Context. The Galilean satellites have very complex orbital dynamics due to the mean-motion resonances and the tidal forces acting in the system. The strong dissipation in the couple Jupiter–Io is spread to all the moons involved in the so-called Laplace resonance (Io, Europa, and Ganymede), leading to a migration of their orbits. Aims. We aim to characterize the future behavior of the Galilean satellites over the Solar System lifetime and to quantify the stability of the Laplace resonance. Tidal dissipation permits the satellites to exit from the current resonances or be captured into new ones, causing large variation in the moons’ orbital elements. In particular, we want to investigate the possible capture of Callisto into resonance. Methods. We performed hundreds of propagations using an improved version of a recent semi-analytical model. As Ganymede moves outwards, it approaches the 2:1 resonance with Callisto, inducing a temporary chaotic motion in the system. For this reason, we draw a statistical picture of the outcome of the resonant encounter. Results. The system can settle into two distinct outcomes: (A) a chain of three 2:1 two-body resonances (Io–Europa, Europa–Ganymede, and Ganymede–Callisto), or (B) a resonant chain involving the 2:1 two-body resonance Io–Europa plus at least one pure 4:2:1 three-body resonance, most frequently between Europa, Ganymede, and Callisto. In case A (56% of the simulations), the Laplace resonance is always preserved and the eccentricities remain confined to small values below 0.01. In case B (44% of the simulations), the Laplace resonance is generally disrupted and the eccentricities of Ganymede and Callisto can increase up to about 0.1, making this configuration unstable and driving the system into new resonances. In all cases, Callisto starts to migrate outward, pushed by the resonant action of the other moons. Conclusions. From our results, the capture of Callisto into resonance appears to be extremely likely (100% of our simulations). The exact timing of its entrance into resonance depends on the precise rate of energy dissipation in the system. Assuming the most recent estimate of the dissipation between Io and Jupiter, the resonant encounter happens at about 1.5 Gyr from now. Therefore, the stability of the Laplace resonance as we know it today is guaranteed at least up to about 1.5 Gyr.

Context. Asteroids with a diameter of up to a few dozen meters may spin very fast and complete an entire rotation within a few minutes. These small and fast-rotating bodies are thought to be monolithic objects because the gravitational force due to their small size is not strong enough to counteract the strong centripetal force caused by the fast rotation. This argument means that the rubble-pile structure is not feasible for these objects. Additionally, it is not clear whether the fast spin prevents dust and small particles (regolith) from being kept on their surface. Aims. We develop a model for constraining the thermal conductivity of the surface of the small, fast-rotating near-Earth asteroids. This model may suggest whether regolith is likely present on these objects. Methods. Our approach is based on the comparison of the measured Yarkovsky drift and a predicted value using a theoretical model that depends on the orbital, physical and thermal parameters of the object. The necessary parameters are either deduced from statistical distribution derived for near-Earth asteroids population or determined from observations with associated uncertainty. With this information, we performed Monte Carlo simulations and produced a probability density distribution for the thermal conductivity. Results. Applying our model to the superfast rotator asteroid (499998) 2011 PT, we find that the measured Yarkovsky drift can only be achieved when the thermal conductivity K of the surface is low. The resulting probability density function for the conductivity is bimodal, with two most likely values being around 0.0001 and 0.005 W m−1 K−1. Based on this, we find that the probability that K is lower than 0.1 W m−1 K−1 is at least 95%. This low thermal conductivity might indicate that the surface of 2011 PT is covered with a thermal insulating layer, composed of a regolith-like material similar to lunar dust.

In [13] several periodic orbits of the Newtonian N -body problem have been found as minimizers of the Lagrangian action in suitable sets of T -periodic loops, for a given T > 0. Each of them share the symmetry of one Platonic polyhedron. In this paper we first present an algorithm to enumerate all the orbits that can be found following the proof in [13]. Then we describe a procedure aimed to compute them and study their stability. Our computations suggest that all these periodic orbits are unstable. For some cases we produce a computerassisted proof of their instability using multiple precision interval arithmetic.

Context. Asteroids smaller than about 100 m in diameter are observed to rotate very fast, with periods often much shorter than the critical spin limit of 2.2 h. Some of these super-fast rotators can also achieve a very large semimajor axis drift induced by the Yarkovsky effect, which, in turn, is determined by internal and surface physical properties. Aims. We consider here a small super-fast-rotating near-Earth asteroid, designated as 2016 GE1. This object rotates in just about 34 s, and a large Yarkovsky effect has been determined from astrometry. By using these results, we aim to constrain the thermal inertia of the surface of this extreme object. Methods. We used a recently developed statistical method to determine the thermal properties of near-Earth asteroids. The method is based on the comparison between the observed and the modeled Yarkovsky effect, and the thermal conductivity (inertia) is determined via a Monte Carlo approach. Parameters of the Yarkovsky effect model are fixed if their uncertainty is negligible, modeled with a Gaussian distribution of the errors if they are measured, or deduced from general properties of the population of near-Earth asteroids when they are unknown. Results. Using a well-established orbit determination procedure, we determined the Yarkovsky effect on 2016 GE1 and confirm a significant semimajor axis drift rate. Using a statistical method, we show that this semimajor axis drift rate can only be explained by low thermal inertia values below 100 J m−2 K−1 s−1/2. We benchmarked our statistical method using the well-characterized asteroid Bennu and find that only knowing the semimajor axis drift rate and the rotation period is generally insufficient for determining the thermal inertia. However, when the statistical method is applied to super-fast rotators, we find that the measured Yarkovsky effect can be achieved only for very low values of thermal inertia: namely, 90% of the probability density function of the model outcomes is contained at values smaller than 100 J m−2 K−1 s−1/2. Conclusions. We propose two possible interpretations for the extremely low thermal inertia of 2016 GE1: a high porosity or a cracked surface, or a thin layer of fine regolith on the surface. Though both possibilities seem somewhat unexpected, this opens up the possibility of a subclass of low-inertia, super-fast-rotating asteroids.