Long-term evolution of the Galilean satellites: the capture of Callisto into resonance

Lari, Giacomo; Saillenfest, Melaine; Fenucci, Marco

doi:10.1051/0004-6361/202037445

Cited by 25 publications

(50 citation statements)

References 68 publications

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“…4 for the two extreme values of λ considered in this article, as well as for the value of λ ≈ 0.2365 proposed by Ward & Canup (2006). Despite the various outcomes of the dynamics described by Lari et al (2020), the result on the evolution of α is almost undistinguishable from one of their simulations to another, even if the eccentricities of the satellites are taken into account in Eq. (5).…”

Section: Precession Constantmentioning

confidence: 65%

“…(5). Indeed, the variation of α mostly depends on the drift of the satellites' semi-major axes, which is almost identical in every simulation of Lari et al (2020).…”

Section: Precession Constantmentioning

confidence: 87%

“…Here, instead of relying on one particular value of λ, we turn to the exploration of the whole range of values given in the literature, namely λ ∈ [0.220, 0.265]. The rotation velocity of Jupiter is taken from Archinal et al (2018) and the other physical parameters are fixed to those used by Lari et al (2020) for consistency with the satellites' orbital evolution (see below). The corresponding value for the current precession constant of Jupiter, computed from Eqs.…”

Section: Precession Constantmentioning

confidence: 99%

“…(5). This increase can be quantified using the long-term orbital solution of Lari et al (2020) depicted in Fig. 3 and interpolating between data points.…”

Section: Precession Constantmentioning

confidence: 99%

“…However, Jupiter's satellites are known to migrate over time because of tidal dissipation. The future long-term orbital evolution of the Galilean satellites has been recently explored by Lari et al (2020). The solutions that they describe can therefore be used as a guide to study the future spin-axis dynamics of Jupiter.…”

Section: Introductionmentioning

confidence: 99%

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The future large obliquity of Jupiter

Saillenfest

Lari

Courtot

2020

A&A

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Aims. We aim to determine whether Jupiter’s obliquity is bound to remain exceptionally small in the Solar System, or if it could grow in the future and reach values comparable to those of the other giant planets. Methods. The spin-axis of Jupiter is subject to the gravitational torques from its regular satellites and from the Sun. These torques evolve over time due to the long-term variations of its orbit and to the migration of its satellites. With numerical simulations, we explore the future evolution of Jupiter’s spin axis for different values of its moment of inertia and for different migration rates of its satellites. Analytical formulas show the location and properties of all relevant resonances. Results. Because of the migration of the Galilean satellites, Jupiter’s obliquity is currently increasing, as it adiabatically follows the drift of a secular spin-orbit resonance with the nodal precession mode of Uranus. Using the current estimates of the migration rate of the satellites, the obliquity of Jupiter can reach values ranging from 6° to 37° after 5 Gyr from now, according to the precise value of its polar moment of inertia. A faster migration for the satellites would produce a larger increase in obliquity, as long as the drift remains adiabatic. Conclusions. Despite its peculiarly small current value, the obliquity of Jupiter is no different from other obliquities in the Solar System: It is equally sensitive to secular spin-orbit resonances and it will probably reach comparable values in the future.

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Section: Precession Constantmentioning

confidence: 65%

“…(5). Indeed, the variation of α mostly depends on the drift of the satellites' semi-major axes, which is almost identical in every simulation of Lari et al (2020).…”

Section: Precession Constantmentioning

confidence: 87%

Section: Precession Constantmentioning

confidence: 99%

“…(5). This increase can be quantified using the long-term orbital solution of Lari et al (2020) depicted in Fig. 3 and interpolating between data points.…”

Section: Precession Constantmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The future large obliquity of Jupiter

Saillenfest

Lari

Courtot

2020

A&A

Self Cite

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Normal forms for the Laplace resonance

Pucacco

2021

Celest Mech Dyn Astr

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We describe a comprehensive model for systems locked in the Laplace resonance. The framework is based on the simplest possible dynamical structure provided by the Keplerian problem perturbed by the resonant coupling truncated at second order in the eccentricities. The reduced Hamiltonian, constructed by a transformation to resonant coordinates, is then submitted to a suitable ordering of the terms and to the study of its equilibria. Henceforth, resonant normal forms are computed. The main result is the identification of two different classes of equilibria. In the first class, only one kind of stable equilibrium is present: the paradigmatic case is that of the Galilean system. In the second class, three kinds of stable equilibria are possible and at least one of them is characterised by a high value of the forced eccentricity for the ‘first planet’: here, the paradigmatic case is the exo-planetary system GJ-876, in which the combination of libration centres admits triple conjunctions otherwise not possible in the Galilean case. The normal form obtained by averaging with respect to the free eccentricity oscillations describes the libration of the Laplace argument for arbitrary amplitudes and allows us to determine the libration width of the resonance. The agreement of the analytic predictions with the numerical integration of the toy models is very good.

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The nature of the Laplace resonance between the Galilean moons

Lari,

Saillenfest

2024

Celest Mech Dyn Astron

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The Laplace resonance is a mean-motion resonance that involves the three inner Galilean moons of Jupiter. However, its true nature is in part unclear; in particular, different views can be found in the literature on whether the Laplace resonance is a pure three-body resonance or a mere superposition of two-body resonances. To settle this question, we conduct a thorough analysis of the many resonances involved, starting from the two-body 2:1 commensurabilities of the couples Io–Europa and Europa–Ganymede, and ending with the three-body 4:2:1 commensurability between the three moons. By artificially varying the parameters of the system and monitoring its fundamental frequencies, we cartography all resonances involved and their interactions. From the analysis of the individual 2:1 commensurabilities, we find that despite the oscillation of the resonant angles they are not genuine resonances, as the trajectory of the system in the phase space is not enclosed by separatrices. On the contrary, as suggested by previous works, we show that the only current true mean-motion resonance is the pure three-body resonance between all three satellites. Moreover, we find that the current values of the moons’ orbital elements make the Laplace resonance sufficiently separated from the individual two-body 2:1 resonances, preventing chaotic effects from appearing.

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Long-term evolution of the Galilean satellites: the capture of Callisto into resonance

Cited by 25 publications

References 68 publications

The future large obliquity of Jupiter

The future large obliquity of Jupiter

Normal forms for the Laplace resonance

The nature of the Laplace resonance between the Galilean moons

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