The dynamical structure of the trans-Neptunian region is still far from being fully understood, especially concerning high-perihelion objects. In that region, the orbital perturbations are very weak, both from inside (the planets) and from outside (passing stars and galactic tides). However, numerous objects have very eccentric orbits, which indicates that they did not form in their current orbital state. Furthermore, some intriguing clusters in the distribution of their orbital elements have attracted attention of the scientific community, leading to numerous conjectures about the origin and evolution of the external Solar System.
Before thinking of "exotic" theories, an exhaustive survey has to be conducted on the different mechanisms that could produce the observed trajectories involving only what we take for granted about the Solar System dynamics, that is, the orbital perturbations by the known planets and/or by galactic tides. However, we cannot rely only on numerical integrations to efficiently explore the space of possible behaviours. In that context, we aim at developing a general picture of the dynamics between Neptune and the Oort Cloud, including the most extreme orbits (even if they are maybe improbable).
The orbits entirely exterior to the planetary region can be divided into two broad classes: on the one hand, the objects undergoing a diffusion of semi-major axis (which prevents any large variation of the perihelion distance); on the other hand, the objects which present an integrable (or quasi-integrable) dynamics on a short timescale. The dynamics of the latter can be described by secular models. There are two kinds of regular orbits: the non-resonant ones (fixed semi-major axis) and those trapped in a mean-motion resonance with a planet (oscillating semi-major axis).
The major part of this Ph.D. work is focussed on the development of secular models for trans-Neptunian objects, both in the non-resonant and resonant cases. One-degree-of-freedom systems can be obtained, which allows to represent any trajectory by a level curve of the Hamiltonian. Such a formalism is pretty efficient to explore the parameter space. It reveals pathways to high perihelion distances, as well as "trapping mechanisms", able to maintain the objects on very distant orbits for billions of years. The application of the resonant secular model to the known objects is also very informative, since it shows graphically which observed orbits require a complex scenario (as the planetary migration or an external perturber), and which ones can be explained by the influence of the known planets. In this last case, the dynamical history of the small bodies can be tracked back to the resonance capture.
The last part of this work is devoted to the extension of the non-resonant secular model to the case of an external massive perturber. If it has a substantial eccentricity and/or inclination, it introduces one or two more degrees of freedom in the system, so the secular dynamics is non integrable in general. In that case, the analysis can be realised by Poincaré sections, which allows to distinguish the chaotic regions of the phase space from the regular ones. For increasing semi-major axes, the chaos spreads very fast. The most persistent structures are secular resonances producing trajectories aligned or anti-aligned with the orbit of the distant planet.
Here we present the current state of knowledge on the long-term evolution of Saturn's moon system due to tides within Saturn. First we provide some background on tidal evolution, orbital resonances and satellite tides. Then we address in detail some of the present and past orbital resonances between Saturn's moons (including the Enceladus-Dione and Titan-Hyperion resonances) and what they can tell us about the evolution of the system. We also present the current state of knowledge on the spin-axis dynamics of Saturn: we discuss arguments for a (past or current) secular resonance of Saturn's spin precession with planetary orbits, and explain the links of this resonance to the tidal evolution of Titan and a possible recent cataclysm in the Saturnian system. We also address how the moons' orbital evolution, including resonances, affects the evolution of their interiors. Finally, we summarize the state of knowledge about the Saturnian system's long-term evolution and discuss prospects for future progress.
Context. Dynamically linking a meteor shower with its parent body is challenging, and chaos in the dynamics of meteoroid streams may contribute to this challenge. For a robust identification of parent bodies, it is therefore necessary to quantify the amount of chaos involved in the evolution of meteoroid streams.
Aims. Characterising chaos in meteoroid streams through the aid of chaos maps is still a new field of study. Thus, we examine two very different meteoroid streams, the Draconids and the Leonids, in order to obtain a general view of this topic.
Methods. We used the method developed in a previous paper dedicated to Geminids, drawing chaos maps with the orthogonal fast Lyapunov indicator. We chose four particle size ranges to investigate the effect of non-gravitational forces. As the dynamics are structured by mean-motion resonances with planets, we computed the locations and widths of the resonances at play. We used semi-analytical formulas valid for any eccentricity and inclination and an arbitrary number of planets.
Results. We pinpoint which mean-motion resonances with Jupiter play a major role in the dynamics of each meteoroid stream. We show how those resonances tend to trap mostly large particles, preventing them from meeting with Jupiter. We also study particles that manage to escape those resonances, for example, due to the gravitational perturbation of Saturn. Finally, we explain why non-gravitational forces do not disturb the dynamics much, contrary to what is observed for the Geminids.
Context. The extremely low density of several long-period exoplanets in mature systems is still unexplained – with HIP 41378 f being archetypical of this category. It has been proposed that such planets could actually have normal densities but be surrounded by a ring observed approximately face on, mimicking the transit depth of a puffy planet. This configuration would imply that the equator of the planet is nearly perpendicular to its orbit plane, which is at odds with the formation process of gas giants. Yet, in the context of the Solar System planets, it has recently been shown that after gigayears of evolution, the tidal migration of a moon can naturally lead to a very tilted planet with a ring.
Aims. As exomoons are expected to be ubiquitous around giant exoplanets, this mechanism may be responsible for the anomalous radii of some observed exoplanets. In preparation for the future discoveries of the PLATO mission, we present a simple method for checking the plausibility of this mechanism for a given exoplanet.
Methods. Analytical formulas give the probability density function of the relevant precession harmonics of the planet. For each harmonic, simple criteria set the moon mass and other properties required for the mechanism to operate.
Results. We applied this methodology to HIP 41378 f, and we show that in order to reproduce the observed configuration, a hypothetical former moon should have had a moon-to-planet mass ratio of a few times 10-4 (i.e. roughly the mass of our Moon) and have migrated over a distance of a few planet's radii on a gigayear timescale. These orders of magnitude match the properties of moons expected to exist around gaseous exoplanets.
Conclusions. We conclude that the migration of a former moon is a viable formation pathway for the proposed ring and tilt of HIP 41378 f. This example strengthens the ring hypothesis and motivates its application to other promising targets.
The dynamics of the innermost Galilean satellites (Io, Europa, and Ganymede) is characterized by a chain of mean motion resonances, called Laplace resonance, and by a strong tidal dissipation that causes wide variations of their semimajor axes over large time-scales. The precise history of energy dissipation in the Jovian system is not known, but several theories have been proposed. Tidal resonance locking states that big outer moons can also migrate fast. If this is the case for Callisto, then it should have crossed the 2:1 mean motion resonance with Ganymede in the past, affecting the motion of all four Galilean satellites. Therefore, we aim to determine whether a fast migration for Callisto is compatible with the current orbital configuration of the system. Due to the chaotic nature of the resonant crossing, different outcomes are possible. A small portion of our simulations shows that Callisto can cross the 2:1 resonance with Ganymede without being captured and preserving the Laplace resonance. However, in most cases, we found that Callisto is captured into resonance, despite its divergent migration. As Callisto continues to migrate fast outwards, the moons depart substantially from the exact 8:4:2:1 commensurability, while still maintaining the resonant chain. Callisto can eventually escape it by crossing a high-order mean motion resonance with Ganymede. Afterwards, the moons' system is able to relax to its current configuration for suitable dissipation parameters of the satellites. Therefore, it is possible, although challenging, to build a self-consistent picture of the past history of the Galilean satellites for a fast migration of Callisto.
Context. The 98°-obliquity of Uranus is commonly attributed to giant impacts that occurred at the end of the planetary formation. This picture, however, is not devoid of weaknesses.
Aims. On a billion-year timescale, the tidal migration of the satellites of Jupiter and Saturn has been shown to strongly affect their spin-axis dynamics. We aim to revisit the scenario of tilting Uranus in light of this mechanism.
Methods. We analyse the precession spectrum of Uranus and identify the candidate secular spin-orbit resonances that could be responsible for the tilting. We determine the properties of the hypothetical ancient satellite required for a capture and explore the dynamics numerically.
Results. If it migrates over 10 Uranus' radii, a single satellite with minimum mass 4x10-4 Uranus' mass is able to tilt Uranus from a small obliquity and make it converge towards 90°. In order to achieve the tilting in less than the age of the Solar System, the mean drift rate of the satellite must be comparable to the Moon's current orbital expansion. Under these conditions, simulations show that Uranus is readily tilted over 80°. Beyond this point, the satellite is strongly destabilised and triggers a phase of chaotic motion for the planet's spin axis. The chaotic phase ends when the satellite collides into the planet, ultimately freezing the planet's obliquity in either a prograde, or plainly retrograde state (as Uranus today). Spin states resembling that of Uranus can be obtained with probabilities as large as 80%, but a bigger satellite is favoured, with mass 1.7x10-3 Uranus' mass or more. Yet, a smaller ancient satellite is not categorically ruled out, and there is room for improving this basic scenario in future studies. Interactions among several pre-existing satellites are a promising possibility.
Conclusions. The conditions required for the tilting seem broadly realistic, but it remains to be determined whether Uranus could have hosted a big primordial satellite subject to substantial tidal migration. The efficiency of tidal energy dissipation within Uranus is required to be much higher than traditionally assumed, more in line with that measured for the migration of Titan. Hints about these issues would be given by a measure of the expansion rate of Uranus' main satellites.
Proper elements are quasi-integrals of motion of a dynamical system, meaning that they can be considered constant over a certain timespan, and they permit to describe the long-term evolution of the system with a few parameters. Near-Earth objects (NEOs) generally have a large eccentricity and therefore they can cross the orbits of the planets. Moreover, some of them are known to be currently in a mean-motion resonance with a planet. Thus, the methods previously used for the computation of main-belt asteroid proper elements are not appropriate for such objects.
In this paper, we introduce a technique for the computation of proper elements of planet-crossing asteroids that are in a mean motion resonance with a planet. First, we numerically average the Hamiltonian over the fast angles while keeping all the resonant terms, and we describe how to continue a solution beyond orbit crossing singularities. Proper elements are then extracted by a frequency analysis of the averaged orbit-crossing solutions. We give proper elements of some known resonant NEOs, and provide comparisons with non-resonant models. These examples show that it is necessary to take into account the effect of the resonance for the computation of accurate proper elements.
Context. As a result of Titan's migration and Saturn's probable capture in secular spin-orbit resonance, recent works show that Saturn's obliquity could be steadily increasing today and may reach large values in the next billions of years. Satellites around high-obliquity planets are known to be unstable in the vicinity of their Laplace radius, but the approximations used so far for Saturn's spin axis are invalidated in this regime.
Aims. We aim to investigate the behaviour of a planet and its satellite when the satellite crosses its Laplace radius while the planet is locked in secular spin-orbit resonance.
Methods. We expand on previous works and revisit the concept of Laplace surface. We use it to build an averaged analytical model that couples the planetary spin-axis and satellite dynamics.
Results. We show that the dynamics is organised around a critical point, S1, at which the phase-space structure is singular, located at 90° obliquity and near the Laplace radius. If the spin-axis precession rate of the planet is maintained fixed by a resonance while the satellite migrates outwards or inwards, then S1 acts as an attractor towards which the system is forced to evolve. When it reaches the vicinity of S1, the entire system breaks down, either because the planet is expelled from the secular spin-orbit resonance or because the satellite is ejected or collides into the planet.
Conclusions. Provided that Titan's migration is not halted in the future, Titan and Saturn may reach instability between a few gigayears and several tens of gigayears from now, depending on Titan's migration rate. The evolution would destabilise Titan and drive Saturn towards an obliquity of 90°. Our findings may have important consequences for Uranus. They also provide a straightforward mechanism for producing transiting exoplanets with a face-on massive ring, a configuration that is often put forward to explain some super-puff exoplanets.
Context. Giant planets are expected to form with near-zero obliquities. It has recently been shown that the fast migration of Titan could be responsible for the current 26.7°-tilt of Saturn's spin axis.
Aims. We aim to quantify the level of generality of this result by measuring the range of parameters allowing for this scenario to happen. Since Titan continues to migrate today, we also aim to determine the obliquity that Saturn will reach in the future.
Methods. For a large variety of migration rates for Titan, we numerically propagated the orientation of Saturn's spin axis both backwards and forwards in time. We explored a broad range of initial conditions after the late planetary migration, including both small and large obliquity values.
Results. In the adiabatic regime, the likelihood of reproducing Saturn's current spin-axis orientation is maximised for primordial obliquities between about 2° and 7°. For a slightly faster migration than expected from radio-science experiments, non-adiabatic effects even allow for exactly null primordial obliquities. Starting from such small tilts, Saturn's spin axis can evolve up to its current state provided that: i) the semi-major axis of Titan changed by more than 5% of its current value since the late planetary migration, and ii) its migration rate does not exceed ten times the nominal measured rate. In comparison, observational data suggest that the increase in Titan's semi-major axis exceeded 50% over 4 Gyrs, and error bars imply that the current migration rate is unlikely to belarger than 1.5 times its nominal value.
Conclusions. If Titan did migrate substantially before today, tilting Saturn from a small obliquity is not only possible, but it is the most likely scenario. Saturn's obliquity is still expected to be increasing today and could exceed 65° in the future. Maximising the likelihood would also put strict constraints on Saturn's polar moment of inertia. However, the possibility remains that Saturn'sprimordial obliquity was already large, for instance as a result of a massive collision. The unambiguous distinction between these two scenarios would be given by a precise measure of Saturn's polar moment of inertia.
The obliquity of a planet is the tilt between its equator and its orbital plane. Giant planets are expected to form with near-zero obliquities. After the formation of Saturn, some dynamical mechanism must therefore have tilted Saturn up to its current obliquity of 26.7°. This event is traditionally thought to have happened more than 4 Gyrs ago during the late planetary migration because of the crossing of a resonance between the spin-axis precession of Saturn and the nodal orbital precession mode of Neptune. Here, we show that the fast tidal migration of Titan for which the measurement is reported by Lainey et al. (2020) is incompatible with this scenario, and that it offers a new explanation for Saturn's current obliquity. A substantial migration of Titan would prevent any early resonance, which would invalidate previous constraints on the late planetary migration that were set by the tilting of Saturn. We propose instead that the resonance was encountered more recently, about 1 Gyr ago, and forced Saturn's obliquity to increase from a small value (possibly less than 3°) to its current state. This scenario suggests that Saturn's normalized polar moment of inertia lies between 0.224 and 0.237. Our findings bring out a new paradigm for the spin-axis evolution of Saturn, Jupiter, and possibly giant exoplanets in multiple systems, whereby obliquities are not settled once for all but evolve continuously as a result of the migration of their satellites.
Aims. We aim to determine whether Jupiter's obliquity is bound to remain exceptionally small in the Solar System, or if it could grow in the future and reach values comparable to those of the other giant planets.
Methods. The spin axis of Jupiter is subject to the gravitational torques from its regular satellites and from the Sun. These torques evolve over time due to the long-term variations of its orbit and to the migration of its satellites. With numerical simulations, we explore the future evolution of Jupiter's spin axis for different values of its moment of inertia and for different migration rates of its satellites. Analytical formulas show the location and properties of all relevant resonances.
Results. Because of the migration of the Galilean satellites, Jupiter's obliquity is currently increasing, as it adiabatically follows the drift of a secular spin-orbit resonance with the nodal precession mode of Uranus. Using the current estimates of the migration rate of the satellites, the obliquity of Jupiter can reach values ranging from 6° to 37° after 5 Gyrs from now, according to the precise value of its polar moment of inertia. A faster migration for the satellites would produce a larger increase in obliquity, as long as the drift remains adiabatic.
Conclusions. Despite its peculiarly small current value, the obliquity of Jupiter is no different from other obliquities in the Solar System: It is equally sensitive to secular spin-orbit resonances and it will probably reach comparable values in the future.
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.
This article reviews the different mechanisms affecting the orbits of trans-Neptunian objects, ranging from internal perturbations (planetary scattering, mean-motion resonances, secular effects) to external perturbations (galactic tides, passing stars). We outline the theoretical tools that can be used to model and study them, focussing on analytical approaches. We eventually compare these mechanisms to the observed distinct populations of trans-Neptunian objects and conclude on how they participate to the sculpting of the whole distribution.
Context. Distant trans-Neptunian objects are subject to planetary perturbations and galactic tides. The former decrease with the distance, while the latter increase. In the intermediate regime where they have the same order of magnitude (the "inert Oort cloud"), both are weak, resulting in very long evolution timescales. To date, three observed objects can be considered to belong to this category.
Aims. We aim to provide a clear understanding of where this transition occurs, and to characterise the long-term dynamics of small bodies in the intermediate regime: relevant resonances, chaotic zones (if any), and timescales at play.
Methods. The different regimes are explored analytically and numerically. We also monitored the behaviour of swarms of particles during 4.5 Gyrs in order to identify which of the dynamical features are discernible in a realistic amount of time.
Results. There exists a tilted equilibrium plane (Laplace plane) about which orbits precess. The dynamics is integrable in the low and high semi-major axis regimes, but mostly chaotic in between. From about 800 to 1100 astronomical units (au), the chaos covers almost all the eccentricity range. The diffusion timescales are large, but not to the point of being indiscernible in a 4.5 Gyrs duration: the perihelion distance can actually vary from tens to hundreds of au. Orbital variations are damped near the ecliptic (where previous studies focussed), but favoured in specific ranges of inclination corresponding to well-defined resonances. Moreover, starting from uniform distributions, the orbital angles cluster after 4.5 Gyrs for semi-major axes larger than 500 au, because of a very slow differential precession.
Conclusions. Even if it is characterised by very long timescales, the inert Oort cloud mostly features chaotic regions; it is therefore much less inert than it appears. Orbits can be considered inert over 4.5 Gyrs only in small portions of the space of orbital elements, which include (90377) Sedna and 2012 VP113. Effects of the galactic tides are discernible down to semi-major axes of about 500 au. We advocate including the galactic tides in simulations of distant trans-Neptunian objects, especially when studying the formation of detached bodies or the clustering of orbital elements.
Context. Seasonal variations and climate stability of a planet are very sensitive to the planet obliquity and its evolution. This is of particular interest for the emergence and sustainability of land-based life, but orbital and rotational parameters of exoplanets are still poorly constrained. Numerical explorations usually realised in this situation are therefore in heavy contrast with the uncertain nature of the available data.
Aims. We aim to provide an analytical formulation of the long-term spin-axis dynamics of exoplanets, linking it directly to physical and dynamical parameters, but still giving precise quantitative results if the parameters are well known. Together with bounds for the poorly constrained parameters of exoplanets, this analysis is designed to enable a quick and straightforward exploration of the spin-axis dynamics.
Methods. The long-term orbital solution is decomposed into quasi-periodic series and the spin-axis Hamiltonian is expanded in powers of eccentricity and inclination. Chaotic zones are measured by the resonance overlap criterion. Bounds for the poorly known parameters of exoplanets are obtained from physical grounds (rotational breakup) and dynamical considerations (equipartition of the angular momentum deficit).
Results. This method gives accurate results when the orbital evolution is well known. The detailed structure of the chaotic zones for the solar system planets can be retrieved from simple analytical formulas. For less-constrained planetary systems, the maximal extent of the chaotic regions can be computed, requiring only the mass, the semi-major axis, and the eccentricity of the planets present in the system. Additionally, some estimated bounds of the precession constant allow to classify which observed exoplanets are necessarily out of major spin-orbit secular resonances (unless the precession rate is affected by the presence of massive satellites).
Aims. We aim at analytically modelling the solar wind proton trajectories during their interaction with a partially ionised cometary atmosphere, not in terms of bulk properties of the flow but in terms of single particle dynamics.
Methods. We first derive a generalised gyromotion, in which the electric field is reduced to its motional component. Steady-state is assumed, and simplified models of the cometary density and of the electron fluid are used to express the force experienced by individual solar wind protons during the interaction.
Results. A three-dimensional (3D) analytical expression of the gyration of two interacting plasma beams is obtained. Applying it to a comet case, the force on protons is always perpendicular to their velocity and has an amplitude proportional to 1/r2. The solar wind deflection is obtained at any point in space. The resulting picture presents a caustic of intersecting trajectories, and a circular region is found that is completely free of particles. The particles do not lose any kinetic energy and this absence of deceleration, together with the solar wind deflection pattern and the presence of a solar wind ion cavity, is in good agreement with the general results of the Rosetta mission.
Conclusions. The qualitative match between the model and the in situ data highlights how dominant the motional electric field is throughout most of the interaction region for the solar wind proton dynamics. The model provides a simple general kinetic description of how momentum is transferred between these two collisionless plasmas. It also shows the potential of this semi-analytical model for a systematic quantitative comparison to the data.
Context. Natural satellite systems present a large variety of orbital configurations in the solar system. While some are clearly the result of known processes, others still have largely unexplained eccentricity and inclination values. Iapetus, the furthest of Saturn's main satellites, has a still unexplained 3% orbital eccentricity and its orbital plane is tilted with respect to its local Laplace plane (8° of free inclination). On the other hand, astrometric measurements of saturnian moons have revealed high tidal migration rates, corresponding to a quality factor Q of Saturn of around 1600 for the mid-sized icy moons.
Aims. We show how a past crossing of the 5:1 mean motion resonance between Titan and Iapetus may be a plausible scenario to explain Iapetus' orbit.
Methods. We have carried out numerical simulations of the resonance crossing using an N-body code as well as using averaged equations of motion. A large span of migration rates were explored for Titan and Iapetus was started on its local Laplace plane (15° with respect to the equatorial plane) with a circular orbit.
Results. The resonance crossing can trigger a chaotic evolution of the eccentricity and the inclination of Iapetus. The outcome of the resonance is highly dependent on the migration rate (or equivalently on Q). For a quality factor Q of over around 2000, the chaotic evolution of Iapetus in the resonance leads in most cases to its ejection, while simulations with a quality factor between 100 and 2000 show a departure from the resonance with post-resonant eccentricities spanning from 0 up to 15%, and free inclinations capable of reaching 11°. Usually high inclinations come with high eccentricities but some simulations (less than 1%) show elements compatible with Iapetus' current orbit.
Conclusions. In the context of high tidal energy dissipation in Saturn, a quality factor between 100 and 2000 at the frequency of Titan would bring Titan and Iapetus into a 5:1 resonance, which would perturb Iapetus' eccentricity and inclination to values observed today. Such rapid tidal migration would have avoided Iapetus' ejection around 40–800 million years ago.
Aims. Observations of solar protons near comet 67P/Churyumov-Gerasimenko (67P) by the Rosetta spacecraft can be modelled by the planar motion in an effective magnetic field proportional to 1/r2. We aim to provide a thorough study of such dynamics, with a clear description of the behaviour of an incoming flux of particles. We will be able, then, to calibrate the free parameters of the model to Rosetta observations.
Methods. Basic tools of dynamical analysis are used. They lead to a definition of the relevant parameters for the system and a classification of the possible types of trajectories. Using the so-obtained formalism, the structures formed by a flux of particles coming from infinity can be studied.
Results. All the trajectories are parametrised by two characteristic radii, rE and rC, derived from first integrals. There are three different types of motion possible divided by a separatrix corresponding to rE=rC. An analytical expression of the trajectories, defined by an integral, is developed. Using this formalism, the application to a flux of particles coming from infinity (modelling the incident solar wind) gives one free parameter only, the radius rE, which scales the problem. A circular cavity of radius 0.28 rE is created, as well as an overdensity curve (analogous to a caustic in optics). At each observation time, rE can be calibrated to Rosetta plasma measurements, giving a qualitative understanding of the solar particle dynamics (incoming direction, cavity and density map). We also deduce that, in order to properly capture the essence of the dynamics, numerical simulations of the solar wind around a comet must use simulation boxes much larger than rE and grids much finer than rE.
Context. The first 1000 km of the ion tail of comet 67P/Churyumov–Gerasimenko were explored by the European Rosetta spacecraft, 2.7 au away from the Sun.
Aims. We characterised the dynamics of both the solar wind and the cometary ions on the night-side of the comet's atmosphere.
Methods. We analysed in situ ion and magnetic field measurements and compared the data to a semi-analytical model.
Results. The cometary ions are observed flowing close to radially away from the nucleus during the entire excursion. The solar wind is deflected by its interaction with the new-born cometary ions. Two concentric regions appear, an inner region dominated by the expanding cometary ions and an outer region dominated by the solar wind particles.
Conclusions. The single night-side excursion operated by Rosetta revealed that the near radial flow of the cometary ions can be explained by the combined action of three different electric field components, resulting from the ion motion, the electron pressure gradients, and the magnetic field draping. The observed solar wind deflection is governed mostly by the motional electric field −uion×B.
We use a secular model to describe the non-resonant dynamics of trans-Neptunian objects in the presence of an external ten-earth-mass perturber. The secular dynamics is analogous to an "eccentric Kozai mechanism" but with both an inner component (the four giant planets) and an outer one (the eccentric distant perturber). By the means of Poincaré sections, the cases of a non-inclined or inclined outer planet are successively studied, making the connection with previous works. In the inclined case, the problem is reduced to two degrees of freedom by assuming a non-precessing argument of perihelion for the perturbing body. The size of the perturbation is typically ruled by the semi-major axis of the small body: we show that the classic integrable picture is still valid below about 70 AU, but it is progressively destroyed when we get closer to the external perturber. In particular, for a>150 AU, large-amplitude orbital flips become possible, and for a>200 AU, the Kozai libration islands at ω=π/2 and 3π/2 are totally submerged by the chaotic sea. Numerous resonance relations are highlighted. The most large and persistent ones are associated to apsidal alignments or anti-alignments with the orbit of the distant perturber.
Aims. Numerous trans-Neptunian objects are known to be in mean-motion resonance with Neptune. We aim to describe their long-term orbital evolution (both past and future) by means of a one-degree-of-freedom secular model. In this paper, we focus only on objects with a semi-major axis larger than 50 astronomical units (au).
Methods. For each resonant object considered, a 500 000-year numerical integration is performed. The output is digitally filtered to get the parameters of the resonant secular model. Their long-term (Giga-year) orbital evolution is then represented by the level curves of the secular Hamiltonian.
Results. For the majority of objects considered, the mean-motion resonance has little impact on the long-term trajectories (the secular dynamics is similar to a non-resonant one). However, a subset of objects is strongly affected by the resonance, producing moderately-high-amplitude oscillations of the perihelion distance and/or libration of the argument of perihelion around a fixed centre. Moreover, the high perihelion distance of the object 2015 FJ345 is plainly explained by long-term resonant dynamics, allowing us to also deduce its orbital elements at the time of capture in resonance (at least 15 million years ago). The same type of past evolution is expected for 2014 FZ71.
We use a secular representation to describe the long-term dynamics of transneptunian objects in mean-motion resonance with Neptune. The model applied is thoroughly described in Saillenfest et al. (2016). The parameter space is systematically explored, showing that the secular trajectories depend little on the resonance order. High-amplitude oscillations of the perihelion distance are reported and localised in the space of the orbital parameters. In particular, we show that a large perihelion distance is not a sufficient criterion to declare that an object is detached from the planets. Such a mechanism, though, is found unable to explain the orbits of Sedna or 2012 VP113, which are insufficiently inclined (considering their high perihelion distance) to be possibly driven by such a resonant dynamics. The secular representation highlights the existence of a high-perihelion accumulation zone due to resonances of type 1:k with Neptune. That region is found to be located roughly at a ∈ [100;300] AU, q ∈ [50;70] AU and I ∈ [30;50]°. In addition to the flux of objects directly coming from the Scattered Disc, numerical simulations show that the Oort Cloud is also a substantial source for such objects. Naturally, as that mechanism relies on fragile captures in high-order resonances, our conclusions break down in the case of a significant external perturber. The detection of such a reservoir could thus be an observational constraint to probe the external Solar System.
Two semi-analytical one-degree-of-freedom secular models are presented for the motion of small bodies beyond Neptune. A special attention is given to trajectories entirely exterior to the planetary orbits. The first one is the well-known non-resonant model of Kozai (1962) adapted to the transneptunian region. Contrary to previous papers, the dynamics is fully characterized with respect to the fixed parameters. A maximum perihelion excursion possible of 16.4 AU is determined. The second model handles the occurrence of a mean-motion resonance with one of the planets. In that case, the one-degree-of-freedom integrable approximation is obtained by postulating the adiabatic invariance, and is much more general and accurate than previous secular models found in the literature. It brings out in a plain way the possibility of perihelion oscillations with a very high amplitude. Such a model could thus be used in future studies to deeper explore that kind of motion. For complex resonant orbits (especially of type 1:k), a segmented secular description is necessary since the trajectories are only "integrable by parts". The two models are applied to the Solar System but the notations are kept general so that it could be used for any quasi-circular and coplanar planetary system.
We revisit the dynamics of Atlas. Using Cassini ISS astrometric observations spanning 2004 February to 2013 August, Cooper et al. found evidence that Atlas is currently perturbed by both a 54:53 corotation eccentricity resonance (CER) and a 54:53 Lindblad eccentricity resonance (LER) with Prometheus. They demonstrated that the orbit of Atlas is chaotic, with a Lyapunov time of order 10 years, as a direct consequence of the coupled resonant interaction (CER/LER) with Prometheus. Here we investigate the interactions between the two resonances using the CoraLin analytical model, showing that the chaotic zone fills almost all the corotation sites occupied by the satellite's orbit. Four 70:67 apse-type mean motion resonances with Pandora are also overlapping, but these resonances have a much weaker effect. Frequency analysis allows us to highlight the coupling between the 54:53 resonances, and confirms that a simplified system including the perturbations due to Prometheus and Saturn's oblateness only captures the essential features of the dynamics.