In the last two decades, new computational tools have been developed in order to aid space missions to orbit around irregular small bodies. One of the techniques consists in rebuilding their shape in tetrahedral polyhedron. This method is well suited to determine the shape and estimate certain physical features of asteroids. However, a large computational effort is necessary depending on the quantity of triangular faces chosen. Another method is based on a representation of the central body in terms of mascons (discrete spherical masses). The main advantage of the method is its simplicity which makes the calculation faster. Nevertheless, the errors are non-negligible when the attraction expressions are calculated near the surface of the body. In this work, we carry out a study to develop a new code that determines the centre of mass of each tetrahedron of a shaped polyhedral source and evaluates the gravitational potential function and its first- and second-order derivatives. We performed a series of tests and compared the results with the classical polyhedron method. We found good agreement between our determination of the attraction expressions close to the surface, and the same determination by the classical polyhedron method. However, this agreement does not occur inside the body. Our model appears to be more accurate in representing the potential very close to the body's surface when we divide the tetrahedron in three parts. Finally, we have found that in terms of CPU time requirements, the execution of our code is much faster compared with the polyhedron method.

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 this paper is to study the dynamical effects induced by three different internal structures (uniform, three- and four-layered) 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 this 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-layered structure and the smallest one occurs in the position of the E3 point for the three-layered 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.

The Cybele region, located between the 2J:-1A and 5J:-3A mean-motion resonances, is adjacent and exterior to the asteroid main belt. An increasing density of three-body resonances makes the region between the Cybele and Hilda populations dynamically unstable, so that the Cybele zone could be considered the last outpost of an extended main belt. The presence of binary asteroids with large primaries and small secondaries suggested that asteroid families should be found in this region, but only relatively recently the first dynamical groups were identified in this area. Among these, the Sylvia group has been proposed to be one of the oldest families in the extended main belt. In this work we identify families in the Cybele region in the context of the local dynamics and non-gravitational forces such as the Yarkovsky and stochastic Yarkovsky–O'Keefe–Radzievskii–Paddack (YORP) effects. We confirm the detection of the new Helga group at ≃3.65 au, which could extend the outer boundary of the Cybele region up to the 5J:-3A mean-motion resonance. We obtain age estimates for the four families, Sylvia, Huberta, Ulla, and Helga, currently detectable in the Cybele region, using Monte Carlo methods that include the effects of stochastic YORP and variability of the solar luminosity. The Sylvia family should be T = 1220 ± 40 Myr old, with a possible older secondary solution. Any collisional Cybele group formed prior to the Late Heavy Bombardment would have been most likely completely dispersed in the jumping Jupiter scenario of planetary migration.

Artificial neural networks (ANNs) have been successfully used in the last years to identify patterns in astronomical images. The use of ANN in the field of asteroid dynamics has been, however, so far somewhat limited. In this work, we used for the first time ANN for the purpose of automatically identifying the behaviour of asteroid orbits affected by the M1:2 mean-motion resonance with Mars. Our model was able to perform well above 85 per cent levels for identifying images of asteroid resonant arguments in term of standard metrics like accuracy, precision, and recall, allowing to identify the orbital type of all numbered asteroids in the region. Using supervised machine learning methods, optimized through the use of genetic algorithms, we also predicted the orbital status of all multi-opposition asteroids in the area. We confirm that the M1:2 resonance mainly affects the orbits of the Massalia, Nysa, and Vesta asteroid families.

Ceres is the largest and most massive body in the asteroid main belt. Observational data from the Dawn spacecraft reveal the presence of at least two impact craters about 280 km in diameter on the Ceres surface, that could have expelled a significant number of fragments. Yet, standard techniques for identifying dynamical asteroid families have not detected any Ceres family. In this work, we argue that linear secular resonances with Ceres deplete the population of objects near Ceres. Also, because of the high escape velocity from Ceres, family members are expected to be very dispersed, with a considerable fraction of km-sized fragments that should be able to reach the pristine region of the main belt, the area between the 5J:-2A and 7J:-3A mean-motion resonances, where the observed number of asteroids is low. Rather than looking for possible Ceres family members near Ceres, here we propose to search in the pristine region. We identified 156 asteroids whose taxonomy, colours, albedo could be compatible with being fragments from Ceres. Remarkably, most of these objects have inclinations near that of Ceres itself.