The stability of planets in the α Centauri AB stellar system has been studied extensively. However, most studies either focus on the orbital plane of the binary or consider inclined circular orbits. ...Here, we numerically investigate the stability of a possible planet in the α Centauri AB binary system for S-type orbits in an arbitrary spatial configuration. In particular, we focus on inclined orbits and explore the stability for different eccentricities and orientation angles. We show that large stable and regular regions are present for very eccentric and inclined orbits, corresponding to libration in the Lidov-Kozai resonance. We additionally show that these extreme orbits can survive over the age of the system, despite the effect of tides. Our results remain qualitatively the same for any compact binary system.
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The number of multiple-planet systems known to be involved in mean motion conmensurabilities has increased significantly since the Kepler mission. Although most correspond to two-planet resonances, ...multiple resonances have also been found. The Laplace resonance is a particular case of a three-body resonance in which the period ratio between consecutive pairs is n
1/n
2 ∼ n
2/n
3 ∼ 2/1. It is not clear how this triple resonance acts to stabilize (or not) the system.
The most reliable extrasolar system located in a Laplace resonance is GJ 876, because it has two independent confirmations. However, best-fit parameters were obtained without previous knowledge of resonance structure, and not all possible stable solutions for the system have been explored.
In the present work we explore the various configurations allowed by the Laplace resonance in the GJ 876 system by varying the planetary parameters of the third outer planet. We find that in this case the Laplace resonance is a stabilization mechanism in itself, defined by a tiny island of regular motion surrounded by (unstable) highly chaotic orbits. Low-eccentricity orbits and mutual inclinations from −20° to 20° are compatible with observations. A definite range of mass ratio must be assumed to maintain orbital stability. Finally, we provide constraints on the argument of pericentres and mean anomalies to ensure stability for this kind of system.
Dynamical studies suggest that most of the circumbinary discs (CBDs) should be coplanar. However, under certain initial conditions, the CBD can evolve toward polar orientation. Here we extend the ...parametric study of polar configurations around detached close-in binaries through N-body simulations. For polar configurations around binaries with mass ratios q below 0.7, the nominal location of the mean motion resonance (MMR) 1 : 4 predicts the limit of stability for eB > 0.1. Alternatively, for eB < 0.1 or q ∼ 1, the nominal location of the MMR 1 : 3 is the closest stable region. The presence of a giant planet increases the region of forbidden polar configurations around low mass ratio binaries with eccentricities eB∼ 0.4 with respect to rocky earth-like planets. For equal mass stars, the eccentricity excitation Δβ of polar orbits smoothly increases with decreasing distance to the binary. For q < 1, Δβ can reach values as high as 0.4. Finally, we studied polar configurations around HD 98800BaBb and show that the region of stability is strongly affected by the relative positions of the nodes. The most stable configurations in the system correspond to polar particles, which are not expected to survive on longer time-scales due to the presence of the external perturber HD 98800AaAb.
In this work, we construct and test an analytical model and a semi-analytical secular model for two planets locked in a coorbital non-coplanar motion, comparing the results with the restricted ...three-body problem. The analytical average model replicates the numerical N-body integrations, even for moderate eccentricities (≲0.3) and inclinations (≲10°), except for the regions corresponding to quasi-satellite and Lidov–Kozai configurations. Furthermore, this model is also useful in the restricted three-body problem, assuming a very low mass ratio between the planets. We also describe a four-degree-of-freedom semi-analytical model valid for any type of coorbital configuration in a wide range of eccentricities and inclinations. Using an N-body integrator, we have found that the phase space of the general three-body problem is different to the restricted case for an inclined system, and we establish the location of the Lidov–Kozai equilibrium configurations depending on the mass ratio. We study the stability of periodic orbits in the inclined systems, and find that apart from the robust configurations, L4, AL4 and QS, it is possible to HARBOUR two Earth-like planets in orbits previously identified as unstable (U) and also in Euler L3 configurations, with bounded chaos.
Satellite systems around giant planets are immersed in a region of complex resonant configurations. Understanding the role of satellite resonances contributes to comprehending the dynamical processes ...in planetary formation and posterior evolution. Our main goal is to analyse the resonant structure of small moons around Uranus and propose different scenarios able to describe the current configuration of these satellites. We focus our study on the external members of the regular satellites interior to Miranda, namely Rosalind, Cupid, Belinda, Perdita, Puck, and Mab, respectively. We use N-body integrations to perform dynamical maps to analyse their dynamics and proximity to two-body and three-body mean-motion resonances (MMR). We found a complicated web of low-order resonances amongst them. Employing analytical prescriptions, we analysed the evolution by gas drag and type-I migration in a circumplanetary disc (CPD) to explain different possible histories for these moons. We also model the tidal evolution of these satellites using some crude approximations and found possible paths that could lead to MMRs crossing between pairs of moons. Finally, our simulations show that each mechanism can generate significant satellite radial drift leading to possible resonant capture, depending on the distances and sizes.
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DOBA, EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, IZUM, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UILJ, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
6.
Dynamics of two planets in co-orbital motion Giuppone, C. A.; Beaugé, C.; Michtchenko, T. A. ...
Monthly Notices of the Royal Astronomical Society,
September 2010, Volume:
407, Issue:
1
Journal Article
Peer reviewed
Open access
We study the stability regions and families of periodic orbits of two planets locked in a co-orbital configuration. We consider different ratios of planetary masses and orbital eccentricities; we ...also assume that both planets share the same orbital plane. Initially, we perform numerical simulations over a grid of osculating initial conditions to map the regions of stable/chaotic motion and identify equilibrium solutions. These results are later analysed in more detail using a semi-analytical model. Apart from the well-known quasi-satellite orbits and the classical equilibrium Lagrangian points L4 and L5, we also find a new regime of asymmetric periodic solutions. For low eccentricities these are located at (Δλ, Δϖ) = (±60°, ∓120°), where Δλ is the difference in mean longitudes and Δϖ is the difference in longitudes of pericentre. The position of these anti-Lagrangian solutions changes with the mass ratio and the orbital eccentricities and are found for eccentricities as high as ∼0.7. Finally, we also applied a slow mass variation to one of the planets and analysed its effect on an initially asymmetric periodic orbit. We found that the resonant solution is preserved as long as the mass variation is adiabatic, with practically no change in the equilibrium values of the angles.
We test a crossing orbit stability criterion for eccentric planetary systems, based on Wisdom's criterion of first-order mean motion resonance overlap. We show that this criterion fits the stability ...regions in real exoplanet systems quite well. In addition, we show that elliptical orbits can remain stable even for regions where the apocentre distance of the inner orbit is larger than the pericentre distance of the outer orbit, as long as the initial orbits are aligned. The analytical expressions provided here can be used to put rapid constraints on the stability zones of multiplanetary systems. As a byproduct of this research, we further show that the amplitude variations of the eccentricity can be used as a fast-computing stability indicator. PUBLICATION ABSTRACT
Context. The stability of satellites in the solar system is affected by the so-called evection resonance. The moons of Saturn, in particular, exhibit a complex dynamical architecture in which ...co-orbital configurations occur, especially close to the planet where this resonance is present. Aims. We address the dynamics of the evection resonance, with particular focus on the Saturn system, and compare the known behavior of the resonance for a single moon with that of a pair of moons in co-orbital Trojan configuration. Methods. We developed an analytic expansion of the averaged Hamiltonian of a Trojan pair of bodies, including the perturbation from a distant massive body. The analysis of the corresponding equilibrium points was restricted to the asymmetric apsidal corotation solution of the co-orbital dynamics. We also performed numerical N-body simulations to construct dynamical maps of the stability of the evection resonance in the Saturn system, and to study the effects of this resonance under the migration of Trojan moons caused by tidal dissipation. Results. The structure of the phase space of the evection resonance for Trojan satellites is similar to that of a single satellite, differing in that the libration centers are displaced from their standard positions by an angle that depends on the periastron difference ϖ2 −ϖ1 and on the mass ratio m2∕m1 of the Trojan pair. In the Saturn system, the inner evection resonance, located at ~8 RS, may capture a pair of Trojan moons by migration; the stability of the captured system depends on the assumed values of the dissipation factor Q of the moons. On the other hand, the outer evection resonance, located at >0.4 RHill, cannot exist at all for Trojan moons, because Trojan configurations are strongly unstable at distances from Saturn longer than ~0.15 RHill. Conclusions. The interaction with the inner evection resonance may have been relevant during the early evolution of the Saturn moons Tethys, Dione, and Rhea. In particular, Rhea may have had Trojan companions in the past that were lost when it crossed the evection resonance, while Tethys and Dione may either have retained their Trojans or have never crossed the evection. This may help to constrain the dynamical processes that led to the migration of these satellites and to the evection itself.
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We analyse the possibilities of detection of hypothetical exoplanets in co-orbital motion from synthetic radial velocity (RV) signals, taking into account different types of stable planar ...configurations, orbital eccentricities and mass ratios. For each nominal solution corresponding to small-amplitude oscillations around the periodic solution, we generate a series of synthetic RV curves mimicking the stellar motion around the barycentre of the system. We then fit the data sets obtained assuming three possible different orbital architectures: (a) two planets in co-orbital motion, (b) two planets in a 2/1 mean-motion resonance (MMR) and (c) a single planet. We compare the resulting residuals and the estimated orbital parameters.
For synthetic data sets covering only a few orbital periods, we find that the discrete RV signal generated by a co-orbital configuration could be easily confused with other configurations/systems, and in many cases the best orbital fit corresponds to either a single planet or two bodies in a 2/1 resonance. However, most of the incorrect identifications are associated with dynamically unstable solutions.
We also compare the orbital parameters obtained with two different fitting strategies: a simultaneous fit of two planets and a nested multi-Keplerian model. We find that, even for data sets covering over 10 orbital periods, the nested models can yield incorrect orbital configurations (sometimes close to fictitious MMRs) that are nevertheless dynamically stable and with orbital eccentricities lower than the correct nominal solutions.
Finally, we discuss plausible mechanisms for the formation of co-orbital configurations, by the interaction between two giant planets and an inner cavity in the gas disc. For equal-mass planets, both Lagrangian and anti-Lagrangian configurations can be obtained from same initial condition depending on final time of integration.
The HD 196885 system is composed of a binary star and a planet orbiting the primary. The orbit of the binary is fully constrained by astrometry, but for the planet the inclination with respect to the ...plane of the sky and the longitude of the node are unknown. Here we perform a full analysis of the HD 196885 system by exploring the two free parameters of the planet and choosing different sets of angular variables. We find that the most likely configurations for the planet are either nearly coplanar orbits (prograde and retrograde), or highly inclined orbits near the Lidov-Kozai equilibrium points, i = 44° or i = 137°. Among coplanar orbits, the retrograde ones appear to be less chaotic, while for the orbits near the Lidov-Kozai equilibria, those around ω = 270° are more reliable, where \hbox{$\omega_\koz$}ω is the argument of pericenter of the planet’s orbit with respect to the binary’s orbit . From the observer’s point of view (plane of the sky) stable areas are restricted to (I1,Ω1) ~ (65°,80°), (65°,260°), (115°,80°), and (115°,260°), where I1 is the inclination of the planet and Ω1 is the longitude of ascending node.
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