General Tumbling-Averaged Rotational Dynamics for Defunct Satellites

Abstract

Understanding and predicting the long-term spin state evolution of defunct satellites and rocket bodies is important for solar radiation pressure modeling, space domain awareness, and active debris removal (ADR). Dynamical modeling and observations indicate that defunct geosynchronous satellite spin states are primarily driven by solar radiation torques via the Yarkovsky–O’Keefe–Radzievskii–Paddack (YORP) effect. In our two recent papers, we uncovered dynamically rich YORP-driven behavior including cycling between uniform rotation and non-principal axis tumbling, angular momentum sun tracking, and tumbling period resonances. These papers only considered the YORP effect. However, tumbling satellites are also subject to energy dissipation from residual fuel slosh and flexure. Gravitational torques and other environmental perturbations may affect long-term evolution as well. In this paper, the third in our series, we develop semi-analytical tumbling-averaged models for internal energy dissipation and gravity gradient torques and combine them with the earlier YORP models. Accounting for YORP and dissipation, we find asymptotically stable tumbling states with constant angular momentum and kinetic energy and a pole fixed in the rotating sun-satellite orbit frame. With gravity gradients, these asymptotic states become stable limit cycles with yearly periodicity. We discuss the implications of these findings for the space debris population, ADR, and satellite decommission procedures.