Relative Orbital Motion of a Charged Object Near a Spaceborne Radially Directed Rotating Magnetic Dipole

The relative orbital motion of a charged object near a spaceborne magnetic dipole is presented in this article, where the intersatellite Lorentz force is taken into consideration. Assuming that a reference point is constrained in a circular reference orbit, a chief satellite and a constantly charged object move close to the reference point. Under the assumptions that the chief satellite generates a rotating magnetic dipole (the axis of the dipole is in the direction of the reference orbital radius vector) and the charged object moves nearby in the artificial magnetic field, a nonlinear dynamical model of the proposed relative motion is established based on the Hill-Clohessy-Wiltshire equation. We first derive the system?s equilibrium points and analyze their stabilities based on the system parameters, such as the charge-to-mass ratio of the charged object, the moment and rotating rate of the magnetic dipole, and the angular velocity of the reference orbit. All of the equilibrium points are classified into ten cases, and their structures of the submanifold (which determine the stable and unstable behaviors near the equilibrium points) are described according to their stability characteristics. In addition, the necessary and sufficient conditions for the ten cases are derived, and the periodic orbits near the equilibrium points are depicted in detail. Subsequently, an integral constant and zero-velocity surfaces in the dynamical system are derived to present the bounded orbits around the magnetic dipole and the transient orbits that travel through the equilibrium points. The flight mechanics of the presented relative orbital motion, including equilibrium points, periodic orbits, bounded orbits, and transient orbits, reveals the prospects of potential applications for proximity operations to a wide range of charged space objects.