We present a numerical study on the stability of the 1/2, 2/1, and 1/1 retrograde mean motion resonances in the three-body problem composed of a solar mass star, a Jupiter mass planet, and an additional body with zero mass (elliptic restricted three-body problem) or masses corresponding to either Neptune, Saturn, or Jupiter (planetary three-body problem). For each system, we obtain stability maps using the n-body numerical integrator REBOUND and computing the chaos indicator mean exponential growth factor of nearby orbits (MEGNO). We show that families of periodic orbits exist in all configurations and they correspond to the libration of either a single resonant argument or all resonant arguments (fixed points). We compare the results obtained in the elliptic restricted three-body problem with previous results in the literature, and we show the differences and similarities between the phase space topology for these retrograde resonances in the circular restricted, elliptic restricted, and planetary three-body problems.

Linear secular resonances happen when there is a commensurability between the precession frequency of the pericenter, g, or longitude of the node, s, of an asteroid and a planet. Non-linear resonances are higher-order combinations of these frequencies. Here, we studied the three most diffusive g −type non-linear secular resonances using Artificial Neural Networks. We identified a population of more than 2100 resonant objects in the g − 2g₆ + g₅ and g − 3g₆ + 2g₅ resonances. This allows the creation of a Convolutional Neural Network model for the g − 2g₆ + g₅ resonance, able to predict the status of several thousands of asteroids in seconds. We identified 12 new possible dynamical groups among the resonant population, including the 5507 and 170776 families, which have both estimated ages of less than 7 Myr. These are the two first-ever identified young families in resonant configurations of the investigated resonances, which allows for setting limits on their original ejection velocity field.

Context. There are 20 co-orbital asteroids of Venus currently known. Only one of them exhibits an eccentricity below 0.38. This is most likely caused by observational biases since asteroids with higher eccentricities have a higher probability of approaching the Earth and are easier to detect. Aims. We aim to assess the possible threat that the as-yet-undetected population of Venus co-orbitals might pose to Earth and investigate their detectability from Earth and space observatories. Methods. We used semi-analytical models of the 1:1 mean-motion resonance with Venus and numerical simulations to monitor close encounters with Earth on several co-orbital cycles. We analyzed the observability windows and brightness variations for potential Venus co-orbitals, as viewed from ground-based telescopes to assess their future detection feasibility with next-generation survey capabilities. Results. There is a range of orbits with e < 0.38, larger at lower inclinations, for which Venus’co-orbitals can pose a collisional hazard to Earth. Conclusions. Current ground-based observations are constrained by periodic observing windows and solar elongation limitations; however, the Rubin Observatory might be able to detect some of these objects during favorable configurations. Space missions based on Venus’orbits could be instrumental in detecting Venus’co-orbitals at low eccentricities.