3D plausible orbital stability close to asteroid (216) Kleopatra

Abstract

Recent data processing showed the existence of a difference that can reach 25 per cent for the dimensions of asteroid (216) Kleopatra between the radar observations and the light curves. We rebuild the shape of (216) Kleopatra from these new data applying a correction's factor of the size of 1.15 and estimate certain physical features by using the polyhedral model method. In our computations, we use a code that avoids singularities from the line integrals of a homogeneous arbitrary shaped polyhedral source. Then, we find the location of the equilibrium points through the pseudo-potential energy and zero-velocity curves. The behaviour of the zero-velocity curves differ substantially if we apply a scale size of 1.15 relative to the original shape of (216) Kleopatra. Taking the rotation of asteroid (216) Kleopatra into consideration, the aim of this work is to analyse the stability against impact and the dynamics of numerical simulations of 3D initially equatorial and polar orbits near the body. As results, we show that the minimum radii are more suited for the stability against impact. We find also that the minimum radius for direct, equatorial circular orbits that cannot impact with (216) Kleopatra surface is 300 km and the lower limit on radius for polar circular orbits is 240 km. Stable orbits occur at 280 km for equatorial circular orbits despite significant perturbations of its orbit. Moreover, as the orbits suffer less perturbations due to the irregular gravitational potential of (216) Kleopatra in the elliptic case, the most significant result of the analysis is that stable orbits exist at a periapsis radius of 250 km for initial eccentricities e<inf>i</inf> = 0.2 in both cases. Finally, the polar orbits with eccentricities ranging between 0.1 and 0.2 appear to be more stable.