Presentation #115.08 in the session Modeling Physical Properties of NEOs.
Under the influence of the YORP effect (Yarkovsky–O’Keefe–Radzievskii–Paddack) the obliquities of asteroids are driven to the equilibrium states of 0 or 180 degrees. However, all small asteroids that have been visited by spacecraft were found with an obliquity slightly off of the expected equilibrium state. In this work we investigate the hypothesis that this deviation is caused by the evolution of the orbital plane under the gravitational influence of the planets of the Solar System.
The obliquity is the angle between the orbital plane normal vector and the spin pole of the asteroid. Thus, to study the evolution of the obliquity over time we need to account for the perturbations in both components. The orbital plane drifts due to the secular perturbations from the planets over long timescales, punctuated by abrupt variations due to close planetary encounters. The spin vector can also experience variations during close encounters, although they must be at much closer distances. The timescales required for the YORP effect to drive the spin states to equilibrium range between millions of years to thousands depending on the size of the asteroid. Using a recently developed semi-analytical propagation tool we keep track of the encounters found by the asteroid. We sample a large number of particles from the uncertainty distribution of the asteroids and propagate them to characterize the frequency of the most disruptive close encounters.
Considering all these effects, we compute an expected deviation from equilibrium for a few asteroids with well-known spin poles like 101955 Bennu, 99942 Apophis and 367943 Duende. For a generic asteroid, we can define the regions in orbit elements and size in which each of the different effects dominates the long-term dynamics of the spin state. A fuller characterization of this effect can enable the recent history of asteroids to be more precisely constrained.
 O. Fuentes-Muñoz, A. J. Meyer, and D. J. Scheeres, “Semi-analytical near-Earth objects propagation: the orbit history of (35107) 1991 VH and (175706) 1996 FG3,” Planet. Sci. J., 2022.