Mean motion resonances are a common feature of both our own Solar System and of extrasolar planetary systems. Bodies can be trapped in resonance when their orbital semi-major axes change, for instance when they migrate through a protoplanetary disc. We use a Hamiltonian model to thoroughly investigate the capture behaviour for first and second order resonances. Using this method, all resonances of the same order can be described by one equation, with applications to specific resonances by appropriate scaling. We focus on the limit where one body is a massless test particle and the other a massive planet. We quantify how the the probability of capture into a resonance depends on the relative migration rate of the planet and particle, and the particle's eccentricity. Resonant capture fails for high migration rates, and has decreasing probability for higher eccentricities. More massive planets can capture particles at higher eccentricities and migration rates. We also calculate libration amplitudes and the offset of the libration centres for captured particles, and the change in eccentricity if capture does not occur. Libration amplitudes are higher for larger initial eccentricity. The model allows for a complete description of a particle's behaviour as it successively encounters several resonances. We discuss implications for several scenarios: (i) Planet migration through gas discs trapping other planets or planetesimals in resonances. (ii) Planet migration through a debris disc. (iii) Dust migration through PR drag. The Hamiltonian model will allow quick interpretation of the resonant properties of extrasolar planets and Kuiper Belt Objects, and will allow synthetic images of debris disc structures to be quickly generated, which will be useful for predicting and interpreting disc images made with ALMA, Darwin/TPF or similar missions. [Abridged]
We present preliminary though statistically significant evidence that shows that multiplanetary systems that exhibit a 2/1 period commensurability are in general younger than multiplanetary systems without commensurabilities, or even systems with other commensurabilities. An immediate possible conclusion is that the 2/1 mean-motion resonance in planetary systems, tends to be disrupted after typically a few Gyrs.
In this paper, we use a semi-analytical approach to analyze the global structure of the phase space of the planar planetary 3/1 mean-motion resonance, in cases where the outer planet is more massive than its inner companion. We show that the resonant dynamics can be described using only two fundamental parameters, the total angular momentum and the scaling parameter. The topology of the Hamiltonian function describing the resonant behaviour is studied on the representative planes that allows us to investigate a large domain of the phase space of the three-body problem without time-expensive nu…
In a recent paper it was reported a planetary system around the star HD60532, composed by two giant planets in a possible 3:1 mean motion resonance, that should be confirmed within the next decade. Here we show that the analysis of the global dynamics of the system allows to confirm this resonance. The present best fit to data already corresponds to this resonant configuration and the system is stable for at least 5Gry. The 3:1 resonance is so robust that stability is still possible for a wide variety of orbital parameters around the best fit solution and also if the inclination of the system …
In spite of planetary resonances being a common dynamical mechanism acting on planetary systems, no general model exists for describing their properties, particularly for commensurabilities of any order and arbitrary values of the eccentricities and inclinations. The present work presents a semi-analytical model that describes the resonance strength, width, location and stability of fixed points, as well as periods of small-amplitude librations. The model is valid to any two gravitationally interacting massive bodies, and thus applicable to planets around single or binary stars. Using a theore…
The differential migration of two planets due to planet-disk interaction can result in capture into the 2:1 eccentricity-type mean-motion resonances. Both the sequence of 2:1 eccentricity resonances that the system is driven through by continued migration and the possibility of a subsequent capture into the 4:2 inclination resonances are sensitive to the migration rate within the range expected for type II migration. If the migration rate is fast, the resonant pair can evolve into a family of 2:1 eccentricity resonances different from those found by Lee (2004). This new family has outer orbita…
A diversity of resonance configurations may be formed under different migration of two giant planets. And the researchers show that the HD 128311 and HD 73526 planetary systems are involved in a 2:1 mean motion resonance but not in apsidal corotation, because one of the resonance argument circulates over the dynamical evolution. In this paper, we investigate potential mechanisms to form the 2:1 librating-circulating resonance configuration. In the late stage of planetary formation, scattering or colliding among planetesimals and planetary embryos can frequently occur. Hence, in our model, we c…
Planets around binary stars and those in multiplanet systems may experience resonant eccentricity excitation and disruption due to perturbations from a distant stellar companion. This "evection resonance" occurs when the apsidal precession frequency of the planet, driven by the quadrupole associated with the inner binary or the other planets, matches the orbital frequency of the external companion. We develop an analytic theory to study the effects of evection resonance on circumbinary planets and multiplanet systems. We derive the general conditions for effective eccentricity excitation or re…
We study the effects of planetary late migration on the gas giants obliquities. We consider the planetary instability models from Nesvorny & Morbidelli (2012), in which the obliquities of Jupiter and Saturn can be excited when the spin-orbit resonances occur. The most notable resonances occur when the $s_7$ and $s_8$ frequencies, changing as a result of planetary migration, become commensurate with the precession frequencies of Jupiter's and Saturn's spin vectors. We show that Jupiter may have obtained its present obliquity by crossing of the $s_8$ resonance. This would set strict constrains o…
The Kepler mission has discovered a plethora of multiple transiting planet candidate exosystems, many of which feature putative pairs of planets near mean motion resonance commensurabilities. Identifying potentially resonant systems could help guide future observations and enhance our understanding of planetary formation scenarios. We develop and apply an algebraic method to determine which Kepler 2-planet systems cannot be in a 1st-4th order resonance, given the current, publicly available data. This method identifies when any potentially resonant angle of a system must circulate. We identify…
Many multi-planet systems have been discovered in recent years. Some of them are in mean-motion resonances (MMR). Planet formation theory was successful in explaining the formation of 2:1, 3:1 and other low resonances as a result of convergent migration. However, higher order resonances require high initial orbital eccentricities in order to be formed by this process and these are in general unexpected in a dissipative disk. We present a way of generating large initial eccentricities using additional planets. This procedure allows us to form high order MMRs and predict new planets using a gene…
We present a numerical study on the stability of the 1/2, 2/1 and 1/1 retrograde mean motion resonances in the 3-body problem composed of a solar mass star, a Jupiter mass planet and an additional body with zero mass (elliptic restricted 3-body problem) or masses corresponding to either Neptune, Saturn or Jupiter (planetary 3-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 c…
We propose a semianalytical method to compute the strengths on each of the three massive bodies participating in a three body mean motion resonance (3BR). Applying this method we explore the dependence of the strength on the masses, the orbital parameters and the order of the resonance and we compare with previous studies. We confirm that for low eccentricity low inclination orbits zero order resonances are the strongest ones; but for excited orbits higher order 3BRs become also dynamically relevant. By means of numerical integrations and the construction of dynamical maps we check some of the…
Motivated by the large number of extrasolar planetary systems that are near mean motion resonances, this paper explores a related type of dynamical behavior known as "nodding". Here, the resonance angle of a planetary system executes libration (oscillatory motion) for several cycles, circulates for one or more cycles, and then enters once again into libration. This type of complicated dynamics can affect our interpretation of observed planetary systems that are in or near mean motion resonance. This work shows that planetary systems in (near) mean motion resonance can exhibit nodding behavior,…
Nonrestricted hierarchical three-body configurations are common in various scales of astrophysical systems. Dynamical structures of the quadrupole-order resonance (the von Zeipel-Lidov-Kozai resonance) and the octupole-order resonance (the apsidal resonance) under the nonrestricted hierarchical planetary systems are investigated in this work by taking advantage of perturbative treatments. Under the quadrupole-order Hamiltonian model, the distribution of libration and circulation regions as well as the distribution of flipping region are analytically explored in the parameter space spanned by t…
Applying the technique of dynamical maps we study the orbital stability of test particles in the Solar System in the space (a,e,i) defined by 0.1<a<38 au, 0<e<0.9 and 0<i<180 identifying the unstable and stable regions. We find stable niches where small bodies can survive even for very high eccentricities. Mean motion resonances play a fundamental role providing stability against the planetary perturbations specially for high inclination orbits. A stability stripe around i=150 is present all along the Solar System. We found that the population of objects with semimajor axes between 10 and 30 a…
We study the excitation of mutual inclination between planetary orbits by a novel secular-orbital resonance in multiplanet systems perturbed by binary companions which we call "ivection". The ivection resonance happens when the nodal precession rate of the planet matches a multiple of the orbital frequency of the binary, and its physical nature is similar to the previously-studied evection resonance. Capture into an ivection resonance requires encountering the resonance with slowly increasing nodal precession rate, and it can excite the mutual inclination of the planets without affecting their…
We present spectroscopic measurements of the Rossiter-McLaughlin effect for the planet b of Kepler-9 multi-transiting planet system. The resulting sky-projected spin-orbit angle is $λ=-13^{\circ} \pm 16^{\circ}$, which favors an aligned system and strongly disfavors highly misaligned, polar, and retrograde orbits. Including Kepler-9, there are now a total of 4 Rossiter-McLaughlin effect measurements for multiplanet systems, all of which are consistent with spin-orbit alignment.
We perform several suites of highly detailed dynamical simulations to investigate the architectures of the 24 Sextantis and HD 200964 planetary systems. The best fit orbital solution for the two planets in the 24 Sex system places them on orbits with periods that lie very close to 2:1 commensurability, while that for the HD 200964 system places the two planets therein in orbits whose periods lie close to a 4:3 commensurability. In both cases, the proposed best-fit orbits are mutually crossing - a scenario that is only dynamically feasible if the planets are protected from close encounters by t…
We present families of symmetric and asymmetric periodic orbits at the 1/1 resonance, for a planetary system consisting of a star and two small bodies, in comparison to the star, moving in the same plane under their mutual gravitational attraction. The stable 1/1 resonant periodic orbits belong to a family which has a planetary branch, with the two planets moving in nearly Keplerian orbits with non zero eccentricities and a satellite branch, where the gravitational interaction between the two planets dominates the attraction from the star and the two planets form a close binary which revolves …
I consider the dynamics of mean motion resonances between pairs of co-planar planets and derive a new integrable Hamiltonian model for planets' resonant motion. The new model generalizes previously-derived integrable Hamiltonians for first-order resonances to treat higher-order resonances by exploiting a surprising near-symmetry of the full, non-integrable Hamiltonians of higher-order resonances. Whereas past works have frequently relied on truncated disturbing function expansions to derive integrable approximations to resonant motion, I show that no such expansion is necessary, thus enabling …
We present a numerical study on the stability of all fourth- and fifth-order retrograde mean motion resonances (1/3, 3/1, 1/4, 4/1, 2/3, and 3/2) in the 3-body problem composed of a solar mass star, a Jupiter mass planet, and an additional body with zero mass (elliptic restricted problem) or masses corresponding to either Neptune, Saturn, or Jupiter (planetary problem). The fixed point families exist in all cases and are identified through libration of all resonant angles simultaneously. In addition, configurations with libration of a single resonant angle were also observed. Our results for t…
It has been established theoretically that atmospheric thermal tides on rocky planets can lead to significant modifications of rotational evolution, both close to synchronous rotation and at faster rotations if certain resonant conditions are met. Here it is demonstrated that the normally considered dissipative gravitational tidal evolution of rocky planet rotation could, in principle, be 'stalled' by thermal tide resonances for Earth-analog worlds in the liquid water orbital zone of stars more massive than ~0.3 Msolar. The possibility of feedback effects between a planetary biosphere and the …
In this study, a new expansion of planetary disturbing function is developed for describing the resonant dynamics of minor bodies with arbitrary inclinations and semimajor axis ratios. In practice, the disturbing function is expanded around circular orbits in the first step and then, in the second step, the resulting mutual interaction between circular orbits is expanded around a reference point. As usual, the resulting expansion is presented in the Fourier series form, where the force amplitudes are dependent on the semimajor axis, eccentricity and inclination and the harmonic arguments are l…
We study the dynamics of the upsilon-Andromedae planetary system proposed by Curiel et al. (2011). We focus on the study of the 3:1 Mean Motion Resonance between upsilon-Andromedae-d and the recently discovered upsilon-Andromedae-e (hereafter upsilon-And-d and upsilon-And-e). Numerical simulations of the dynamics of the four planet system are conducted. The previously reported apsidal resonance between upsilon-And-c and upsilon-And-d is confirmed. In addition, we find that upsilon-And-d and upsilon-And-e are also in an apsidal resonance condition. Our results further indicate that the upsilon-…
The dynamical interactions that occur in newly formed planetary systems may reflect the conditions occurring in the protoplanetary disk out of which they formed. With this in mind, we explore the attainment and maintenance of orbital resonances by migrating planets in the terrestrial mass range. Migration time scales varying between millions of years and thousands of years are considered. In the former case, for which the migration time is comparable to the lifetime of the protoplanetary gas disk, a 2:1 resonance may be formed. In the latter, relatively rapid migration regime commensurabilitie…
In order to study the origin of the architectures of low mass planetary systems, we perform numerical surveys of the evolution of pairs of coplanar planets in the mass range $(1-4)\ \rmn{M}_{\oplus}.$ These evolve for up to $2\times10^7 \rmn{yr}$ under a range of orbital migration torques and circularization rates assumed to arise through interaction with a protoplanetary disc. Near the inner disc boundary, significant variations of viscosity, interaction with density waves or with the stellar magnetic field could occur and halt migration, but allow ircularization to continue. This was modelle…
The present work studies the secular resonance associated with the critical argument $σ= \varpi$ ($\varpi$ is the longitude of pericentre) for inner test particles moving in low-eccentricity region with inclination $i$ smaller than $39^{\circ}$. To formulate the dynamical model, the double-averaged Hamiltonian is formulated up to an arbitrary order in the semimajor axis ratio, and then those high-order periodic terms are removed from the double-averaged Hamiltonian by means of Hori--Deprit transformation technique. The resulting Hamiltonian determines a resonant model with a single degree of f…
Chaotic diffusion is supposed to be responsible for orbital instabilities in planetary systems after the dissipation of the protoplanetary disk, and a natural consequence of irregular motion. In this paper we show that resonant multi-planetary systems, despite being highly chaotic, not necessarily exhibit significant diffusion in phase space, and may still survive virtually unchanged over timescales comparable to their age.Using the GJ-876 system as an example, we analyze the chaotic diffusion of the outermost (and less massive) planet. We construct a set of stability maps in the surrounding r…
The geometric arrangement of planet and moon orbits into a regularly spaced pattern of distances is the result of a self-organizing system. The positive feedback mechanism that operates a self-organizing system is accomplished by harmonic orbit resonances, leading to long-term stable planet and moon orbits in solar or stellar systems. The distance pattern of planets was originally described by the empirical Titius-Bode law, and by a generalized version with a constant geometric progression factor (corresponding to logarithmic spacing). We find that the orbital periods $T_i$ and planet distance…
Orbital mean motion resonances in planetary systems originate from dissipative processes in disk-planet interactions that lead to orbital migration. In multi-planet systems that host giant planets, the perturbation of the protoplanetary disk strongly affects the migration of companion planets. By studying the well-characterized resonant planetary system around GJ 876 we aim to explore which effects shape disk-driven migration in such a multi-planet system to form resonant chains. We modelled the orbital migration of three planets embedded in a protoplanetary disk using two-dimensional locally …
Aim. The eccentric von Zeipel-Lidov-Kozai (ZLK) effect is widely used to explain dynamical phenomena in varieties of astrophysical systems. The purpose of this work is to make clear the dynamical essence of the eccentric ZLK effect by constructing an inherent connection between such an effect and dynamics of secular resonance in restricted hierarchical planetary systems. Methods. Dynamical structures of apsidal resonance are analytically studied by means of perturbative treatments. The resonant model is formulated by averaging the Hamiltonian (up to octupole order) over rotating ZLK cycles, pr…
In Gayon & Bois (2008) and Gayon etal (2009), (i) we studied the theoretical feasibility and efficiency of retrograde mean motion resonances (i.e. two planets are both in orbital resonance and in counter-revolving configuration), (ii) we showed that retrograde resonances can generate interesting mechanisms of stability, and (iii) we obtained a dynamical fit involving a counter-revolving configuration that is consistent with the observations of the HD73526 planetary system. In the present paper, we present and analyze data reductions assuming counter-revolving configurations for eight compact m…
A system of four super-Jupiter planets around HR 8799 is the first multi-planet configuration discovered via the direct imaging technique. Despite over decade of research, the system's architecture remains not fully resolved. The main difficulty comes from still narrow observing window of ~20 years that covers small arcs of orbits with periods from roughly 50 to 500 years. Soon after the discovery it became clear that unconstrained best-fitting astrometric configurations self-disrupt rapidly, due to strong mutual gravitational interactions between ~10-Jupiter-mass companions. Recently, we show…
HR 8799 is a nearby star hosting at least four ~10 Jovian mass planets in wide orbits up to ~70au, detected through the direct, high-contrast infrared imaging. Large companions and debris disks reported interior to ~10au, and exterior to ~100au indicate massive protoplanetary disc in the past. The dynamical state of the HR 8799 system is not yet fully resolved, due to limited astrometric data covering tiny orbital arcs. We construct a new, orbital model of the HR 8799 system, assuming rapid migration of the planets after their formation in wider orbits. We found that the HR 8799 planets are li…
We consider the chaotic motion of low-mass bodies in two-body high-order mean-motion resonances with planets in model planetary systems, and analytically estimate the Lyapunov and diffusion timescales of the motion in multiplets of interacting subresonances corresponding to the mean-motion resonances. We show that the densely distributed (though not overlapping) high-order mean-motion resonances, when certain conditions on the planetary system parameters are satisfied, may produce extended planetary chaotic zones -- "zones of weak chaotization," -- much broader than the well-known planetary co…
Resonant Hamiltonian Dynamics in the CR3BP: Bistability and Stochastic Resonance in Binary Planetary Systems
Sapienza, Universitá di Roma（罗马第一大学）；INFN, Sezione di Roma, Sapienza, Universitá di Roma（罗马大学罗马分部意大利国家核物理研究所）；INAF, Observatory of Roma at Monteporzio Catone（蒙波尔齐奥卡托内罗马天文台）；Centro Ricerche Enrico Fermi（恩里科·费米研究中心）
The planetary dynamics of $4/3$, $3/2$, $5/2$, $3/1$ and $4/1$ mean motion resonances is studied by using the model of the general three body problem in a rotating frame and by determining families of periodic orbits for each resonance. Both planar and spatial cases are examined. In the spatial problem, families of periodic orbits are obtained after analytical continuation of vertical critical orbits. The linear stability of orbits is also examined. Concerning initial conditions nearby stable periodic orbits, we obtain long-term planetary stability, while unstable orbits are associated with ch…
Planets close to their stars are thought to form farther out and migrate inward due to angular momentum exchange with gaseous protoplanetary disks. This process can produce systems of planets in co-orbital (Trojan or 1:1) resonance, in which two planets share the same orbit, usually separated by 60 degrees. Co-orbital systems are detectable among the planetary systems found by the Kepler mission either directly or by transit timing variations. However, no co-orbital systems have been found within the thousands of Kepler planets and candidates. Here we study the orbital evolution of co-orbital …
An ever-growing observational aggregate of extrasolar planets has revealed that systems of planets that reside in or near mean-motion resonances are relatively common. While the origin of such systems is attributed to protoplanetary disk-driven migration, a qualitative description of the dynamical evolution of resonant planets remains largely elusive. Aided by the pioneering works of the last century, we formulate an approximate, integrable theory for first-order resonant motion. We utilize the developed theory to construct an intuitive, geometrical representation of resonances within the cont…
It is well known that asteroids and comets fall into the Sun. Metal pollution of white dwarfs and transient spectroscopic signatures of young stars like $β$-Pic provide growing evidence that extra solar planetesimals can attain extreme orbital eccentricities and fall onto their parent stars. We aim to develop a general, practically implementable, semi-analytical theory of secular eccentricity excitation of small bodies in mean motion resonances with an eccentric planet valid for arbitrary values of the eccentricities and including the short-range force due to General Relativity. Our semi-analy…
We study the evolution of two planets around a star, in mean-motion resonance and undergoing tidal effect. We derive an integrable analytical model of mean-motion resonances of any order which reproduce the main features of the resonant dynamics. Using this simplified model, we obtain a criterion showing that depending on the balance of the tidal dissipation in both planets, their final period ratio may stay at the resonant value, increase above, or decrease below the resonant value. Applying this criterion to the two inner planets orbiting GJ163, we deduce that the current period ratio (2.97)…
Many extrasolar planetary systems containing multiple super-Earths have been discovered. N-body simulations taking into account standard type-I planetary migration suggest that protoplanets are captured into mean-motion resonant orbits near the inner disk edge at which the migration is halted. Previous N-body simulations suggested that orbital stability of the resonant systems depends on number of the captured planets. In the unstable case, through close scattering and merging between planets, non-resonant multiple systems are finally formed. In this paper, we investigate the critical number o…
Orbital resonances play an important role in the dynamics of planetary systems. Classical theoretical analyses found in textbooks report that libration widths of first order mean motion resonances diverge for nearly circular orbits. Here we examine the nature of this divergence with a non-perturbative analysis of a few first order resonances interior to a Jupiter-mass planet. We show that a first order resonance has two branches, the pericentric and the apocentric resonance zone. As the eccentricity approaches zero, the centers of these zones diverge away from the nominal resonance location bu…
We extract Transit Timing Variation (TTV) signals for 12 pairs of transiting planet candidates that are near first-order Mean Motion Resonances (MMR), using publicly available Kepler light curves (Q0-Q14). These pairs show significant sinusoidal TTVs with theoretically predicted periods, which demonstrate these planet candidates are orbiting and interacting in the same system. Although individual masses cannot be accurately extracted based only on TTVs because of the well known degeneracy between mass and eccentricity, TTV phases and amplitudes can still place upper limits on the masses of the…
By logging encounters between planetesimals and planets we compute the distribution of encounters in a numerically integrated two planet system that is migrating due to interactions with an exterior planetesimal belt. Capture of an irregular satellite in orbit about a planet through an exchange reaction with a binary planetesimal is only likely when the binary planetesimal undergoes a slow and close encounter with the planet. In our simulations we find that close and slow encounters between planetesimals and a planet primarily occur with the outermost and not innermost planet. Taking care to c…
The recently discovered planetary system HD45364 which consists of a Jupiter and Saturn mass planet is very likely in a 3:2 mean motion resonance. The standard scenario to form planetary commensurabilities is convergent migration of two planets embedded in a protoplanetary disc. When the planets are initially separated by a period ratio larger than two, convergent migration will most likely lead to a very stable 2:1 resonance for moderate migration rates. To avoid this fate, formation of the planets close enough to prevent this resonance may be proposed. However, such a simultaneous formation …
The gravitational influence of a planet on a nearby disk provides a powerful tool for detecting and studying extrasolar planetary systems. Here we demonstrate that gaps can be opened in dynamically cold debris disks at the mean-motion resonances of an orbiting planet. The gaps are opened away from the orbit of the planet itself, revealing that not all disk gaps need contain a planetary body. These gaps are large and deep enough to be detectable in resolved disk images for a wide range of reasonable disk-planet parameters, though we are not aware of any such gaps detected to date. The gap shape…
We explore scenarios for the origin of two different density planets in the Kepler 36 system in adjacent orbits near the 7:6 mean motion resonance. We find that fine tuning is required in the stochastic forcing amplitude, the migration rate and planet eccentricities to allow two convergently migrating planets to bypass mean motion resonances such as the 4:3, 5:4 and 6:5, and yet allow capture into the 7:6 resonance. Stochastic forcing can eject the system from resonance causing a collision between the planets, unless the disk inducing migration and stochastic forcing is depleted soon after res…
Motivated by the population of multi-planet systems with orbital period ratios 1<P2/P1<2, we study the long-term stability of packed two planet systems. The Hamiltonian for two massive planets on nearly circular and nearly coplanar orbits near a first order mean motion resonance can be reduced to a one degree of freedom problem (Sessin & Ferraz Mello (1984), Wisdom (1986), Henrard et al. (1986)). Using this analytically tractable Hamiltonian, we apply the resonance overlap criterion to predict the onset of large scale chaotic motion in close two planet systems. The reduced Hamiltonian has only…
Planets form in active protoplanetary disks that sustain stellar jets. Momentum loss from the jet system may excite the planets' orbital eccentricity and inclination (Namouni 2005, AJ 130, 280). Evaluating quantitatively the effects of such excitation requires a realistic modeling of the momentum loss profiles associated with stellar jets. In this work, we model linear momentum loss as a time-variable stochastic process that results in a zero mean stellar acceleration. Momentum loss may involve periodic or random polarity reversals. We characterize orbital excitation as a function of the varia…
We use numerical integrations to investigate the dynamical evolution of resonant Trojan and quasi-satellite companions during the late stages of migration of the giant planets Jupiter, Saturn, Uranus, and Neptune. Our migration simulations begin with Jupiter and Saturn on orbits already well separated from their mutual 2:1 mean-motion resonance. Neptune and Uranus are decoupled from each other and have orbital eccentricities damped to near their current values. From this point we adopt a planet migration model in which the migration speed decreases exponentially with a characteristic timescale…
We present a new mechanism of generating large planetary eccentricities. This mechanism applies to planets within the inner cavities of their companion protoplanetary disks. A massive disk with an inner truncation may become eccentric due to non-adiabatic effects associated with gas cooling, and can retain its eccentricity in long-lived coherently-precessing eccentric modes; as the disk disperses, the inner planet will encounter a secular resonance with the eccentric disk when the planet and the disk have the same apsidal precession rates; the eccentricity of the planet is then excited to a la…
We explore planetary migration scenarios for formation of high inclination Neptune Trojans (NTs) and how they are affected by the planetary migration of Neptune and Uranus. If Neptune and Uranus's eccentricity and inclination were damped during planetary migration, then their eccentricities and inclinations were higher prior and during migration than their current values. Using test particle integrations we study the stability of primordial NTs, objects that were initially Trojans with Neptune prior to migration. We also study Trans-Neptunian objects captured into resonance with Neptune and be…
In this study, dynamics of secular resonances for inner test particles are investigated under the octupole-level approximation by taking non-perturbative approaches. In practice, webs of the major secular resonances are produced by identifying families of stable periodic orbits and the associated stable libration zones are obtained by analysing Poincaré surfaces of section. By taking different values of the factor $ε$ ($ε$ measures the contribution of octupole terms), the influences of the octupole-order terms upon the dynamical structures are evaluated. Under the condition of $ε= 0$ (no octup…
Aims. To date, more than 600 multi-planetary systems have been discovered. Due to the limitations of the detection methods, our knowledge of the systems is usually far from complete. In particular, for planetary systems discovered with the radial velocity (RV) technique, the inclinations of the orbital planes, and thus the mutual inclinations and planetary masses, are unknown. Our work aims to constrain the spatial configuration of several RV-detected extrasolar systems that are not in a mean-motion resonance. Methods. Through an analytical study based on a first-order secular Hamiltonian expa…
Mean motion commensurabilities in multi-planet systems are an expected outcome of protoplanetary disk-driven migration, and their relative dearth in the observational data presents an important challenge to current models of planet formation and dynamical evolution. One natural mechanism that can lead to the dissolution of commensurabilities is stochastic orbital forcing, induced by turbulent density fluctuations within the nebula. While this process is qualitatively promising, the conditions under which mean motion resonances can be broken are not well understood. In this work, we derive a si…
