scholarly journals An integrable model for first-order three-planet mean motion resonances

2021 ◽  
Vol 133 (8) ◽  
Author(s):  
Antoine C. Petit
Keyword(s):  
Integrable Model ◽  
Degree Of Freedom ◽  
Mass Ratio ◽  
Zeroth Order ◽  
Mean Motion Resonances ◽  
First Order ◽  
Mean Motion ◽  
Formation And Evolution ◽  
The Stability ◽  
Three Body

AbstractRecent works on three-planet mean motion resonances (MMRs) have highlighted their importance for understanding the details of the dynamics of planet formation and evolution. While the dynamics of two-planet MMRs are well understood and approximately described by a one-degree-of-freedom Hamiltonian, little is known of the exact dynamics of three-body resonances besides the cases of zeroth-order MMRs or when one of the bodies is a test particle. In this work, I propose the first general integrable model for first-order three-planet mean motion resonances. I show that one can generalize the strategy proposed in the two-planet case to obtain a one-degree-of-freedom Hamiltonian. The dynamics of these resonances are governed by the second fundamental model of resonance. The model is valid for any mass ratio between the planets and for every first-order resonance. I show the agreement of the analytical model with numerical simulations. As examples of application, I show how this model could improve our understanding of the capture into MMRs as well as their role in the stability of planetary systems.

scholarly journals Survivability of moon systems around ejected gas giants

2018 ◽  
Vol 489 (2) ◽  
pp. 2323-2329
Author(s):  
Ian Rabago ◽  
Jason H Steffen
Keyword(s):  
Large Fraction ◽  
Giant Planets ◽  
The Moon ◽  
Orbital Elements ◽  
Mean Motion Resonances ◽  
Mean Motion ◽  
Subsurface Ocean ◽  
Gas Giant ◽  
The Stability ◽  
Three Body

ABSTRACT We examine the effects that planetary encounters have on the moon systems of ejected gas giant planets. We conduct a suite of numerical simulations of planetary systems containing three Jupiter-mass planets (with the innermost planet at 3 au) up to the point where a planet is ejected from the system. The ejected planet has an initial system of 100 test-particle moons. We determine the survival probability of moons at different distances from their host planet, measure the final distribution of orbital elements, examine the stability of resonant configurations, and characterize the properties of moons that are stripped from the planets. We find that moons are likely to survive in orbits with semi-major axes out beyond 200 planetary radii (0.1 au in our case). The orbital inclinations and eccentricities of the surviving moons are broadly distributed and include nearly hyperbolic orbits and retrograde orbits. We find that a large fraction of moons in two-body and three-body mean-motion resonances also survive planetary ejection with the resonance intact. The moon–planet interactions, especially in the presence of mean-motion resonance, can keep the interior of the moons molten for billions of years via tidal flexing, as is seen in the moons of the gas giant planets in the solar system. Given the possibility that life may exist in the subsurface ocean of the Galilean satellite Europa, these results have implications for life on the moons of rogue planets – planets that drift through our Galaxy with no host star.

scholarly journals Dynamical interactions in the planetary system GJ4276

2019 ◽  
Vol 490 (2) ◽  
pp. 2732-2739
Author(s):  
Fergus Horrobin ◽  
Hanno Rein
Keyword(s):  
Planetary System ◽  
Stable Region ◽  
Mean Motion Resonances ◽  
Orbital Parameters ◽  
First Order ◽  
Mean Motion ◽  
The Mean ◽  
The Stability ◽  
The One ◽  
Mean Motion Resonance

ABSTRACT GJ4276 is an M4.0 dwarf star with an inferred Neptune mass planet from radial velocity (RV) observations. We re-analyse the RV data for this system and focus on the possibility of a second, super-Earth mass, planet. We compute the time-scale for fast resonant librations in the eccentricity to be $\sim \!2000 \, \mathrm{d}$. Given that the observations were taken over $700\, \mathrm{d}$, we expect to see the effect of these librations in the observations. We perform a fully dynamical fit to test this hypothesis. Similar to previous results, we determine that the data could be fit by two planets in a 2:1 mean motion resonance. However, we also find solutions near the 5:4 mean motion resonance that are not present when planet–planet interactions are ignored. Using the mean exponential growth of nearby orbits indicator, we analyse the stability of the system and find that our solutions lie in a stable region of parameter space. We also find that though out-of-resonance solutions are possible, the system favours a configuration that is in a first-order mean motion resonance. The existence of mean motion resonances has important implications in many planet formation theories. Although we do not attempt to distinguish between the one- and two-planet models in this work, in either case, the predicted orbital parameters are interesting enough to merit further study. Future observations should be able to distinguish between the different scenarios within the next 5 yr.

scholarly journals Orbital evolution of Saturn’s satellites due to the interaction between the moons and the massive rings

2020 ◽  
Vol 640 ◽  
pp. L15
Author(s):  
Ayano Nakajima ◽  
Shigeru Ida ◽  
Yota Ishigaki
Keyword(s):  
Orbital Evolution ◽  
The Self ◽  
Mean Motion Resonances ◽  
First Order ◽  
Mean Motion ◽  
Saturn’S Satellites ◽  
Orbital Configuration ◽  
Self Gravity ◽  
Spiral Arm ◽  
Orbital Migration

Context. Saturn’s mid-sized moons (satellites) have a puzzling orbital configuration with trapping in mean-motion resonances with every-other pairs (Mimas-Tethys 4:2 and Enceladus-Dione 2:1). To reproduce their current orbital configuration on the basis of a recent model of satellite formation from a hypothetical ancient massive ring, adjacent pairs must pass first-order mean-motion resonances without being trapped. Aims. The trapping could be avoided by fast orbital migration and/or excitation of the satellite’s eccentricity caused by gravitational interactions between the satellites and the rings (the disk), which are still unknown. In our research we investigate the satellite orbital evolution due to interactions with the disk through full N-body simulations. Methods. We performed global high-resolution N-body simulations of a self-gravitating particle disk interacting with a single satellite. We used N ∼ 105 particles for the disk. Gravitational forces of all the particles and their inelastic collisions are taken into account. Results. Dense short-wavelength wake structure is created by the disk self-gravity and a few global spiral arms are induced by the satellite. The self-gravity wakes regulate the orbital evolution of the satellite, which has been considered as a disk spreading mechanism, but not as a driver for the orbital evolution. Conclusions. The self-gravity wake torque to the satellite is so effective that the satellite migration is much faster than was predicted with the spiral arm torque. It provides a possible model to avoid the resonance capture of adjacent satellite pairs and establish the current orbital configuration of Saturn’s mid-sized satellites.

scholarly journals A Global Analysis of The Generalized Sitnikov Problem

1999 ◽  
Vol 172 ◽  
pp. 291-302
Author(s):  
Steven R. Chesley
Keyword(s):  
Angular Momentum ◽  
Global Analysis ◽  
Mass Ratio ◽  
Three Body Problem ◽  
Bounded Motion ◽  
Type Symmetry ◽  
The Stability ◽  
Two Parameters ◽  
Three Body ◽  
Area Preserving

AbstractThe isosceles three-body problem with Sitnikov-type symmetry has been reduced to a two-dimensional area-preserving Poincaré map depending on two parameters: the mass ratio, and the total angular momentum. The entire parameter space is explored, contrasting new results with ones obtained previously in the planar (zero angular momentum) case. The region of allowable motion is divided into subregions according to a symbolic dynamics representation. This enables a geometric description of the system based on the intersection of the images of the subregions with the preimages. The paper also describes the regions of allowable motion and bounded motion, and discusses the stability of the dominant periodic orbit.

scholarly journals The orbital stability of planets trapped in the first-order mean-motion resonances

Icarus ◽  
2012 ◽  
Vol 221 (2) ◽  
pp. 624-631 ◽  
Author(s):  
Yuji Matsumoto ◽  
Makiko Nagasawa ◽  
Shigeru Ida
Keyword(s):  
Orbital Stability ◽  
Mean Motion Resonances ◽  
First Order ◽  
Mean Motion

scholarly journals Planetary and satellite three body mean motion resonances

Icarus ◽  
2016 ◽  
Vol 274 ◽  
pp. 83-98 ◽  
Author(s):  
Tabaré Gallardo ◽  
Leonardo Coito ◽  
Luciana Badano
Keyword(s):  
Mean Motion Resonances ◽  
Mean Motion ◽  
Three Body

scholarly journals Study of the stability of the perturbed solutions of the restricted three body problem

BIBECHANA ◽  
2015 ◽  
Vol 13 ◽  
pp. 18-22
Author(s):  
MAA Khan ◽  
MR Hassan ◽  
RR Thapa
Keyword(s):  
Body Problem ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Variational Equations ◽  
First Order ◽  
Characteristic Exponents ◽  
Method Of Determination ◽  
The Stability ◽  
Three Body

In this paper we have been examined the stability of the perturbed solutions of the restricted three body problem. We have been restricted ourselves only to the first order variational equations. Our variational equations depend on the periodic solutions. Here the applications of the method of Fuchs and Floquet Proves to be complicated and hence we have been preferred Poincare's Method of determination of the characteristic exponents. With the determination of the characteristic exponents we have been abled to conclude regarding the stability of the generating solution. We have obtained that the motions are unstable in all the cases. By Poincare's implicit function theorem we have concluded that the stability would remain the same for small value of the parameter m and in all types of motion of the restricted three-body problem.BIBECHANA 13 (2016) 18-22 

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