Magnetic Attitude Disturbance Caused by Asymmetrical Magnetic Substances in LEO Satellites

This study considers the attitude disturbance torque caused by the magnetic shape anisotropy of onboard magnetic substances in low Earth orbit (LEO) satellites. The gravity gradient, solar radiation pressure, aero drag, and residual magnetic disturbance torques are normally considered in attitude control in LEO satellites. In general, attitude disturbance, magnetic disturbance to be specific, strongly affects these small-sized satellites. The residual magnetic torque in nano- and microsatellites is based on a simple steady magnetic moment; however, in most satellite cases, an unsteady magnetic moment is not considered. This study aims to understand attitude dynamics in small satellites more accurately on the basis of an unsteady magnetic moment, with a focus on magnetic disturbance due to the magnetic shape anisotropy or, in similar terms, to study the magnetic torque caused by a magnetic substance with an asymmetrical shape in a uniform magnetic field. Asymmetrical magnetic substances, such as the iron cores of magnetic torquers and magnetic hysteresis dampers of passive attitude control systems, are installed in a variety of small satellites. In LEO, these substances can cause disturbance torques to the satellites of approximately the same magnitude with the residual magnetic disturbance, which are typically stronger than the aero drag and solar radiation attitude disturbances. In the case of Cubesat XI-IV, the torque strength of the magnetic substance is on the order of $1\times {10}^{-6}\mathrm{Nm}$ in the worst case, which is the same order of the residual magnetic disturbance torque. In this paper, first, the magnetic substance torque is analyzed with a simple ellipsoid model with an analytical approach to clarify the characteristics of the magnetic disturbance. Then the magnetic disturbance is investigated using a finite-element method (FEM) to obtain more accurate findings. The results of the simple ellipsoid model and the numerical FEM simulations conclude that the magnetic torque due to the magnetic shape anisotropy is one of the strong attitude disturbance torques in LEO in small satellites, although this magnetic disturbance torque has not been considered clearly in previous satellites.