Effects of the triaxiality on the rotation of celestial bodies: Application to the Earth, Mars and Eros

Abstract

In this paper we discuss the influence of the triaxiality of a celestial body on its free rotation, i.e. in absence of any external gravitational perturbation. We compare the results obtained through two different analytical formalisms, one established from Andoyer variables by using Hamiltonian theory, the other one from Euler's variables by using Lagrangian equations. We also give a very accurate formulation of the polar motion (polhody) in the case of a small amplitude of this motion. Then, we carry out a numerical integration of the problem, with a Runge-Kutta-Felberg algorithm, and for the two kinds of methods above, that we apply to three different celestial bodies considered as rigid : the Earth, Mars, and Eros. The reason of this choice is that each of this body corresponds to a more or less triaxial shape. In the case of the Earth and Mars we show the good agreement between analytical and numerical determinations of the polar motion, and the amplitude of the effect related to the triaxial shape of the body, which is far from being negligible, with some influence on the polhody of the order of 10 cm for the Earth, and 1 m for Mars. In the case of Eros, we use recent output data given by the NEAR probe, to determine in detail the nature of its free rotational motion, characterized by the presence of important oscillations for the Euler angles due to the particularly large triaxial shape of the asteroid.