arXiv subjects

Hugo A. Folonier

Publications and source records attributed to Hugo A. Folonier.

5 recordsLinked to original sources

arXiv2022

Creep tide theory. Equations for differentiated bodies with aligned layers

The creep tide theory is used to establish the basic equations of the tidal evolution of differentiated bodies formed by aligned homogeneous layers in co-rotation. The mass concentration of the body is given by the fluid Love number $k_f$. The formulas are given by series expansions valid for high eccentricity systems. They are equivalent to Darwin's equations, but formally more compact. An application to the case of Enceladus, with $k_f=0.942$, is discussed.

astro-ph.EP↗

arXiv2021

Ellipsoidal equilibrium figure and Cassini states of rotating planets and satellites deformed by a tidal potential in the spatial case

The equilibrium figure of an inviscid tidally deformed body is the starting point for the construction of many tidal theories such as Darwinian tidal theories or the hydrodynamical Creep tide theory. This paper presents the ellipsoidal equilibrium figure when the spin rate vector of the deformed body is not perpendicular to the plane of motion of the companion. We obtain the equatorial and the polar flattenings as functions of the Jeans and the Maclaurin flattenings, and of the angle $θ$ between the spin rate vector and the radius vector. The equatorial vertex of the equilibrium ellipsoid does not point toward the companion, which produces a torque perpendicular to the rotation vector, which introduces terms of precession and nutation. We find that the direction of spin may differ significantly from the direction of the principal axis of inertia $C$, so the classical approximation $\mathsf{I}\vecω\approx C\vecω$ only makes sense in the neighborhood of the planar problem. We also study the so-called Cassini states. Neglecting the short-period terms in the differential equation for the spin direction and assuming a uniform precession of the line of the orbital ascending node, we obtain the same differential equation as that found by Colombo (1966). That is, a tidally deformed inviscid body has exactly the same Cassini states as a rotating axisymmetric rigid body, the tidal bulge having no secular effect at first order.

astro-ph.EP↗

arXiv2019

Rotation and figure evolution in the creep tide theory. A new approach and application to Mercury

This paper deals with the rotation and figure evolution of a planet near the 3/2 spin-orbit resonance and the exploration of a new formulation of the creep tide theory (Folonier et al. 2018). This new formulation is composed by a system of differential equations for the figure and the rotation of the body simultaneously (which is the same system of equations used in Folonier et al. 2018), different from the original one (Ferraz-Mello, 2013, 2015a) in which rotation and figure were considered separately. The time evolution of the figure of the body is studied for both the 3/2 and 2/1 spin-orbit resonances. Moreover, we provide a method to determine the relaxation factor gamma of non-rigid homogeneous bodies whose endpoint of rotational evolution from tidal interactions is the 3/2 spin-orbit resonance, provided that (i) an initially faster rotation is assumed and (ii) no permanent components of the flattenings of the body existed at the time of the capture in the 3/2 spin-orbit resonance. The method is applied to Mercury, since it is currently trapped in a 3/2 spin-orbit resonance with its orbital motion and we obtain 4.8 times 10 -8 s -1 lower than gamma lower than 4.8 times 10 -9 s -1 . The equatorial prolateness and polar oblateness coefficients obtained for Mercury's figure with such range of values of gamma are the same as the ones given by the Darwin-Kaula model (Matsuyama and Nimmo 2009). However, comparing the values of the flattenings obtained for such range of gamma with those obtained from MESSENGER's measurements (Perry et al. 2015), we see that the current values for Mercury's equatorial prolateness and polar oblateness are 2-3 orders of magnitude larger than the values given by the tidal theories.

astro-ph.EP↗

arXiv2019

Tidal synchronization of close-in satellites and exoplanets. III. Tidal dissipation revisited and application to Enceladus

This paper deals with a new formulation of the creep tide theory (Ferraz-Mello, Cel. Mech. Dyn. Astron. {\bf 116}, 109, 2013 $-$ Paper I) and with the tidal dissipation predicted by the theory in the case of stiff bodies whose rotation is not synchronous but is oscillating around the synchronous state with a period equal to the orbital period. We show that the tidally forced libration influences the amount of energy dissipated in the body and the average perturbation of the orbital elements. This influence depends on the libration amplitude and is generally neglected in the study of planetary satellites. However, they may be responsible for a 27 percent increase in the dissipation of Enceladus. The relaxation factor necessary to explain the observed dissipation of Enceladus ($γ=1.2-3.8\times 10^{-7}\ {\rm s}^{-1}$) has the expected order of magnitude for planetary satellites and corresponds to the viscosity $0.6-1.9 \times 10^{14}$ Pa s, which is in reasonable agreement with the value recently estimated by Efroimsky (2018) ($0.24 \times 10^{14}$ Pa s) and with the value adopted by Roberts and Nimmo (2008) for the viscosity of the ice shell ($10^{13}-10^{14}$ Pa s). For comparison purposes, the results are extended also to the case of Mimas and are consistent with the negligible dissipation and the absence of observed tectonic activity. The corrections of some mistakes and typos of paper II (Ferraz-Mello, Cel. Mech. Dyn. Astron. {\bf 122}, 359, 2015) are included at the end of the paper.

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arXiv2017

Tidal synchronization of an anelastic multi-layered body: Titan's synchronous rotation

This paper presents one analytical tidal theory for a viscoelastic multi-layered body with an arbitrary number of homogeneous layers. Starting with the static equilibrium figure, modified to include tide and differential rotation, and using the Newtonian creep approach, we find the dynamical equilibrium figure of the deformed body, which allows us to calculate the tidal potential and the forces acting on the tide generating body, as well as the rotation and orbital elements variations. In the particular case of the two-layer model, we study the tidal synchronization when the gravitational coupling and the friction in the interface between the layers is added. For high relaxation factors (low viscosity), the stationary solution of each layer is synchronous with the orbital mean motion (n) when the orbit is circular, but the spin rates increase if the orbital eccentricity increases. For low relaxation factors (high viscosity), as in planetary satellites, if friction remains low, each layer can be trapped in different spin-orbit resonances with frequencies n/2,n,3n/2,... . We apply the theory to Titan. The main results are: i) the rotational constraint does not allow us confirm or reject the existence of a subsurface ocean in Titan; and ii) the crust-atmosphere exchange of angular momentum can be neglected. Using the rotation estimate based on Cassini's observation, we limit the possible value of the shell relaxation factor, when a subsurface ocean is assumed, to 10^-9 Hz, which correspond to a shell's viscosity 10^18 Pa s, depending on the ocean's thickness and viscosity values. In the case in which the ocean does not exist, the maximum shell relaxation factor is one order of magnitude smaller and the corresponding minimum shell's viscosity is one order higher.

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