The YORP effect with finite thermal conductivity

The Yarkovsky–OʹKeefe–Radzievskii–Paddack (YORP) effect has been recently suggested to significantly change, on a long-term, rotation state of small asteroids and meteoroids. Though YORP is closely related to the Yarkovsky (orbital) effect, it differs from the latter in two aspects: (i) YORP needs bodies of irregular shape to be effective, and (ii) YORP acts on bodies of zero surface thermal conductivity. To simplify computations, YORP has been so far investigated in the zero surface thermal conductivity limit only. Here we analyze the role of the surface conductivity and we find it substantially changes previous conclusions. Most importantly, unlike in the zero-conductivity limit, (i) YORP preferentially tilts obliquity toward two asymptotic states perpendicular to the orbital plane, and (ii) YORP asymptotically decelerates and accelerates rotation rate in about equal number of cases. Our work also indicates that direct detection of the YORP effect for a small asteroid may significantly constrain its mass.