Yarkovsky-O’Keefe-Radzievskii-Paddack effect on tumbling objects

Abstract

A semi-analytical model of the Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect on an asteroid spin in a non-principal axis rotation state is developed. The model describes the spin-state evolution in Deprit-Elipe variables, first-order averaged with respect to rotation and Keplerian orbital motion. Assuming zero conductivity, the YORP torque is represented by spherical harmonic series with vectorial coefficients, allowing us to use any degree and order of approximation. Within the quadrupole approximation of the illumination function we find the same first integrals involving rotational momentum, obliquity and dynamical inertia that were obtained by Cicaló & Scheeres. The integrals do not exist when higher degree terms of the illumination function are included, and then the asymptotic states known from Vokrouhlický et al. appear. This resolves an apparent contradiction between earlier results. Averaged equations of motion admit stable and unstable limit cycle solutions that were not previously detected. Non-averaged numerical integration by the Taylor series method for an exemplary shape of 3103 Eger is in good agreement with the semi-analytical theory.

Compact YORP formulation and stability analysis

“…Thus the dynamical mechanisms are usually divided into two categories: the net propulsion force changing the orbital motion (the Yarkovsky effect), and the net torque affecting the rotational dynamics (the Yarkovsky-O'Keefe-Radzievskii-Paddack or YORP effect). Both have been observed directly (Chesley 2003;Kaasalainen et al 2007;Lowry et al 2007;Ďurech et al 2008, and there is clear indirect evidence of their long-term role in the evolution of asteroid orbits and spin states (Bottke et al 2001;Vokrouhlický et al 2003Vokrouhlický et al , 2006.…”

“…For example, it is easy to identify the enigmatic YORP instability with the "trash coefficients" of a Laplace series, and to show that, while quadrantsymmetric bodies have no secular YORP torques for zero thermal inertia (K = 0), they acquire a nonvanishing component for K 0. Breiter et al (2011;hereafter BRV11) arrive at some of the results of Sect. 3 (K = 0) by a different context and approach.…”

Escape of asteroids from the main belt

“…This neglects the possibility of a free precession of the angular velocity vector in the body frame (that is, tumbling), which is frequently seen at the slow-rotation state (e.g., Pravec et al 2005). It is very likely that YORP itself naturally drives asteroids to slow rotation and directly triggers the tumbling state (e.g., Vokrouhlický et al 2007;Cicalò & Scheeres 2010;Breiter et al 2011). While it would be too computationally challenging to implement such a complex evolution for the purpose of this paper, we admit that its omission necessarily produces some uncertainty in our work (see below).…”

Disaggregation of small, cohesive rubble pile asteroids due to YORP

“…This simple model sidesteps known issues with how an asteroid's rotational dynamics evolves when it gets to a slow spin rate. Previous investigations have detected a statistically larger number of slowly rotating asteroids [28,33], which could be a signature of more complex rotational evolution and a slow-down in the rate at which a body's spin rate varies [51,7,3]. We do not pursue this topic here, however, and instead use a simple model which could be adjusted by a scale factor, once a consistent theory for the evolution of a slowly-rotating and tumbling asteroid is developed.…”