Averaged Solar Torque Rotational Dynamics for Defunct Satellites

TL;DR

This paper develops a semi-analytical model to predict the long-term tumbling and spin behaviors of defunct satellites in GEO, significantly improving computational efficiency over previous methods.

Contribution

It introduces a novel tumbling-averaged rotational dynamics model that analytically averages over torque-free rotation, enabling faster long-term behavior predictions.

Findings

Model captures general long-term satellite behavior

Reduces computation time by approximately three orders of magnitude

Enables rapid exploration of rotational dynamics

Abstract

Spin state predictions for defunct satellites in geosynchronous earth orbit (GEO) are valuable for active debris removal and servicing missions as well as material shedding studies and attitude-dependent solar radiation pressure (SRP) modeling. Previous studies have shown that solar radiation torques can explain the observed spin state evolution of some GEO objects via the Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect. These studies have focused primarily on uniform rotation. Nevertheless, many objects are in non-principal axis rotation (i.e. tumbling). Recent exploration of the tumbling regime for the family of retired GOES 8-12 satellites has shown intriguing YORP-driven behavior including spin-orbit coupling, tumbling cycles, and tumbling period resonances. To better explore and understand the tumbling regime, we develop a semi-analytical tumbling-averaged rotational dynamics model. The derivation requires analytically averaging over the satellite's torque-free rotation, defined by Jacobi elliptic functions. Averaging is facilitated by a second order Fourier series approximation of the facet illumination function. The averaged model is found to capture and explain the general long-term behavior of the full dynamics while reducing computation time by roughly three orders of magnitude. This improved computation efficiency promises to enable rapid exploration of general long-term rotational dynamics for defunct satellites and rocket bodies.