Exchange orbits in the planar <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si60.gif" display="inline" overflow="scroll"><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mn>4</mml:mn></mml:math> body problem

Bengochea, Abimael; Galán, J.; Pérez‐Chavela, Ernesto

doi:10.1016/j.physd.2015.03.006

Cited by 10 publications

(5 citation statements)

References 21 publications

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“…Bengochea, Galán & Pérez-Chavela 2015). Few-or many-body co-orbital dynamics may also be informed by the periodic orbits of the N = 3 case (Hadjidemetriou, Psychoyos & Voyatzis 2009;Hadjidemetriou & Voyatzis 2011;Antoniadou, Voyatzis & Varvoglis 2014).…”

Section: O -O R B I Ta L Dy Na M I C Smentioning

confidence: 99%

“…Effectively, the case N > 3 requires numerical simulations unless the system in question can be linked to central configurations (Moeckel 1994;Renner & Sicardy 2004), a multi-body hierarchical restricted problem -which can be expressed entirely in terms of orbital element equations of motion - (Veras 2014a), or specialised symmetric cases (e.g. Bengochea et al 2015). Few-or many-body co-orbital dynamics may also be informed by the periodic orbits of the N = 3 case (Hadjidemetriou et al 2009;Hadjidemetriou & Voyatzis 2011;Antoniadou et al 2014).…”

Section: Co-orbital Dynamicsmentioning

confidence: 99%

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Dynamical mass and multiplicity constraints on co-orbital bodies around stars

Veras

Marsh

Gänsicke

2016

Mon. Not. R. Astron. Soc.

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Objects transiting near or within the disruption radius of both main-sequence (e.g. KOI 1843) and white dwarf (WD 1145+017) stars are now known. Upon fragmentation or disintegration, these planets or asteroids may produce co-orbital configurations of nearly equal mass objects. However, as evidenced by the co-orbital objects detected by transit photometry in the WD 1145+017 system, these bodies are largely unconstrained in size, mass, and total number (multiplicity). Motivated by potential future similar discoveries, we perform N-body simulations to demonstrate if and how debris masses and multiplicity may be bounded due to second-to-minute deviations and the resulting accumulated phase shifts in the osculating orbital period amongst multiple co-orbital equal point masses. We establish robust lower and upper mass bounds as a function of orbital period deviation, but find the constraints on multiplicity to be weak. We also quantify the fuzzy instability boundary, and show that mutual collisions occur in less than 5, 10, and 20 per cent of our simulations for masses of 10 21 , 10 22 , and 10 23 kg. Our results may provide useful initial rough constraints on other stellar systems with multiple co-orbital bodies.

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Section: O -O R B I Ta L Dy Na M I C Smentioning

confidence: 99%

Section: Co-orbital Dynamicsmentioning

confidence: 99%

Dynamical mass and multiplicity constraints on co-orbital bodies around stars

Veras

Marsh

Gänsicke

2016

Mon. Not. R. Astron. Soc.

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“…3. Reversing symmetries and periodic orbits The reversing symmetries [13,15] have been used successfully for studying the periodic orbits of problems described by differential equations [1,2,11,19,20]. In the following we give a brief review of some useful results.…”

Section: Equations Of Motionmentioning

confidence: 99%

A restricted four-body problem for the eight figure choreography

Lara,

Bengochea

2019

Preprint

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In this work we introduce a planar restricted four-body problem where a massless particle moves under the gravitational influence due to three bodies following the eight figure choreography, and we explore some symmetric periodic orbits of this system which turns out to be non autonomous. We demonstrate that certain families of involutions are reversing symmetries of certain N -body problem. We consider a particular case of such families of reversing symmetries and we use it to study both theoretically and numerically certain type of symmetric periodic orbits of this system. The symmetric periodic orbits (initial conditions) were determined by means of solving some boundary value problems.

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“…1). Technics of reversibility have been successfully applied for studying periodic orbits of ordinary differential equations [18]; see [4,5,12,25] for the case of the N -body problem. For more details on reversibility technics, the interested reader is referred to [19], where comet and moon orbits have been computed numerically for three primary bodies following the eight choreography.…”

Section: Introductionmentioning

confidence: 99%

Comet and moon solutions in the time-dependent restricted $(n+1)$-body problem

Barrera¹,

Bengochea²,

García-Azpeitia³

2020

Preprint

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The time-dependent restricted (n + 1)-body problem concerns the study of a massless body (satellite) under the influence of the gravitational field generated by n primary bodies following a periodic solution of the n-body problem. We prove that the satellite has periodic solutions close to the large-amplitude circular orbits of the Kepler problem (comet solutions), and in the case that the primaries are in a relative equilibrium, close to small-amplitude circular orbits near a primary body (moon solutions). The comet and moon solutions are constructed with the application of a Lyapunov-Schmidt reduction to the action functional. In addition, using reversibility technics, we compute numerically the comet and moon solutions for the case of four primaries following the super-eight choreography.

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Exchange orbits in the planar 1+4 body problem

Cited by 10 publications

References 21 publications

Dynamical mass and multiplicity constraints on co-orbital bodies around stars

Dynamical mass and multiplicity constraints on co-orbital bodies around stars

A restricted four-body problem for the eight figure choreography

Comet and moon solutions in the time-dependent restricted $(n+1)$-body problem

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