Influence of the largest asteroids on the orbital motions of terrestrial planets: application to the Earth and Mars

The level of precision of modern numerical ephemeris of the Solar System necessitates taking into account the gravitational influence of the largest asteroids on the terrestrial planets. This can be done in a straightforward manner when assuming that the mass of the asteroid is well known. Nevertheless, this is rarely the case, even for the largest asteroids. In this paper, we use recent determinations of the masses of Ceres, Pallas, and Vesta to both qualitatively and quantitatively determine the action of these asteroids on the orbital parameters of the Earth and Mars. This is done by the numerical integration by comparing the orbital motions of the perturbed planet when adding or not the perturbing asteroid to the classical 9 bodies problem (the Sun + the eight planets). Some preliminary results are discussed. Published in Russian in Astronomicheskii Vestnik, 2009, Vol. 43, No. 1, pp. 83–86. The text was submitted by the autors in English.     

Analysis And Comparison Of Different Estimations Of Mars' Polar Motion

We have summed up three recent modellings of Mars' polar motion (Hilton, 1992; Yoder and Standish, 1997; Zhang, 1998) from which we have studied in particular the Chandler wobble (CW) of the planet and expressions of its period T_CW. We add a fourth study (Kubo, 1991) which deals with the polar motion on the Earth, but whose the results can easily be applied to Mars. To conpare the different expressions of the period T_CW from the authors above, we have chosen common parameters of the planet coming from recent data and we have calculated values of the period corresponding to these parameters after having determined from analytical developments the moments of inertia of the core and of the mantle. We show how the different formula proposed by the authors lead to different values of T_CW and we study in particular the contribution of somc parameters such as the core radius, the mass of the core and the Love number of these values.