of these five trajectories? How about their total energy? Hand draw (MATLB is optional) these five orbits and any other details you would like to add to your drawing. (30pt)