The influence on the spin vectors of asteroids from the Yarkovsky effect

Abstract

The spin vector evolution of a solar system object is connected to the orbital evolution of the body. The orbital and spin elements of the asteroids are affected by gravitational as well as thermal forces. When the spin rate, shape and orbital evolution of an object are known. the secular spin vector evolution may be determined. In this study, the orbital and spin vector evolutions of a number of artificial objects are numerically integrated, with special consideration taken to the seasonal and diurnal variants of the Yarkovsky force. The thermal force known as the Yarkovsky effect may perturb the orbital elements of an asteroid and thereby also affect the direction of the spin vector. Concentrating on spherical bodies, the spin axis evolution of bare and regolith covered main belt objects with radii larger than 50 m is examined, especially considering the seasonal and diurnal Yarkovsky forces. The combined effects on the spin vector evolution from these forces and induced periodical perturbations on the orbital elements are also studied. It is found that the effects on the spin vector evolution from the Yarkovsky force always are small or negligible for kilometer sized objects over lime periods of ∼100 Myr or more. The effects are doubled when the object radius is halved. During a given time period, the influences from the seasonal Yarkovsky force on the spin vector evolution of hare basaltic bodies are about 2-3 times as large as those on iron-rich ones. However, since the expected time, t r o , before the spin axis direction is changed by a collisional event is about half as long for a bare basaltic object as for an equal sized iron-rich one, the seasonal Yarkovsky force may be of approximately the same importance for both classes of objects. The effects on regolith covered objects from this force are considerably smaller. On the other hand, the influences from the diurnal Yarkovsky effect are much stronger on regolith covered objects than on bare ones. The effect on the spin vector evolution from both variants of the Yarkovsky force seems to he small for all the objects studied unless very long time periods are considered. The size of t r o t is dependent on several factors, hut the influences from the Yarkovsky force on the psin axis evolution over the present age of the solar system are always negligible when the object radius is larger than ∼10 km. Note that the effects studied in this paper should not be confused with the Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect.