The aim of this paper is the development of a model to propagate space debris in the geostationary ring considering the J 2 effect due to the Earth oblateness, the Sun and Moon perturbations, and the solar radiation pressure. We justify the importance of considering the J 2 effect when propagating space debris independently of the ratio A/m for short and longterm propagation. We study the role of the Sun and the Moon in the period and amplitude of the inclination for different values of A/m. Thanks to the Hamiltonian formulation of the problem and the use of Poincaré's variables it is possible to express the evolution of the space debris through a simplified dynamical system. We test and validate our obtained analytical solutions with the numerical ones, computed with a powerful integrator named NIMASTEP. We analyse the improvements obtained when we include the J 2 effect and the third body perturbations by a rigorous comparison with a previous model, which only considers the solar radiation pressure. Finally, we study the effect of the area-to-mass ratio on short and long-term propagation.

No abstract

Context. Several asteroids have recently been visited by spacecrafts that give us precious information and new constraints on their physical and rotational properties. In parallel, there are already several well-established theories to model the rotational motion of a rigid body, but accurate models of the rotational motion of asteroids have been poorly investigated so far. Aims. We aim to model the rotational motion of the asteroids (1) Ceres, (4) Vesta, (433) Eros, (2867) Steins, and (25143) Itokawa with high precision. Their physical parameters have been or will be (in the case of Ceres) better constrained by data from space missions. We concentrate in particular on the motion of their spin axis in space, a component that is generally not studied. Methods. We used Kinoshita's theory, based on a Hamiltonian approach for the rotation of a rigid body. We deduced an analytical model for determining the precession rate and the nutation coefficients for the set of five asteroids selected above. Results. For each asteroid considered we make a summary of the rotational and physical characteristics necessary for our calculations, and we give both the precession rate and accurate tables of nutation. Results show a very high precession rate for (25143) Itokawa, of more than one degree per decade (ψ = −(461.52 ± 6.57) /yr), and rather high ones for (433) Eros and (2867) Steins. We present the complete tables of nutation for both (1) Ceres and (4) Vesta, and give the peak-to-peak amplitudes for the five asteroids. At last, we show the curves described by the spin axis in space. Results agree with previous ones for (4)Vesta and (433) Eros. Conclusions. In this paper we show that it is possible to accurately compute the combined precession-nutation motion of asteroids that are well constrained by observational data as we do for a set of five asteroids. This enables one to understand the rotational behavior of their spin axis in space and constitutes an interesting step toward knowing of their rotational evolution and its consequences on their history. This work should serve as a basis for more extended ones dealing with the long-term rotational dynamics of the asteroids studied.

No abstract