Planar retrograde periodic orbits of the asteroids trapped in two–body mean motion resonances with Jupiter

Kotoulas, Thomas; Voyatzis, George

doi:10.1016/j.pss.2020.104846

Cited by 20 publications

(16 citation statements)

References 29 publications

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“…In practice, strictly planar systems do not exist hence we do not expect to find real systems in resonant configurations which are vertically unstable. The 2/-1 resonance at Jupiter to Sun mass ratio was also studied in the ER3BP by Kotoulas & Voyatzis (2020b). Our results are in agreement regarding the fixed point point families at in Figure 8 (a).…”

Section: Masssupporting

confidence: 86%

“…According to these works, the 𝜙 0 = 0 is present at nearly all values of 𝑒 in agreement with our results (purple regions at 𝑒 𝑝 = 0 on right and left hand sides of Figure 8 (a)), while the 𝜙 0 = 𝜋 exists from 𝑒 > 0.6 in the planar problem when 𝑒 𝑝 = 0. This latter family does not appear in Figure 8 (b) because it is vertically unstable (Kotoulas & Voyatzis 2020b). As we integrate the 3D equations of motion, our problem is not strictly 2D and therefore we do not recover vertically unstable families.…”

Section: Massmentioning

confidence: 97%

“…The 2/-1 resonance at Jupiter to Sun mass ratio in the CR3BP was studied in Morais & Namouni (2016a) and Kotoulas & Voyatzis (2020b). According to these works, the 𝜙 0 = 0 is present at nearly all values of 𝑒 in agreement with our results (purple regions at 𝑒 𝑝 = 0 on right and left hand sides of Figure 8 (a)), while the 𝜙 0 = 𝜋 exists from 𝑒 > 0.6 in the planar problem when 𝑒 𝑝 = 0.…”

Section: Massmentioning

confidence: 99%

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A numerical study of the 1/2, 2/1, and 1/1 retrograde mean motion resonances in planetary systems

Caritá

Signor

Morais

2022

Monthly Notices of the Royal Astronomical Society

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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 correspond to the libration of either a single resonant argument or all resonant arguments (fixed points). We compare the results obtained in the elliptic restricted 3-body problem with previous results in the literature and we show the differences and similarities between the phase space topology for these retrograde resonances in the circular restricted, elliptic restricted and planetary 3-body problems.

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Section: Masssupporting

confidence: 86%

Section: Massmentioning

confidence: 97%

Section: Massmentioning

confidence: 99%

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A numerical study of the 1/2, 2/1, and 1/1 retrograde mean motion resonances in planetary systems

Caritá

Signor

Morais

2022

Monthly Notices of the Royal Astronomical Society

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“…Examples of planar direct orbits of the CRTBP in internal MMRs can be found in Hadjidemetriou (1993a); Hadjidemetriou & Voyatzis (2000); , while planar retrograde orbits in the exterior MMRs were systematically computed by Kotoulas & Voyatzis (2020).…”

Section: A2 the Perturbed Case (µ > 0)mentioning

confidence: 99%

Bridges and gaps at low-eccentricity first-order resonances

Antoniadou,

Libert

2021

Preprint

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Previous works on the divergence of first-order mean-motion resonances (MMRs) have studied in detail the extent of the pericentric and apocentric libration zones of adjacent first-order MMRs, highlighting possible bridges between them in the low-eccentricity circular restricted three-body problem. Here, we describe the previous results in the context of periodic orbits and show that the so-called circular family of periodic orbits is the path that can drive the passage between neighbouring resonances under dissipative effects. We illustrate that the circular family can bridge first and higher order resonances while its gaps at first-order MMRs can serve as boundaries that stop transitions between resonances. In particular, for the Sun-asteroid-Jupiter problem, we show that, during the migration of Jupiter in the protoplanetary disc, a system initially evolving below the apocentric branch of a first-order MMR follows the circular family and can either be captured into the pericentric branch of an adjacent first-order MMR if the orbital migration is rapid or in a higher order MMR in case of slow migration. Radial transport via the circular family can be extended to many small body and planetary system configurations undergoing dissipative effects (e.g., tidal dissipation, solar mass-loss and gas drag).

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“…Morais & Namouni (2019) computed for the 1st time the families of stable POs for the planar retrograde 1/1 resonance and obtained the spatial families which bifurcate from them. Subsequently, Kotoulas & Voyatzis (2020a) computed the families of planar POs for interior retrograde resonances with Jupiter (i.e. with semimajor axis smaller than the planet's) and more recently the same authors computed the families of 3-dimensional symmetric POs for the exterior 1/2, 2/3 and 3/4 resonances with Neptune (i.e.…”

Section: Introductionmentioning

confidence: 99%

A study of the 1/2 retrograde resonance: Periodic orbits and resonant capture

Morais,

Namouni,

Voyatzis

et al. 2021

Preprint

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We describe the families of periodic orbits in the 2-dimensional 1/2 retrograde resonance at mass ratio 10 −3 , analyzing their stability and bifurcations into 3-dimensional periodic orbits. We explain the role played by periodic orbits in adiabatic resonance capture, in particular how the proximity between a stable family and an unstable family with a nearly critical segment, associated with Kozai separatrices, determines the transition between distinct resonant modes observed in numerical simulations. Combining the identification of stable, critical and unstable periodic orbits with analytical modeling, resonance capture simulations and computation of stability maps helps to unveil the complex 3-dimensional structure of resonances.

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Planar retrograde periodic orbits of the asteroids trapped in two–body mean motion resonances with Jupiter

Cited by 20 publications

References 29 publications

A numerical study of the 1/2, 2/1, and 1/1 retrograde mean motion resonances in planetary systems

A numerical study of the 1/2, 2/1, and 1/1 retrograde mean motion resonances in planetary systems

Bridges and gaps at low-eccentricity first-order resonances

A study of the 1/2 retrograde resonance: Periodic orbits and resonant capture

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