Evolution of the rotational motion of space debris acted upon by eddy current torque

Abstract

Finding analytical solutions to the eddy current torque produced by a conducting body rotating within a magnetic field is arduous. In this paper, the finite difference method is adopted to solve numerically the boundary problem regarding the distributions of eddy currents in determining eddy current torque. Through analysis of the solutions, this paper presents the expression of eddy current torque that applies to a model of arbitrary shape rotating around an arbitrary axis. The parameters of the physical properties of the rigid body are integrated into the eddy current torque tensor, the features of which are analogous to the inertia tensor. The elements in the tensor are constants for a specific rigid body; thus, in the expression, the torque is associated only with the relative angular velocity and magnetic field. The expression is used to investigate the evolution of the rotation of space debris subjected to eddy current torque, through numerical integration with the angular velocity of the variation of the geomagnetic field, which is assumed a dipole. The results explain the observed phenomenon of change in the spin decay rate. Moreover, the effects of gravity-gradient torque and orbit precession cause the self-spin of the space debris to resonate with the orbital motion and ultimately, to reach a steady state.