The dynamics of asteroid rotation, governed by YORP effect: the kinematic ansatz

TL;DR

This paper analytically explores asteroid rotation dynamics in elliptic orbits, considering destabilizing effects like YORP and deriving new solutions for rotation evolution with negligible applied torques.

Contribution

It introduces a novel analytical method for solving Euler equations of asteroid rotation, incorporating non-gravitational effects like YORP.

Findings

New solutions for asteroid spin evolution under non-gravitational influences.

Demonstration of spin evolution towards maximal-inertia axis rotation.

Analytical approach to asteroid rotation dynamics in elliptic orbits.

Abstract

The main motivation of this research is the analytical exploration of the dynamics of asteroid rotation when it moves in elliptic orbit through Space. According to the results of Efroimsky, Frouard (2016), various perturbations (collisions, close encounters, YORP effect) destabilize the rotation of a small body (asteroid), deviating it from the initial-current spin state. This yields evolution of the spin towards rotation about maximal-inertia axis due to the process of nutation relaxation or to the proper spin state corresponding to minimal energy with a fixed angular momentum. We consider in our research the aforementioned spin state of asteroid but additionally under non-vanishing influence of the effects of non-gravitational nature (YORP effect), which is destabilizing the asteroid rotation during its motion far from giant planets. Meanwhile, new solutions for asteroid rotation dynamics in case of negligible (time-dependent) applied torques have been obtained in our development. New method for solving Euler equations for rigid body rotation is suggested; an elegant example for evolution of spin towards the rotation about maximal-inertia axis is calculated.