Evolution of angular velocity for defunct satellites as a result of YORP: An initial study

Observations of defunct satellites show that these objects are generally rotating, with some having very fast rotation rates, yet the cause of these rapid rates is unknown. The observed secular change in the spin rate and spin axis orientation of asteroids is known to be caused by the Yarkovsky-O’Keefe-Radzievskii-Paddack (YORP) effect, however, its effect on inactive satellites in Earth orbit remains unexplored. This paper applies the YORP effect to defunct satellites and analyzes its effect on the spin rate and obliquity of these objects. This work uses two different satellite geometries to explore the secular change of the spin rate and obliquity caused by the YORP effect for inactive Geostationary Earth Orbit (GEO) satellites. One of the model satellites has an asymmetric geometry, which leads to the classical YORP effect as originally formulated for asteroids. The other model satellite is geometrically symmetric, but relies on mass distribution asymmetry to generate the YORP effect. For both models the secular change is explored with averaged dynamics, and the solutions of the averaged theory are compared with numerical integrations of the non-averaged equations of motion. Additionally, previously published observations of inactive GEO satellites are used to estimate the YORP torque acting on those bodies. A comparison between this torque and the expected torque on a defunct satellite shows that the two are of the same order of magnitude. These results motivate further study on the YORP effect in the realm of inactive satellites.