Long-term attitude dynamics of space debris in Sun-synchronous orbits: Cassini cycles and chaotic stabilization

Abstract

Comprehensive analysis of space debris rotational dynamics is vital for active debris removal missions that require physical capture or de-tumbling of a target. We study the attitude motion of used rocket bodies acknowledgedly belonging to one of the categories of large space debris objects that pose an immediate danger to space operations in low Earth orbits. Particularly, we focus on Sun-synchronous orbits (SSO) with altitudes in the interval 600 ÷ 800 km, where the density of space debris is maximal. Our mathematical model takes into account the gravity gradient torque and the torque due to eddy currents induced by the interaction of conductive materials with the geomagnetic field. Using perturbation techniques and numerical methods we examine the deceleration of the initial fast rotation and the subsequent transition to a relative equilibrium with respect to the local vertical. A better understanding of the latter phase is achieved owing to a more accurate model of the eddy currents torque than in most prior research. We show that SSO precession is also an important factor influencing the motion properties. One of its effects is manifested at the deceleration stage as the angular momentum vector oscillates about the direction to the south celestial pole.

Analytical Propagation of Space Debris Density for Collisions near Sun-Synchronous Orbits

“…They applied the material point method to describe the impact process of a debris object and spacecraft. Efimov et al [16] investigated the attitude evolution of space debris in SSO combining perturbation methods and a numerical approach. It was shown that the orbital precession and influence of orbital motion on induced eddy currents might make a significant impact on the attitude evolution.…”

Chaotic Oscillation of Satellite due to Aerodynamic Torque

“…Rawashdeh [26] studied the attitude analysis of small satellites using model-based simulation. Efimov et al [27] discussed about long-term attitude dynamics of space debris for sun-synchronous orbits and studied about Cassini cycles and chaotic stabilization. Chang [28] gave an idea of stability, chaos detection, and quenching chaos for the swing equation system.…”

Effectiveness of CubeSat-Based Architectures for Active Removal of On-Orbit Rocket Bodies

“…In a 2012 study, Yanagisawa and Kurosaki used photometric light flashes to determine that the object possesses a rotational period of 41.00 seconds, corresponding to an angular rate of = 0.153 / about the major axis [12]. The effects of eddy current damping, as described by Efimov et al [13], Praly et al [14], and Williams and Meadows [15], are likely to have considerably reduced the spin rate of the object during the eight years since the photometric observations took place. However, since no future studies have taken place on the same object, this study makes the assumption that the spin rate is still unchanged.…”