Relative orbital motion of two charged objects near a spaceborne radially-directed rotating magnetic dipole

The relative orbital motion of two charged objects near a spaceborne magnetic dipole are presents in this study. Assuming that a spacecraft generating a rotating magnetic dipole moves in a Keplerian circular reference orbit and two constantly charged objects move close to the artificial magnetic field, which indicates that both the Lorentz force and coulomb Force acting on the charged objects are taken into consideration, a nonlinear dynamical model of the proposed relative orbital motion is established based on the Hill-Clohessy-Wiltshire (HCW) equation and the system parameters such as the charge-to-mass ratio of the charged object, the moment and rotating rate of magnetic dipole (the axis of the dipole is assumes to be perpendicular to the reference orbital plane), and the angular velocity of the circular reference orbit. Firstly, the equilibrium points of the system, integral constant, and zero-velocity curves for the proposed relative motion are derived and bounded periodic orbits are searched out by using Poincare maps in terms of the zero-velocity curves. Moreover, the stability characteristic of equilibrium points were analyzed and planar periodic orbits near the equilibrium points were numerically computed by differential correction. The presented periodic orbits of relative motion in this article are different from those in traditional satellite formation flying, which suggests potential applications of the presented periodic orbits, such as propellantless satellite formation maintenance and noncontact capture of electrostatically charged space debris.