Numerical Results on a Simple Model for the Confinement of Saturn’s F Ring

Benet, Luis; Jorba, Àngel

doi:10.1007/978-3-642-38830-9_5

Cited by 1 publication

(4 citation statements)

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“…The last observation confirms the naive expectation that only the most stable particles will remain trapped, in the sense that their radial excursions are strongly limited (Benet and Jorba, 2013;Cuzzi et al, 2014). While this statement may sound trivial, we emphasize that the Hamiltonian ( 2) is explicitly time-dependent, and its time dependence reflects the dynamics of the N -body Hamiltonian.…”

Section: Initial Conditions and Trapped Orbitssupporting

confidence: 81%

“…We consider a simplified planar restricted five-body model and follow the dynamics of a large number of test particles (∼ 2.5 millions) up to 6×10 6 orbital revolutions of Prometheus, slightly more than 10000 years. The model includes the gravitational field of Saturn with its second gravitational harmonic J 2 , Prometheus, Pandora and Titan; preliminary results appear in (Benet and Jorba, 2013). We find a broad set of test-particle initial conditions that remain trapped within the region between Prometheus and Pandora.…”

Section: Introductionmentioning

confidence: 86%

“…The starting point of our model (Benet and Jorba, 2013) is to consider the motion of an ensemble of non-interacting massless test particles, defined by the initial conditions which are in the proximity of the location of the F ring. Their time evolution shall determine whether a test particle remains (dynamically) trapped and hence belongs to the ring, or if it simply escapes away.…”

Section: A Simplified Model For Saturn's F Ring: the Scattering Approachmentioning

confidence: 99%

“…That is, Titan does not confine the trapped test particles to a narrow region in a, where a (narrow) ring could be located and compared with the observations. The fact that Titan promotes more extended radial excursions without clearing out efficiently (in a short-time scale) the region between the shepherds motivates to explore the stability properties of the motion of the test particles (Benet and Jorba, 2013). We shall do so considering a variation of the frequency analysis (Laskar, 1990).…”

Section: Initial Conditions and Trapped Orbitsmentioning

confidence: 99%

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A simple model for the location of Saturn’s F ring

Benet

Jorba

2017

Icarus

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In this paper, we introduce a simplified model to understand the location of Saturn's F ring. The model is a planar restricted five-body problem defined by the gravitational field of Saturn, including its second zonal harmonic J 2 , the shepherd moons Prometheus and Pandora, and Titan. We compute accurate long-time numerical integrations of (about 2.5 million) non-interacting test-particles initially located in the region between the orbits of Prometheus and Pandora, and address whether they escape or remain trapped in this region. We obtain a wide region of initial conditions of the test particles that remain confined. We consider a dynamical stability indicator for the test particles' motion defined by computing the ratio of the standard deviation over the average value of relevant dynamical quantities, in particular, for the mean-motion and the semi-major axis. This indicator separates clearly a subset of trapped initial conditions that appear as very localized stripes in the initial semi-major axis and eccentricity space for the most stable orbits. Retaining only these test particles, we obtain a narrow eccentric ring which displays sharp edges and collective alignment. The semi-major axis of the accumulation stripes of the stable ring-particles can be associated with resonances, mostly involving Prometheus' outer Lindblad and co-rotation resonances, but not exclusively. Pandora's inner Lindblad and co-rotation resonances as well as low-order three-body resonances typically coincide with gaps, i.e., regions of instabilities.

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Section: Initial Conditions and Trapped Orbitssupporting

confidence: 81%

Section: Introductionmentioning

confidence: 86%

Section: A Simplified Model For Saturn's F Ring: the Scattering Approachmentioning

confidence: 99%

Section: Initial Conditions and Trapped Orbitsmentioning

confidence: 99%

See 2 more Smart Citations