2/1 resonant periodic orbits in three dimensional planetary systems

Voyatzis

2013

Astrophys Space Sci

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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 chaotic evolution that destabilizes the planetary system. Stable periodic orbits are of particular importance in planetary dynamics, since they can host real planetary systems. We found stable orbits up to 60 • of mutual planetary inclination, but in most families, the stability does not exceed 20 • -30 • , depending on the planetary mass ratio. Most of these orbits are very eccentric. Stable inclined circular orbits or orbits of low eccentricity were found in the 4/3 and 5/2 resonance, respectively.keywords Extrasolar planets, general three body problem, mean motion resonances, periodic orbits, planetary systems.

Section: Introductionmentioning

confidence: 99%

Resonant periodic orbits in the exoplanetary systems

Voyatzis

2013

Astrophys Space Sci

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“…8, we observe that the orbital elements evolve regularly around their initial values (23), while the resonant angles, θ 1 , ∆ and θ 2 librate around the angles 0…”

Section: Hd 45364mentioning

confidence: 84%

Regular and chaotic orbits in the dynamics of exoplanets

Eur. Phys. J. Spec. Top.

2016

Many of exoplanetary systems consist of more than one planet and the study of planetary orbits with respect to their long-term stability is very interesting. Furthermore, many exoplanets seem to be locked in a meanmotion resonance (MMR), which offers a phase protection mechanism, so that, even highly eccentric planets can avoid close encounters. However, the present estimation of their initial conditions, which may change significantly after obtaining additional observational data in the future, locate most of the systems in chaotic regions and consequently, they are destabilized. Hence, dynamical analysis is imperative for the derivation of proper planetary orbital elements. We utilize the model of spatial general three body problem, in order to simulate such resonant systems through the computation of families periodic orbits. In this way, we can figure out regions in phase space, where the planets in resonances should be ideally hosted in favour of long-term stability and therefore, survival. In this review, we summarize our methodology and showcase the fact that stable resonant planetary systems evolve being exactly centered at stable periodic orbits.

“…Hereafter, we follow the notation of Antoniadou & Voyatzis (2013, and denote the spatial families of xzsymmetric periodic orbits by F , where p+q p is the MMR. N stands either for the configuration ((θ1, θ2), (θ3, θ1) or (θ4, θ1)) of the planar family in the 2D-ERTBP or for the name of the planar family, either the circular family or the family of the 2D-CRTBP from which they emanate, accordingly.…”

Section: Methods IImentioning

confidence: 99%

“…Firstly, additional spatial families can exist, such as spatial isolated families of symmetric periodic orbits (see e.g. Antoniadou & Voyatzis 2013, for an illustration of spatial isolated families in the 3D-GTBP in Fig. 22) or families of spatial asymmetric periodic orbits.…”

Section: Asteroid Dynamicsmentioning

confidence: 99%

Spatial resonant periodic orbits in the restricted three-body problem

Monthly Notices of the Royal Astronomical Society

Libert

2018

The quest of exo-Earths has become a prominent field. In this work, we study the stability of non-coplanar planetary configurations consisting of an inclined inner terrestrial planet in mean-motion resonance with an outer giant planet. We examine the families of circular and elliptic symmetric periodic orbits with respect to the vertical stability, and identify the vertical critical orbits from which the spatial families emanate. We showcase that stable spatial periodic orbits can exist for both prograde and retrograde motion in 3/2, 2/1, 5/2, 3/1, 4/1 and 5/1 resonances for broad ranges of inclinations, when the giant evolves on a circular orbit. When the orbit of the giant is elliptic, only the 2/1 resonance has stable periodic orbits up to high inclinations, while the 3/1, 4/1 and 5/1 resonances possess segments of stability for low inclinations. Furthermore, we show that regular motion can also take place in the vicinity of both horizontally and vertically stable planar periodic orbits, even for very high inclinations. Finally, the results are discussed in the context of asteroid dynamics.