Lorentz force time-optimal transfer trajectory design in Jovian magnetic field

In this paper, the Lorentz force in Jupiter's magnetic field is used to design the transfer trajectory between Galileo moons' Lagrange points. The equatorial orbits of charged spacecraft in three-body axis-aligned nontilted-dipole magnetic field model are analyzed and the results show that the libration point L1 and L2 become nearer or further away from Europa with the variable size and polarity of the charge. The bang-bang charge control with the variable size and polarity of the charge can be used to change orbit's direction and shape. Analytical and numerical iteration methods give the fast and accurate bang-bang charge control to send the spacecraft to the L2 point of Europa, respectively. Finally, two numerical methods, the indirect and direct methods, give the time-optimal charge controls which are similar to but different from the semi-revolution variable polarity control maneuver. The optimal results achieve the final position and the flight angle at the same time, and need less time and less magnitude of charge compared with the numerical iteration method.