Mercury is locked in an unusual 3:2 spin-orbit resonance and as such is expected to be in a state of equilibrium called Cassini state. In that state, the angle between the spin axis and orbit normal, called obliquity, remains almost constant while the spin axis remains almost in the plane, also called Cassini plane, defined by the normal to the Laplace plane and the normal to the orbital plane. The spin axis and the orbit normal precess together with a period of about 300 kyr. The orientation of the spin axis of Mercury has been estimated using different approaches: (i) Earth-based radar observations, (ii) Messenger images and altimeter data, and (iii) Messenger radio tracking data. The different estimates all tend to confirm that Mercury occupies the Cassini state. The observed obliquity is small and close to 2 arcmin. It indicates a normalized polar moment of inertia of about 0.34. This information, combined with the existence of a liquid iron core, as evidenced by the librations, allows to constrain the interior structure of Mercury. However, the different estimates of the orientation of the spin axis locate the spin axis somewhat behind or ahead of the Cassini plane, and it is difficult to reconcile and interpret them coherently in terms of detailed interior properties. We review recent models for the obliquity and spin orientation of Mercury, which include the effects of complex orbital dynamics, tidal deformations and associated dissipation, and internal couplings related to the presence of fluid and solid cores. We discuss some implications regarding the interpretations of the orientation estimates in term of interior properties.

Circumstellar planets in binary star systems provide unique constraints on the formation and dynamical evolution of planets. We present an empirical formula for the stability boundary of coplanar retrograde orbits, similar to the classic one for coplanar prograde orbits. We discuss two of the tightest binaries with circumstellar planets: HD 59686 and ν Octantis. For HD 59686, dynamical fitting of the radial velocity data and stability analysis show that the planet must be either on a nearly coplanar retrograde orbit or in one of the narrow regions of prograde orbits stabilized by secular apsidal alignment. For ν Octantis, a nearly coplanar retrograde planetary orbit is the only option for dynamical stability. We also discuss the mysterious case of ε Cygni. It shows short-period radial velocity variations that closely resemble the signal of a Jupiter-mass planet, but the period and amplitude change over time and dynamical stability analysis rules out a planet.

Exoplanet detection surveys revealed the existence of numerous multi-planetary systems packed close to their stability limit. In this proceeding, we review the mechanism driving the instability of compact systems, originally published in (Petit et al. 2020). Compact systems dynamics are dominated by the interactions between resonances involving triplets of planets. The complex network of three-planet mean motion resonances drives a slow chaotic semi-major axes diffusion, leading to a fast and destructive scattering phase. This model reproduces quantitatively the instability timescale found numerically. We can observe signpost of this process on exoplanet systems architecture. The critical spacing ensuring stability scales as the planet-to star mass ratio to the power 1/4. It explains why the Hill radius is not an adapted measure of dynamical compactness of exoplanet systems, particularly for terrestrial planets. We also provide some insight on the theoretical tools developped in the original work and how they can be of interest in other problems.

In this Review, I discuss recent developments on the long-term dynamical evolution of exoplanet systems, focusing on how distinctive dynamical processes may have shaped the orbital architectures of observed populations. I include three applications that highlight part of my own work. First, I examine the high-eccentricity tidal migration of hot Jupiters from a phase of dynamical instability and subsequent secular interactions in two-planet systems. Second, secular chaos as the origin of ultra-short-period planets with extreme period ratios. Third, secular resonance sweeping driven by a dispersing protoplanetary disk as the origin hot Neptunes residing in polar orbits. Finally, I discuss how upcoming observations will allow further constraining the prevalence of these dynamical processes.

The paper concerns the determination of the Angular Momentum Relative Amended Potential (AMR potential) in the framework of the Full n-Body problem and some of its basic properties are discussed. The AMR potential is derived using two different approaches : first using a Routh reduction of the system relative to rotation about the total angular momentum, second as a variation of the Sundman Inequality, using the Cauchy inequality.

The BEBOP (Binaries Escorted By Orbiting Planets) survey is a search for circumbinary planets using the radial velocity spectrographs HARPS and SOPHIE, currently focusing on single-lined binaries with a mass ratio < 0.3. Circumbinary systems are an important testing ground for planet formation theories as the dynamically complex influence of the binary makes planet formation and survival more difficult. Here we present the results of the survey so far including: confirmed planets such as BEBOP-1c the first circumbinary planet detected in radial velocity; the status of our observations; and preliminary occurrence rates. We compare the early results of the radial velocity survey to the population of circumbinary planets discovered in transit, and suggest that there may be a population of inflated planets close to the inner binary which are detectable in transit but more difficult in radial velocity. Using time-lag tidal theory, we show that this inflation is unlikely caused by tides.

In this contribution we describe the jet transport techniques that we used in Pérez-Hernández and Benet (2022) for the estimation of the Yarkovsky transversal acceleration for (99942) Apophis, which included optical and radar astrometry observations obtained during 2021 Apophis’ fly-by. Our numerical approach exploits automatic differentiation techniques which improve the orbital determination problem. We obtain a non-zero Yarkovsky parameter A2 = (−2.899±0.025) × 10−14 au d−2 which is consistent with other recent determinations of this parameter. Our results allow to constrain the collision probabilities for the close approaches in 2029, 2036 and 2068.

Systems near mean-motion resonances (MMRs) are subject to large transit-timing variations (TTVs). The amplitude and period of the TTVs strongly depend on the distance to exact MMR and the planetary eccentricities which are shaped during the formation and long-term evolution of the system. For close-in planets, the tides raised by the star provide a source of dissipation, placing the planets further away from the MMR. In this work, we will discuss how the tidal interactions with the central star play an important role in shaping the period ratios and resonant angles in resonant chains. Moreover, we will show how they can impact the TTVs and therefore how the TTVs could serve as a means to put constraints on the tidal history of planetary systems. The study will focus on the four-planet resonant chain of Kepler-80.

Like our Moon, the large icy satellites of Jupiter are thought to be in a Cassini State, an equilibrium rotation state characterized by a synchronous rotation rate and a precession rate of the rotation axis equal to that of the normal to the orbit. In these equilibrium states (up to four Cassini States are possible for a solid and rigid satellite), the spin axis of the satellite, the normal to its orbit and the normal to the inertial plane remain coplanar with an obliquity that remains theoretically constant. However, as the gravitational torque exerted on the satellite shows small periodic variations, the orientation of the rotation axis will also vary with time and nutations in obliquity will appear.

Here we present a dynamical model for the study of the Cassini States. This model includes the coupling between the polar motion and the spin axis precession/nutation which is neglected in the classical studies. We study the influence of the triaxiality of Ganymede on its four possible Cassini States, use a Toy model of the Moon to illustrate the nutations in obliquity obtained with the dynamical model, and investigate the influence of the presence of a subsurface ocean on the Cassini State I of Europa.

We present our recent contributions to the theory of Lagrangian descriptors for discriminating ordered and deterministic chaotic trajectories. The class of Lagrangian descriptors we are dealing with is based on the Euclidean length of the orbit over a finite time window. The framework is free of tangent vector dynamics and is valid for both discrete and continuous dynamical systems. We review its last advancements and touch on how it illuminated recently Dvorak’s quantities based on maximal extent of trajectories’ observables, as traditionally computed in planetary dynamics.

The asteroid belt is a unique source of information on some of the most important questions facing solar system science. These questions include the sizes, numbers, types and orbital distributions of the planetesimals that formed the planets, and the identification of those asteroids that are the sources of meteorites and near-Earth asteroids. Answering these questions requires an understanding of the dynamical evolution of the asteroid belt, but this evolution is governed by a complex interplay of mechanisms that include catastrophic disruption, orbital evolution driven by Yarkovsky radiation forces, and chaotic orbital evolution driven by gravitational forces. While the timescales of these loss mechanisms have been calculated using estimates of some critical parameters that include the thermal properties, strengths and mean densities of the asteroids, we argue here that the uncertainties in these parameters are so large that deconvolution of the structure of the asteroid belt must be guided primarily by observational constraints. We argue that observations of the inner asteroid belt indicate that the size-frequency distribution is not close to the equilibrium distribution postulated by Dohnanyi (1969). We also discuss the correlations observed between the sizes and the orbital elements of the asteroids. While some of these correlations are significant and informative, others are spurious and may arise from the limitations of the Hierarchical Clustering Method that is currently used to define family membership.

Solar-like stars evolve through the Asymptotic Giant Branch (AGB) phase. This phase is characterized by increased radii, high luminosities, and significant mass loss. In order to understand the survival of companions during this phase, and explain the presence of planets orbiting white dwarfs, it is essential to examine the orbital evolution of these systems. Several physical mechanisms come into play for AGB stars, including stellar mass loss and tidal interactions between the star and its companion. Assessing mass-loss rates and accretion to the companion requires complex radiation-hydro-chemical simulations. Furthermore, comprehending the full history of tidal dissipation in low-mass stars during their late evolutionary stages, which strongly depends on their internal structure, requires dedicated analytical and numerical studies.

HD34445 is a system that consists of a star and six planets. In some previous work, we investigated the dynamical stability of the system by means of numerical simulations. Here, we explore the system further by carrying out additional numerical experiments. A total of 100000 simulations confirm previous findings of the stability status of the system at the 1σ and 99% c.i. level. We find that only 2.7% of the systems with parameters varied within 1σ from the mean were unstable, while that percentage rose to about 28% for systems with parameter values taken within the 99% c.i. These preliminary results are presented and discussed herein.

The evolution of the five largest satellites of Uranus during the crossing of the 5/3 mean motion resonance between Ariel and Umbriel is strongly affected by chaotic motion. Studies with numerical integrations of the equations of motion and analysis of Poincaré surface sections provided helpful insights to the role of chaos on the system. However, they lack of a quantification of this chaos in the phase-space. Here, we construct stability maps using the frequency analysis method. We determine that for low energies (small eccentricity and/or inclinations), the phase-space is mainly stable. As the energy increases, the chaotic regions replace the stable motion, until only small, localized libration regions remain stable.

Using 2D hydrodynamical simulations, we show that in a low viscosity protoplanetary disc, Jupiter and Saturn get locked in the 2:1 mean motion resonance and migrate slowly inwards, unlike cases at higher viscosities. We conclude that in such discs the scenario of the Grand-Tack is not possible. Additionally, we investigate how the migration of the four (potentially five) giant planets in low viscous discs may affect the initial conditions of another important model for the formation history of our Solar System: the Nice Model. Adding ice giants in our hydrodynamical simulations, we find different possible resonant chains induced by migration. We then let the disc evolve until the gas phase dissipates and study the dynamical stability of the system. We find it possible to recreate the Solar System from such resonant chains, however the likelihood of this outcome remains low.

We present the results of a study of secular resonances in a binary star system and their effects on the formation of terrestrial planets. The systems of our interest are binaries with moderate separations (i.e., smaller than 40 AU) where planets revolve around one of the stars. Using numerical simulations, we demonstrate the appearance and evolution of secular resonances in systems with two giant planets. Results indicate that the perturbation of the binary companion suppresses secular resonances and they do not play a significant role on the formation and orbital architecture of terrestrial planets. Unlike in our solar system where the secular resonance of Saturn confines the formation of terrestrial planets to regions interior to its location, in a binary star, terrestrial planets can form interior and exterior to this resonance. We present details of our simulations and discuss the implications of their results.

Continental silicate weathering and seafloor carbonate precipitation are key steps in the carbonate-silicate cycle to draw down CO2. Contrary to the classic understanding of negative feedback, silicate weathering can exhibit positive feedback at high temperatures. Taking into account this positive feedback, the compensation depth (CCD) in exoplanet oceans becomes shallower, implying a potential instability in the carbonate-silicate cycle at high temperatures.

We present in the following the introductory talk on “Hazardous asteroids and the Hera mission”, made during the round table on Space Awareness. It reminds the context of our awareness for near-Earth objects, the characterisation of risk, current international surveillance programmes, and mitigation measures in particular with space missions, and last, a rendez-vous with Apophis to note in your agenda for 2029.

A complete list of combinations of the rates of asteroid perihelia and nodes and the corresponding fundamental frequencies of planets, giving rise to secular resonances and involving up to 4 frequencies, is known from the previous work, while for the resonances with 6 frequencies a systematically derived comprehensive list is given here for the first time. There are 28 divisors in the theory of degree up to 4, not all of which can give rise to resonances, while at degree 6 there are (at least) 33 such possibly resonant frequency combinations.

Mapping the secular resonances by plotting the resonant lines in the phase space of proper elements or of secular frequencies, possibly also against the background of known asteroids, enables to straightforwardly identify resonances causing large long periodic variations of asteroid orbital elements, resonances that interact with known families, those that bound the dynamically distinct regions, deplete or disturb asteroids in these regions, etc.

We study the motion of an asteroid being in retrograde 1/1 resonance with Jupiter (co-orbital motion). We consider the planar case (i=180°) and Jupiter is on a circular or elliptic orbit (e′ = 0.048). In the cirular model we compute families of symmetric periodic orbits and their stability type. In the elliptic model we have isolated periodic orbits which affect the orbital modes of motion as it is shown by the FLI dynamical maps.