Complexity of Capture Phenomena in the Conservative and the Dissipative Restricted Three-Body Problems

Cordeiro, R. R.; Martins, R. Vieira; Leonel, Edson D.

doi:10.1086/300764

Cited by 7 publications

(5 citation statements)

References 15 publications

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“…In general, gravitational capture is studied in the framework of the restricted three-body problem, with numerical simulations. The complexity of this problem can be seen in Cordeiro, Viera Martins, & Leonel (1999). However, a precise deÐnition of gravitational capture has not been well established.…”

Section: Introductionmentioning

confidence: 99%

Time Analysis for Temporary Gravitational Capture: Satellites of Uranus

Neto

Winter²

2001

The Astronomical Journal

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We study the problem of gravitational capture in the framework of the Sun-Uranus-particle system. Part of the space of initial conditions is systematically explored, and the duration of temporary gravitational capture is measured. The location and size of di †erent capture-time regions are given in terms of diagrams of initial semimajor axis versus eccentricity. The other initial orbital elementsÈinclination (i), longitude of the node ()), argument of pericenter (u), and time of pericenter passage (q)Èare Ðrst taken to be zero. Then we investigate the cases with u \ 90¡, 180¡, and 270¡. We also present a sample of results for) \ 90¡, considering the cases i \ 60¡, 120¡, 150¡, and 180¡. Special attention is given to the inÑuence of the initial orbital inclination, taking orbits initially in opposition at pericenter. In this case, the initial inclination is varied from 0¡ to 180¡ in steps of 10¡. The success of the Ðnal stage of the capture problem, which involves the transformation of temporary captures into permanent ones, is highly dependent on the initial conditions associated with the longest capture times. The largest regions of the initial-conditions space with the longest capture times occur at inclinations of 60¡È70¡ and 160¡. The regions of possible stability as a function of initial inclination are also delimited. These regions include not only a known set of retrograde orbits, but also a new sort of prograde orbit with inclinations greater than zero.

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Section: Introductionmentioning

confidence: 99%

Time Analysis for Temporary Gravitational Capture: Satellites of Uranus

Neto

Winter²

2001

The Astronomical Journal

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“…the central star) are present (e.g. Cordeiro et al 1999;Araujo et al 2008). Our system is of course more complicated because additional gravitational perturbations arise from the gas disk.…”

Section: Gravitationally Bound Pairs Of Embryosmentioning

confidence: 99%

Binary Planet Formation by Gas-assisted Encounters of Planetary Embryos

Chrenko

Brož

Nesvorný

2018

ApJ

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We present radiation hydrodynamic simulations in which binary planets form by close encounters in a system of several super-Earth embryos. The embryos are embedded in a protoplanetary disk consisting of gas and pebbles and evolve in a region where the disk structure supports convergent migration due to Type I torques. As the embryos accrete pebbles, they become heated and thus affected by the thermal torque (Benítez-Llambay et al. 2015) and the hot-trail effect (Chrenko et al. 2017) which excites orbital eccentricities. Motivated by findings of Eklund & Masset (2017), we assume the hot-trail effect operates also vertically and reduces the efficiency of inclination damping. Non-zero inclinations allow the embryos to become closely packed and also vertically stirred within the convergence zone. Subsequently, close encounters of two embryos assisted by the disk gravity can form transient binary planets which quickly dissolve. Binary planets with a longer lifetime ∼10 4 yr form in 3-body interactions of a transient pair with one of the remaining embryos. The separation of binary components generally decreases in subsequent encounters and due to pebble accretion until the binary merges, forming a giant planet core. We provide an order-of-magnitude estimate of the expected occurrence rate of binary planets, yielding one binary planet per ≃2-5 × 10 4 planetary systems. Therefore, although rare, the binary planets may exist in exoplanetary systems and they should be systematically searched for.

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“…When combined with some dissipative mechanisms, the temporary capture can become permanent. The dissipative mechanisms can be gas drag (e.g., Hunten 1979;Pollack et al 1979;Cordeiro et al 1999;Vieira Neto et al 2009), a gradual increase in the mass of the central planet (e.g., Heppenheimer & Porco 1977;Vieira Neto et al 2004), and collisions (e.g., Colombo & Franklin 1971). The capture can also become permanent when a binary asteroid system encounters a planet, in which case one of the bodies is permanently attached to the planet and the other escapes due to the exchange of orbital energies (e.g., Agnor & Hamilton 2006).…”

Section: Introductionmentioning

confidence: 99%

“…In such a case, the dynamics are usually chaotic. Murison (1989) and Cordeiro et al (1999) pointed out the complexity of the capture process in the circular restricted three-body problem (hereafter referred to as CRTBP), since the capture structure in the phase space is partially fractal-like and self-similar. Researchers therefore generally prefer to use numerical methods to study the capture process, and usually make some reasonable assumptions to simplify the situation and reduce the computational difficulty.…”

Section: Introductionmentioning

confidence: 99%

Capture Efficiency Analysis in the Circular Restricted Three-body Problem

Miao,

Hou

2024

Res. Astron. Astrophys.

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The temporary capture problem of massless particles around the secondary is studied in the circular restricted three-body problem. The gravitational influence of the secondary on the orbit distribution of the particles is taken into account by means of a numerical iterative process. A relatively steady state of the orbital element distribution of the particles is used to compute the capture efficiency. Our study finds that the final computed result is influenced by the circumsphere around the secondary, and a way is proposed to determine the size of the circumsphere. Two methods of computing the capture efficiency are used and compared, and consistent results are obtained. When the mass ratio μ is 3.0035 × 10-6 (which is the same as in the Sun-Earth system), a recommended value of the circumsphere size is 6 Hill Radii of the secondary, and the computed capture efficiency is ∼ 1.54 × 10-4. The influence of the mass parameter of the secondary on the capture efficiency is also investigated and a power-law relationship between the capture efficiency p and the mass ratio μ holds as p ≈ 0.14 × μ0.52, when 3.0035 × 10−6 ≤ μ ≤ 3.0034 × 10−5. The current study can be extended to more realistic force models and may help us understand the temporary capture of natural bodies by the major celestial bodies in our solar system (e.g. the Sun-Earth system).

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Complexity of Capture Phenomena in the Conservative and the Dissipative Restricted Three-Body Problems

Cited by 7 publications

References 15 publications

Time Analysis for Temporary Gravitational Capture: Satellites of Uranus

Time Analysis for Temporary Gravitational Capture: Satellites of Uranus

Binary Planet Formation by Gas-assisted Encounters of Planetary Embryos

Capture Efficiency Analysis in the Circular Restricted Three-body Problem

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