Orbital Motion of Lorentz Spacecraft During the Low-Energy Jupiter Flyby

In the exploration of the outer solar system, Jupiter is an ideal celestial body for gravity assist due to its huge mass. On the other hand, Jupiter and its moons are also high-value exploration targets. However, the traditional Jupiter flyby with a hyperbolic orbit has a fast speed and high energy with only one chance to close encounter Jupiter. Hence, its space and time conditions for the exploration of Jupiter and its moons is poor. In the Sun-Jupiter circular restricted three-body problem (CRTBP), it is possible to realize multiple Jupiter flybys without fuel costs. However, such orbits usually have only two chances to explore Jovian system closely, and their apojoves are too high. We postulate that the ideal Jupiter flybys should have more chances to close encounter the Jupiter system, and low apojoves. Lorentz spacecraft, as a kind of spacecraft using propellantless propulsion, can perform various kinds of maneuver in Jovian magnetic field, so it can be used to solve the above defects. This paper mainly studies the orbital motion of Lorentz spacecraft during the low-energy Jupiter flyby. Firstly, we establish the dipole model of Jupiter’s magnetic field and calculate the error between the dipole model and the accurate model. Based on the dipole model, we establish the dynamic equations of CRTBP considering Lorentz force, and analyze the orbital characters of Lorentz spacecraft. Then, several formulas of variations of Jacobi constant, energy and angular momentum relative to Jovian barycenter are derived. In addition, the phase space structure of Lorentz spacecraft with constant and variable charge-to-mass ratio is analyzed. Numerical computation shows that the orbital difference between Lorentz spacecrafts with and without the constant charge-to-mass ratio are quite small, but Lorentz spacecrafts with variable charge-to-mass ratio can increase the number of Jupiter flybys and decrease their apojove attitudes. The research results of this paper can be applied to the future explorations of the outer solar system.