Secular evolution of the orbits of hypothetical satellites of Uranus

Vashkov’yak, M. A.

doi:10.1134/s0038094616060046

Cited by 4 publications

(8 citation statements)

References 5 publications

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“…As mentioned above, the TPQ approximation can successfully describe the evolution for a verity of test particle systems in the solar system. For example, it was used to explain the inclinations of gas giant satellites and Jovian irregular satellites (e.g., Kinoshita and Nakai 1991;Vashkov'yak 1999;Carruba et al 2002;Nesvorný et al 2003;Ćuk and Burns 2004;Kinoshita and Nakai 2007). Furthermore, the importance of secular interactions for the dynamics of comets and other test particles in the solar system was noted in several studies (e.g., Kozai 1979;Quinn et al 1990;Bailey et al 1992;Thomas and Morbidelli 1996;Duncan and Levison 1997;Gronchi and Milani 1999;Gomes et al 2005;Tamayo et al 2013).…”

Section: Figure 18mentioning

confidence: 99%

The Eccentric Kozai-Lidov Effect and Its Applications

Naoz

2016

Annu. Rev. Astron. Astrophys.

694

564

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The hierarchical triple body approximation has useful applications to a variety of systems from planetary and stellar scales to supermassive black holes. In this approximation, the energy of each orbit is separately conserved and therefore the two semi-major axes are constants. On timescales much larger than the orbital periods, the orbits exchange angular momentum which leads to eccentricity and orientation (i.e., inclination) oscillations. The orbits' eccentricity can reach extreme values leading to a nearly radial motion, which can further evolve into short orbit periods and merging binaries. Furthermore, the orbits' mutual inclination may change dramatically from pure prograde to pure retrograde leading to misalignment and a wide range of inclinations. This dynamical behavior is coined as the "eccentric Kozai-Lidov" mechanism. The behavior of such a system is exciting, rich and chaotic in nature. Furthermore, these dynamics are accessible from a large part of the triple body parameter space and can be applied to diverse range of astrophysical settings and used to gain insights to many puzzles.Comment: 60 pages 25 figures, to appear in Annual Review of Astronomy and Astrophysics, comments welcom

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Section: Figure 18mentioning

confidence: 99%

The Eccentric Kozai-Lidov Effect and Its Applications

Naoz

2016

Annu. Rev. Astron. Astrophys.

694

564

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“…Explicit formulae describing the evolution of osculating elements in terms of elliptic functions can be found in (Gordeeva 1968;Kinoshita and Nakai 2007;Vashkovyak 1999) for both types of the KL cycles. Studying the EKL effect, we shall deal only with the relations characterising the rotating cycles.…”

Section: The Kozai-lidov Hamiltonianmentioning

confidence: 99%

“…The formulae ( 5) and ( 6) can be obtained from the related expressions for periods Tg = 2π/ng and T h = 2π/ |n h | , presented in (Vashkovyak 1999). The reader, who wants to check it, must take into account that our choice of the unit of time differs from (Vashkovyak 1999) by a factor 3/16 .…”

Section: The Kozai-lidov Hamiltonianmentioning

confidence: 99%

“…Formulae determining the change in eccentricity in KL-cycles are given in (Gordeeva 1968;Vashkovyak 1999). In our notation the formula for the rotating cycles takes the form:…”

Section: Appendix a Evolution Of The Laplace Vector In Rotating Kl-cy...mentioning

confidence: 99%

“…The importance of the Kozai-Lidov effect follows from its universality. Various celestial bodies provide examples of this effect in their orbital motion: asteroids (Froeschle et al 1991;Vashkovyak 1986), satellites of the giant planets (Nesvorny et al 2003;Vashkovyak 1999Vashkovyak , 2003, triple stars (Eggleton and Kiseleva-Eggleton 2001;Harrington 1968), and even black holes (Blaes et al 2002;Wen 2003). A special role is given to the Kozai-Lidov effect in various scenarios describing the formation of the dynamical architecture of exoplanetary systems (Innanen et al 1997;Libert and Henrard 2007).…”

Section: Dedicated To the Loving Memory Of Lyudmila 1 Introductionmentioning

confidence: 99%

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The eccentric Kozai–Lidov effect as a resonance phenomenon

Сидоренко

2017

Celest Mech Dyn Astr

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Exploring weakly perturbed Keplerian motion within the restricted three-body problem, Lidov (1962) and, independently, Kozai (1962 discovered coupled oscillations of eccentricity and inclination (the KL-cycles). Their classical studies were based on an integrable model of the secular evolution, obtained by double averaging of the disturbing function approximated with its first non-trivial term. This was the quadrupole term in the series expansion with respect to the ratio of the semimajor axis of the disturbed body to that of the disturbing body. If the next (octupole) term is kept in the expression for the disturbing function, long-term modulation of the KL-cycles can established (Ford et al. 2000;Katz et al. 2011). Specifically, flips between the prograde and retrograde orbits become possible. Since such flips are observed only when the perturber has a non-zero eccentricity, the term "Eccentric Kozai-Lidov Effect" (or EKL-effect) was proposed by Lithwick and Naoz (2011) to specify such behaviour. We demonstrate that the EKL-effect can be interpreted as a resonance phenomenon. To this end, we write down the equations of motion in terms of "action-angle" variables emerging in the integrable Kozai-Lidov model. It turns out that for some initial values the resonance is degenerate and the usual "pendulum" approximation is insufficient to describe the evolution of the resonance phase. Analysis of the related bifurcations allows us to estimate the typical time between the successive flips for different parts of the phase space.

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The evolution of the orbits of the planetary satellites

Emel'Yanov¹

2021

The Dynamics of Natural Satellites of the Planets

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Secular evolution of the orbits of hypothetical satellites of Uranus

Cited by 4 publications

References 5 publications

The Eccentric Kozai-Lidov Effect and Its Applications

The Eccentric Kozai-Lidov Effect and Its Applications

The eccentric Kozai–Lidov effect as a resonance phenomenon

The evolution of the orbits of the planetary satellites

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