The spin state of 433 Eros and its possible implications

In this paper, we show that Asteroid (433) Eros is currently residing in a spin–orbit resonance, with its spin axis undergoing a small-amplitude libration about the Cassini state 2 of the proper mode in the nonsingular orbital element sin I / 2 exp ( ı Ω ) , where I the orbital inclination and Ω the longitude of the node. The period of this libration is ≃53.4 kyr. By excluding these libration wiggles, we find that Erosʹ pole precesses with the proper orbital plane in inertial space with a period of ≃61.4 kyr. Erosʹ resonant state forces its obliquity to oscillate with a period of ≃53.4 kyr between ≃76° and ≃89.5°. The observed value of ≃89° places it near the latter extreme of this cycle. We have used these results to probe Erosʹ past orbit and spin evolution. Our computations suggest that Eros is unlikely to have achieved its current spin state by solar and planetary gravitational perturbations alone. We hypothesize that some dissipative process such as thermal torques (e.g., the so-called YORP effect) may be needed in our model to obtain a more satisfactory match with data. A detailed study of this problem is left for future work.