Resonance-Averaged Solar Torque Dynamics for Tumbling Satellites

Abstract

Observations indicate that the spin states of retired and otherwise defunct satellites are diverse and can change significantly over time. Understanding defunct satellite spin state evolution is important for solar radiation pressure modeling, active debris removal, satellite servicing, and space situational awareness. Research has shown that many defunct satellites in geosynchronous earth orbit (GEO) are primarily driven by solar radiation torques via the Yarkovsky–O’Keefe–Radzievskii–Paddack (YORP) effect. Recent exploration of YORP-driven nonprincipal axis tumbling has uncovered rich dynamic behavior, including tumbling cycles, spin–orbit coupling, and tumbling period resonances. Radar and optical observations of the defunct Geostationary Operational Environmental Satellite (GOES) 8 strongly suggest that it has been captured in a tumbling resonance at least once since 2018. Motivated by these findings, we develop a numerical resonance-averaged dynamic model to understand YORP-driven resonance capture, building on our earlier nonresonant averaging framework. This resonance-averaged model illuminates resonance capture mechanisms. Also, by averaging over the satellite’s rotation, this model is roughly 20 times faster to propagate than the full (Euler) dynamics. Overall, this allows for rapid, broad exploration to determine resonance capture durations, spin states changes, and the influence of initial spin rate and resonance order on resonance strength. This resonance-averaged model can be easily applied to other environmental perturbations.