1) It is desired to use an encounter with Jupiter to send a spacecraft on a trajectory which barely escapes the solar system. The space craft is launched from Earth onto a trajectory whose aphelion is at Jupiter’ s orbit. Determine how close to the surface of Jupiter the spacecraft must pass during the encounter. I seem to feel that energy conservation would be required here but am not entirely sure as to what the approach should be exactly. 2) Given the Debye potential V( r ) = (A/r) exp(-r/lambda) where r is spherical radius and A and lambda are constants, find the range of radii for which circular orbits are stable in this potential. For on this question, I am genuinely lost and am open to all options and suggestions !