The dynamical environment of asteroid 21 Lutetia according to different internal models

Abstract

One of the most accurate models currently used to represent the gravity field of irregular bodies is the polyhedral approach. In this model, the mass of the body is assumed to be homogeneous, which may not be true for a real object. The main goal of the present paper is to study the dynamical effects induced by three different internal structures (uniform, three-and four-layers) of asteroid (21) Lutetia, an object that recent results from space probe suggest being at least partially differentiated. The Mascon gravity approach used in the present work, consists of dividing each tetrahedron into eight parts to calculate the gravitational field around the asteroid. The zero-velocity curves show that the greatest displacement of the equilibrium points occurs in the position of the E4 point for the four-layers structure and the smallest one occurs in the position of the E3 point for the three-layers structure. Moreover, stability against impact shows that the planar limit gets slightly closer to the body with the four-layered structure.We then investigated the stability of orbital motion in the equatorial plane of (21) Lutetia and propose numerical stability criteria to map the region of stable motions. Layered structures could stabilize orbits that were unstable in the homogeneous model.

Orbital stability near the (87) Sylvia system

“…We then examine the stability of the equilibria calculating the eigenvalues of the linearized system (Table 3). We found that the differences in the internal structure models of the central body did not affect the stability of the equilibria, which is in agreement with Aljbaae et al (2017). Only the exact location of the equilibrium points is affected.…”

“…This means that the expansion of the gravitational field is fixed around the centre of mass, and the shape is precisely oriented along the principal axes of inertia (Scheeres, Williams & Miller 2000). However, we did not use these coefficients in our analyses, but the mascon approach developed by Chanut, Aljbaae & Carruba (2015a), based on the idea originally presented in the theses of Venditti (2013) and applied in Aljbaae et al (2017) to calculate the exterior gravitational potential. That is more accurate than the harmonic coefficients even if these coefficients were measured up to a degree higher than 4.…”

“…However, other internal structures of this asteroid could be plausible. In this work, we tested two other different internal structures similar to that considered in Aljbaae et al (2017), i.e. three-and four-layered (Fig.…”

“…is the distance between the bodies i and j, ω is the spin rate of (87) Sylvia, and U x j , U y j , and U z j are the first-order partial derivatives of the gravitation potential of the central body U(x j , x j , x j ), calculated using the approach of Mascon 8 (Chanut et al 2015a;Aljbaae et al 2017). The vector P = (P x , P y , P z ) describes the interaction between components i and j.…”

“…While there are minor differences for unstable orbits in the different models, we observe that the stable ones remain the same (see Table 5 for quantifing the difference on the stable orbits). We refer the interested reader to Aljbaae et al (2017) for detailed analyses comparing the effects of different internal structures. However, we argue that a close approach of a spacecraft to our target is necessary to fit the real gravity data to find the plausible internal structure of this asteroid.…”