Journal Article

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

S. Breiter, A. Rożek and D. Vokrouhlický

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 417, issue 4, pages 2478-2499
Published in print November 2011 | ISSN: 0035-8711
Published online November 2011 | e-ISSN: 1365-2966 | DOI: http://dx.doi.org/10.1111/j.1365-2966.2011.19411.x
Yarkovsky–O’Keefe–Radzievskii–Paddack effect on tumbling objects

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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.

Keywords: radiation mechanisms: thermal; methods: analytical; celestial mechanics; minor planets, asteroids: general

Journal Article.  8500 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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