Orbital stability near the (87) Sylvia system

Abstract

The main goal of our work is to study the orbital dynamics of a spacecraft near the (87) Sylvia system. Here, we consider a non-homogeneous mass distribution with a dense core inside the primary asteroid. The Mascon gravity framework using the shaped polyhedral source, from light-curve data, is chosen to calculate the gravitational field. The zero-velocity curves show four unstable equilibrium points. In the absence of any solar or other celestial body perturbations, a numerical analysis of the orbital dynamics in the potential field of Sylvia is done to delineate the region of stable and unstable motions. In our model, the motions of the two moons of Sylvia and of the spacecraft are integrated with the classical equations of motion in the body-fixed frame of reference. An orbit is considered stable if the variation of its periapsis radius does not exceed a threshold value (i.e. 6 km), and the variation of its eccentricity does not exceed 0.05, although the orientation of these orbits may change. We found that the first stable orbit is detected at a distance of 550 km from the centre of Sylvia. No collision occurs with the central body beyond 350 km. The collisions with Remus occur between 300 and 900 km, while with Romulus they occur between 900 and 1450 km. Moreover, the orbits escape from the system when the distance is smaller than 350 km. Finally, we found that the stability region around our system decreases when the initial eccentricity increases.