Adiabatic chaos in the Prometheus-Pandora system

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Adiabatic chaos in the Prometheus-Pandora system. / Shevchenko, Ivan I.

In: Monthly Notices of the Royal Astronomical Society, Vol. 384, No. 3, 01.03.2008, p. 1211-1220.

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Author

Shevchenko, Ivan I. / Adiabatic chaos in the Prometheus-Pandora system. In: Monthly Notices of the Royal Astronomical Society. 2008 ; Vol. 384, No. 3. pp. 1211-1220.

BibTeX

@article{12b163fb3db74319aca31e1a8e961dbe,

title = "Adiabatic chaos in the Prometheus-Pandora system",

abstract = "The chaotic orbital motion of Prometheus and Pandora, the 16th and 17th satellites of Saturn, is studied. Chaos in their orbital motion, as found by Goldreich & Rappaport and Renner & Sicardy, is due to interaction of resonances in the resonance multiplet corresponding to the 121:118 commensurability of the mean motions of the satellites. It is shown rigorously that the system moves in adiabatic regime. The Lyapunov time (the 'time horizon of predictability' of the motion) is calculated analytically and compared to the available numerical-experimental estimates. For this purpose, a method of analytical estimation of the maximum Lyapunov exponent in the perturbed pendulum model of non-linear resonance is applied. The method is based on the separatrix map theory. An analytical estimate of the width of the chaotic layer is made as well, based on the same theory. The ranges of chaotic diffusion in the mean motion are shown to be almost twice as big compared to previous estimates for both satellites.",

keywords = "Celestial mechanics, Planets and satellites: individual: Saturn",

author = "Shevchenko, {Ivan I.}",

year = "2008",

month = mar,

day = "1",

doi = "10.1111/j.1365-2966.2007.12795.x",

language = "English",

volume = "384",

pages = "1211--1220",

journal = "Monthly Notices of the Royal Astronomical Society",

issn = "0035-8711",

publisher = "Wiley-Blackwell",

number = "3",

}

RIS

TY - JOUR

T1 - Adiabatic chaos in the Prometheus-Pandora system

AU - Shevchenko, Ivan I.

PY - 2008/3/1

Y1 - 2008/3/1

N2 - The chaotic orbital motion of Prometheus and Pandora, the 16th and 17th satellites of Saturn, is studied. Chaos in their orbital motion, as found by Goldreich & Rappaport and Renner & Sicardy, is due to interaction of resonances in the resonance multiplet corresponding to the 121:118 commensurability of the mean motions of the satellites. It is shown rigorously that the system moves in adiabatic regime. The Lyapunov time (the 'time horizon of predictability' of the motion) is calculated analytically and compared to the available numerical-experimental estimates. For this purpose, a method of analytical estimation of the maximum Lyapunov exponent in the perturbed pendulum model of non-linear resonance is applied. The method is based on the separatrix map theory. An analytical estimate of the width of the chaotic layer is made as well, based on the same theory. The ranges of chaotic diffusion in the mean motion are shown to be almost twice as big compared to previous estimates for both satellites.

AB - The chaotic orbital motion of Prometheus and Pandora, the 16th and 17th satellites of Saturn, is studied. Chaos in their orbital motion, as found by Goldreich & Rappaport and Renner & Sicardy, is due to interaction of resonances in the resonance multiplet corresponding to the 121:118 commensurability of the mean motions of the satellites. It is shown rigorously that the system moves in adiabatic regime. The Lyapunov time (the 'time horizon of predictability' of the motion) is calculated analytically and compared to the available numerical-experimental estimates. For this purpose, a method of analytical estimation of the maximum Lyapunov exponent in the perturbed pendulum model of non-linear resonance is applied. The method is based on the separatrix map theory. An analytical estimate of the width of the chaotic layer is made as well, based on the same theory. The ranges of chaotic diffusion in the mean motion are shown to be almost twice as big compared to previous estimates for both satellites.

KW - Celestial mechanics

KW - Planets and satellites: individual: Saturn

UR - http://www.scopus.com/inward/record.url?scp=43049135133&partnerID=8YFLogxK

U2 - 10.1111/j.1365-2966.2007.12795.x

DO - 10.1111/j.1365-2966.2007.12795.x

M3 - Article

AN - SCOPUS:43049135133

VL - 384

SP - 1211

EP - 1220

JO - Monthly Notices of the Royal Astronomical Society

JF - Monthly Notices of the Royal Astronomical Society

SN - 0035-8711

IS - 3

ER -

ID: 45988430