Peculiarities of Uranus’s satellite system

Vashkov’yak, M. A.; Teslenko, N. M.

doi:10.1134/1.1505729

Cited by 6 publications

(2 citation statements)

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“…The secular dynamics of binaries presented in this paper have been investigated thoroughly by other authors in the LK (Γ = 1) limit (the 'test particle quadrupole' LK problem). In particular, Vashkov'yak (1999) and Kinoshita & Nakai (2007) derived analytically the maximum and minimum eccentricities and the timescale of LK oscillations. Antognini (2015) rederived the same results and provided an approximate fitting formula for the timescale.…”

Section: Relation To Previous Workmentioning

confidence: 99%

Secular dynamics of binaries in stellar clusters – II. Dynamical evolution

Hamilton

Rafikov

2019

Monthly Notices of the Royal Astronomical Society

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Dense stellar clusters are natural sites for the origin and evolution of exotic objects such as relativistic binaries (potential gravitational wave sources), blue stragglers, etc. We investigate the secular dynamics of a binary system driven by the global tidal field of an axisymmetric stellar cluster in which the binary orbits. In a companion paper (Hamilton & Rafikov 2019a) we developed a general Hamiltonian framework describing such systems. The effective (doublyaveraged) Hamiltonian derived there encapsulates all information about the tidal potential experienced by the binary in its orbit around the cluster in a single parameter Γ. Here we provide a thorough exploration of the phase-space of the corresponding secular problem as Γ is varied. We find that for Γ > 1/5 the phase-space structure and the evolution of binary orbital elements are qualitatively similar to the Lidov-Kozai problem. However, this is only one of four possible regimes, because the dynamics are qualitatively changed by bifurcations at Γ = 1/5, 0, −1/5. We show how the dynamics are altered in each regime and calculate characteristics such as secular evolution timescale, maximum possible eccentricity, etc. We verify the predictions of our doubly-averaged formalism numerically and find it to be very accurate when its underlying assumptions are fulfilled, typically meaning that the secular timescale should exceed the period of the binary around the cluster by 10 − 10 2 (depending on the cluster potential and binary orbit). Our results may be relevant for understanding the nature of a variety of exotic systems harboured by stellar clusters.1 To sufficient accuracy, the binary's barycentre follows the trajectory of a test particle, d 2 Rg/dt 2 = −∇Φ where Φ is the smooth cluster potential.

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Section: Relation To Previous Workmentioning

confidence: 99%

Secular dynamics of binaries in stellar clusters – II. Dynamical evolution

Hamilton

Rafikov

2019

Monthly Notices of the Royal Astronomical Society

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“…Lidov & Yarskaya (1974) tabulate and explore the integrable cases in the problem. Kudielka (1994) and Vashkov'yak (1996) built on these works and discovered solutions where most or all of the orbital elements remained stationary. However, they limited their analysis to low obliquities, applicable to the Earth-Moon system.…”

Section: Introductionmentioning

confidence: 99%

Dynamical Instabilities in High-Obliquity Systems

Tamayo

Burns

Hamilton

et al. 2013

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High-inclination circumplanetary orbits that are gravitationally perturbed by the central star can undergo Kozai oscillations-large-amplitude, coupled variations in the orbital eccentricity and inclination. We first study how this effect is modified by incorporating perturbations from the planetary oblateness. Tremaine et al. (2009) found that, for planets with obliquities > 68.875 • , orbits in the equilibrium local Laplace plane are unstable to eccentricity perturbations over a finite radial range, and execute large-amplitude chaotic oscillations in eccentricity and inclination. In the hope of making that treatment more easily understandable, we analyze the problem using orbital elements, confirming this threshold obliquity. Furthermore, we find that orbits inclined to the Laplace plane will be unstable over a broader radial range, and that such orbits can go unstable for obliquities less than 68.875 • . Finally, we analyze the added effects of radiation pressure, which are important for dust grains and provide a natural mechanism for particle semimajor axes to sweep via Poynting-Robertson drag through any unstable range. We find that generally the effect persists; however, the unstable radial range is shifted and small retrograde particles can avoid the instability altogether. We argue that this is occurs because radiation pressure modifies the equilibrium Laplace plane.Subject headings: celestial mechanics-planets and satellites: dynamical evolution and stability

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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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Peculiarities of Uranus’s satellite system

Cited by 6 publications

References 1 publication

Secular dynamics of binaries in stellar clusters – II. Dynamical evolution

Secular dynamics of binaries in stellar clusters – II. Dynamical evolution

Dynamical Instabilities in High-Obliquity Systems

The evolution of the orbits of the planetary satellites

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