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Understanding the behavior of Prometheus and Pandora

Farmer, Alison J. and Goldreich, Peter (2006) Understanding the behavior of Prometheus and Pandora. Icarus, 180 (2). pp. 403-411. ISSN 0019-1035. doi:10.1016/j.icarus.2005.10.005.

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We revisit the dynamics of Prometheus and Pandora, two small moons flanking Saturn's F ring. Departures of their orbits from freely precessing ellipses result from mutual interactions via their 121:118 mean motion resonance. Motions are chaotic because the resonance is split into four overlapping components. Orbital longitudes were observed to drift away from predictions based on Voyager ephemerides. A sudden jump in mean motions took place close to the time at which the orbits' apses were antialigned in 2000. Numerical integrations reproduce both the longitude drifts and the jumps. The latter have been attributed to the greater strength of interactions near apse antialignment (every 6.2 yr), and it has been assumed that this drift-jump behavior will continue indefinitely. We re-examine the dynamics of the Prometheus–Pandora system by analogy with that of a nearly adiabatic, parametric pendulum. In terms of this analogy, the current value of the action of the satellite system is close to its maximum in the chaotic zone. Consequently, at present, the two separatrix crossings per precessional cycle occur close to apse antialignment. In this state libration only occurs when the potential's amplitude is nearly maximal, and the “jumps” in mean motion arise during the short intervals of libration that separate long stretches of circulation. Because chaotic systems explore the entire region of phase space available to them, we expect that at other times the Prometheus–Pandora system would be found in states of medium or low action. In a low action state it would spend most of the time in libration, and separatrix crossings would occur near apse alignment. We predict that transitions between these different states can happen in as little as a decade. Therefore, it is incorrect to assume that sudden changes in the orbits only happen near apse antialignment.

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Additional Information:This research was supported by NASA grant PGG 344-30-55-07 and NSF grant AST 00-98301. AJF thanks the Institute for Advanced Study for its hospitality. Published article: Alison J. Farmer and Peter Goldreich (2006) Understanding the Behavior of Prometheus and Pandora. Icarus 180:403-411
Funding AgencyGrant Number
NASAPGG 344-30-55-07
NSFAST 00-98301
Subject Keywords:Orbits; Satellites of Saturn
Issue or Number:2
Record Number:CaltechAUTHORS:FARicarus06
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Official Citation:Alison J. Farmer, Peter Goldreich, Understanding the behavior of Prometheus and Pandora, Icarus, Volume 180, Issue 2, February 2006, Pages 403-411, ISSN 0019-1035, DOI: 10.1016/j.icarus.2005.10.005. (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:2442
Deposited By: Archive Administrator
Deposited On:04 Apr 2006
Last Modified:08 Nov 2021 19:48

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