Chaotic motions of prometheus and pandora

Goldreich, Peter; Rappaport, N. J.

doi:10.1016/s0019-1035(02)00080-5

Cited by 37 publications

(25 citation statements)

References 15 publications

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“…The F ring is between the orbits of these two moons. However, the interaction terms between these moons have a significant effect on their orbits as recent observations and simulations show (see Goldreich and Rapporport [3]). …”

Section: Analysis Of the Moons Of Saturnmentioning

confidence: 93%

Coorbital Periodic Orbits in the Three Body Problem

Cors

Hall²

2003

SIAM J. Appl. Dyn. Syst.

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Abstract. We consider the dynamics of coorbital motion of two small moons about a large planet which have nearly circular orbits with almost equal radii. These moons avoid collision because they switch orbits during each close encounter. We approach the problem as a perturbation of decoupled Kepler problems as in Poincaré's periodic orbits of the first kind. The perturbation is large but only in a small region in the phase space. We discuss the relationship required among the small quantities (radial separation, mass, and minimum angular separation). Persistence of the orbits is discussed.

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Section: Analysis Of the Moons Of Saturnmentioning

confidence: 93%

Coorbital Periodic Orbits in the Three Body Problem

Cors

Hall²

2003

SIAM J. Appl. Dyn. Syst.

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“…For some small solar system bodies, such as Prometheus and Pandora (Goldreich & Rappaport 2003a, 2003bFarmer & Goldreich 2006), the orbital variations are dominated by mutual interactions between a single pair of moons. At the other extreme are systems where all the small bodies are dynamically linked, like the convoy of resonant planetesimals formed near the edge of a proto-planetary disk in simulations by Ogihara et al (2010).…”

Section: Orbital Variations Caused By Mutual Gravitational Interactionsmentioning

confidence: 99%

“…Lyapunov times have been computed for a variety of solar system bodies. Goldreich & Rappaport (2003a) calculated a Lyapunov time of about 3 yr for Prometheus and Pandora, accounting for the discrepancy between positions of those moons in the 1995 HST images and their predicted positions based on 1980 Voyager measurements. These results have been independently confirmed using a later set of Cassini observations (Cooper et al 2015).…”

Section: The Timescale Of Chaosmentioning

confidence: 99%

“…An important source of chaotic orbital behavior for planetary bodies is resonance overlap, the mechanism that clears out the Kirkwood Gaps in the asteroid belt (Wisdom 1982), destabilizes the outer planets (Murray & Holman 1999) and Mercury (Batygin & Laughlin 2008), perturbs Saturn's moons Prometheus and Pandora (Poulet & Sicardy 2001;Goldreich & Rappaport 2003a, 2003bCooper & Murray 2004;Farmer & Goldreich 2006;Cooper et al 2015) and Jupiter's Metis and Adrastea (Cooper 2004), and causes rapid chaos in the Kepler-36 exoplanetary system (Deck et al 2012). Overlap can occur between/among multiple components of a single two-satellite resonance, two or more resonances between a pair of satellites, or resonances between multiple pairs.…”

Section: Introductionmentioning

confidence: 99%

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Resonances, Chaos, and Short-Term Interactions Among the Inner Uranian Satellites

French

Dawson

Showalter

2015

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The Portia group of Uranian satellites, representing 9 of the planet's 13 tiny innermost moons, form a densely packed dynamical system. Hubble Space Telescope observations indicate that their orbits have changed significantly over two decades, and long-term numerical integrations show that their orbits are unstable over millions of years. To investigate the dynamical interactions of the Portia group satellites on the decade timescale over which orbital changes have been observed, we have performed a suite of 100-1000 yr N-body numerical integrations for a range of assumed satellite masses, which are at present not tightly constrained by observations. :114), and Belinda and Perdita (88:86)), some of which result in quite strongly coupled variations in the inclinations of the interacting satellites. Using a robust formulation of orbital elements that accounts for the oblateness of Uranus, we probe the dynamical interactions among the moons in the time and frequency domains, and also in phase space, using numerical integrations of subsets of the inner moons, for a range of assumed masses. Several of the satellites are near meanmotion resonance with more than one neighbor, and undergo orbital variations at two nearly equal resonant frequencies. Such configurations of two interlinked resonances can result in chaotic behavior, associated with the transition of one resonant argument from circulation to libration. We demonstrate that, even on the short timescales investigated here, the dynamical interactions, onset of chaos, and associated Lyapunov times are highly sensitive to the masses of the interacting satellites.

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“…The Lyapunov time of the orbital motion in satellite systems has been estimated so far only for the Prometheus-Pandora system (the 16th and the 17th satellites of Saturn): Goldreich and Rappaport (2003) obtained numerical estimates for the Lyapunov time of the orbital motion in the vicinity of the 121 : 118 meanmotion orbital resonance in this system. According to the results of Goldreich and Rappaport (2003), the Lyapunov time is ≈ 3.3 years.…”

Section: Introductionmentioning

confidence: 99%

Chaotic Dynamics of Satellite Systems

Melnikov

Shevchenko

2005

Sol Syst Res

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We consider the problem of calculating the Lyapunov time (the characteristic time of predictable dynamics) of chaotic motion in the vicinity of separatrices of orbital resonances in satellite systems. The primary objects of study are the chaotic regimes that have occurred in the history of the orbital dynamics of the second and fifth Uranian satellites (Umbriel and Miranda) and the first and third Saturnian satellites (Mimas and Tethys). We study the dynamics in the vicinity of separatrices of the resonance multiplets corresponding to the 3 : 1 commensurability of mean motions of Miranda and Umbriel and the multiplets corresponding to the 2 : 1 commensurability of mean motions of Mimas and Tethys. These chaotic regimes have most probably contributed much to the long-term orbital evolution of the two satellite systems. The equations of motion have been numerically integrated to estimate the Lyapunov time in models corresponding to various epochs of the system evolution. Analytical estimates of the Lyapunov time have been obtained by a method (Shevchenko, 2002) based on the separatrix map theory. The analytical estimates have been compared to estimates obtained by direct numerical integration.

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Chaotic motions of prometheus and pandora

Cited by 37 publications

References 15 publications

Coorbital Periodic Orbits in the Three Body Problem

Coorbital Periodic Orbits in the Three Body Problem

Resonances, Chaos, and Short-Term Interactions Among the Inner Uranian Satellites

Chaotic Dynamics of Satellite Systems

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