50 research outputs found
Coupling between corotation and Lindblad resonances in the elliptic planar three-body problem
We investigate the dynamics of two satellites with masses and
orbiting a massive central planet in a common plane, near a first
order mean motion resonance +1: ( integer). We consider only the
resonant terms of first order in eccentricity in the disturbing potential of
the satellites, plus the secular terms causing the orbital apsidal precessions.
We obtain a two-degree of freedom system, associated with the two critical
resonant angles and , where and are the mean
longitude and longitude of periapsis of , respectively, and where the
primed quantities apply to . We consider the special case where (restricted problem). The symmetry between the two angles
and is then broken, leading to two different kinds of resonances,
classically referred to as Corotation Eccentric resonance (CER) and Lindblad
Eccentric Resonance (LER), respectively. We write the four reduced equations of
motion near the CER and LER, that form what we call the CoraLin model. This
model depends upon only two dimensionless parameters that control the dynamics
of the system: the distance between the CER and LER, and a forcing
parameter that includes both the mass and the orbital eccentricity
of the disturbing satellite. Three regimes are found: for the system is
integrable, for of order unity, it exhibits prominent chaotic regions,
while for large compared to 2, the behavior of the system is regular and
can be qualitatively described using simple adiabatic invariant arguments. We
apply this model to three recently discovered small Saturnian satellites
dynamically linked to Mimas through first order mean motion resonances :
Aegaeon, Methone and Anthe
The dynamics of rings around Centaurs and Trans-Neptunian Objects
Since 2013, dense and narrow rings are known around the small Centaur object
Chariklo and the dwarf planet Haumea. Dense material has also been detected
around the Centaur Chiron, although its nature is debated. This is the first
time ever that rings are observed elsewhere than around the giant planets,
suggesting that those features are more common than previously thought. The
origins of those rings remain unclear. In particular, it is not known if the
same generic process can explain the presence of material around Chariklo,
Chiron, Haumea, or if each object has a very different history. Nonetheless, a
specific aspect of small bodies is that they may possess a non-axisymmetric
shape (topographic features and or elongation) that are essentially absent in
giant planets. This creates strong resonances between the spin rate of the
object and the mean motion of ring particles. In particular, Lindblad-type
resonances tend to clear the region around the corotation (or synchronous)
orbit, where the particles orbital period matches that of the body. Whatever
the origin of the ring is, modest topographic features or elongations of
Chariklo and Haumea explain why their rings should be found beyond the
outermost 1/2 resonance, where the particles complete one revolution while the
body completes two rotations. Comparison of the resonant locations relative to
the Roche limit of the body shows that fast rotators are favored for being
surrounded by rings. We discuss in more details the phase portraits of the 1/2
and 1/3 resonances, and the consequences of a ring presence on satellite
formation.Comment: Chapter to be published in the book "The Transneptunian Solar
System", Dina Prialnik, Maria Antonietta Barucci, Leslie Young Eds. Elsevie
Cupid Is Not Doomed Yet: On the Stability of the Inner Moons of Uranus
Some of the small inner moons of Uranus have very closely-spaced orbits.
Multiple numerical studies have found that the moons Cressida and Desdemona,
within the Portia sub-group, are likely to collide in less than 100 Myr. The
subsequent discovery of three new moons (Cupid, Perdita, and Mab) made the
system even more crowded. In particular, it has been suggested that the Belinda
group (Cupid, Belinda, and Perdita) will become unstable in as little as 10
years. Here we revisit the issue of the stability of the inner moons of Uranus
using updated orbital elements and considering tidal dissipation. We find that
the Belinda group can be stable on -year timescales due to an orbital
resonance between Belinda and Perdita. We find that tidal evolution cannot form
the Belinda-Perdita resonance, but convergent migration could contribute to the
long-term instability of the Portia group. We propose that Belinda captured
Perdita into the resonance during the last episode of disruption and
re-accretion among the inner moons, possibly hundreds of Myr ago.Comment: 11 pages, 4 figures, accepted for A
Influence of the coorbital resonance on the rotation of the Trojan satellites of Saturn
The Cassini spacecraft collects high resolution images of the saturnian
satellites and reveals the surface of these new worlds. The shape and rotation
of the satellites can be determined from the Cassini Imaging Science Subsystem
data, employing limb coordinates and stereogrammetric control points. This is
the case for Epimetheus (Tiscareno et al. 2009) that opens elaboration of new
rotational models (Tiscareno et al. 2009; Noyelles 2010; Robutel et al. 2011).
Especially, Epimetheus is characterized by its horseshoe shape orbit and the
presence of the swap is essential to introduce explicitly into rotational
models. During its journey in the saturnian system, Cassini spacecraft
accumulates the observational data of the other satellites and it will be
possible to determine the rotational parameters of several of them. To prepare
these future observations, we built rotational models of the coorbital (also
called Trojan) satellites Telesto, Calypso, Helene, and Polydeuces, in addition
to Janus and Epimetheus. Indeed, Telesto and Calypso orbit around the L_4 and
L_5 Lagrange points of Saturn-Tethys while Helene and Polydeuces are coorbital
of Dione. The goal of this study is to understand how the departure from the
Keplerian motion induced by the perturbations of the coorbital body, influences
the rotation of these satellites. To this aim, we introduce explicitly the
perturbation in the rotational equations by using the formalism developed by
Erdi (1977) to represent the coorbital motions, and so we describe the
rotational motion of the coorbitals, Janus and Epimetheus included, in compact
form
Dynamique des petits satellites de Saturne
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