The small and large lags of the elastic and anelastic tides. The virtual identity of two rheophysical theories

The aim of this letter is to discuss the virtual identity of two recent tidal theories: the creep tide theory of Ferraz-Mello (Cel. Mech. Dyn. Astron. 116, 109, 2013) and the Maxwell model developed by Correia et al. (Astron. Astrophys. 571, A50, 2014). It includes the discussion of the basic equations of the theories, which, in both cases, include an elastic and an anelastic component, and shows that the basic equations of the two theories are equivalent and differ by only a numerical factor in the anelastic tide. It also includes a discussion of the lags: the lag of the full tide (geodetic), dominated by the elastic component, and the phase of the anelastic tide. In rotating rocky bodies not trapped in a spin-orbit resonance (e.g., the Earth) the geodetic lag is close to zero and the phase of the semi-diurnal argument in the anelastic tide is close to 90 degrees. The results obtained from combining tidal solutions from satellite tracking data and from Topex/Poseidon satellite altimeter data, by Ray et al., are extended to determine the phase of the semi-diurnal argument in the Earth's anelastic tide as sigma_0=89.80 \pm 0.05 degrees.Comment: Accepted for publication in Astronomy and Astrophysic

On Tides and Exoplanets

This paper reviews the basic equations used in the study of the tidal variations of the rotational and orbital elements of a system formed by one star and one close-in planet as given by the creep tide theory and Darwin's constant time lag (CTL) theory. At the end, it reviews and discusses the determinations of the relaxation factors (and time lags) in the case of host stars and hot Jupiters based on actual observations of orbital decay, stellar rotation and age, etc. It also includes a recollection of the basic facts concerning the variations of the rotation of host stars due to the leakage of angular momentum associated with stellar winds.Comment: 4 figures, IAU Symposium No. 36

Formation and transformation of the 3:1 mean-motion resonance in 55 Cancri System

We report in this paper the numerical simulations of the capture into the 3:1 mean-motion resonance between the planet b and c in the 55 Cancri system. The results show that this resonance can be obtained by a differential planetary migration. The moderate initial eccentricities, relatively slower migration and suitable eccentricity damping rate increase significantly the probability of being trapped in this resonance. Otherwise, the system crosses the 3:1 commensurability avoiding resonance capture, to be eventually captured into a 2:1 resonance or some other higher-order resonances. After the resonance capture, the system could jump from one orbital configuration to another one if the migration continues, making a large region of the configuration space accessible for a resonance system. These investigations help us understand the diversity of resonance configurations and put some constrains on the early dynamical evolution of orbits in the extra-solar planetary systems.Comment: 6 pages with 2 figures. Submitted for publication in the proceedings of IAU Symposium No.249. A paper telling much more details than this paper is under preparin

Chirikov diffusion in the asteroidal three-body resonance (5, −2, −2)

The theory of diffusion in many-dimensional Hamiltonian system is applied to asteroidal dynamics. The general formulation developed by Chirikov is applied to the Nesvorný-Morbidelli analytic model of three-body (three-orbit) mean-motion resonances (Jupiter-Saturn-asteroid). In particular, we investigate the diffusion along and across the separatrices of the (5, −2, −2) resonance of the (490) Veritas asteroidal family and their relationship to diffusion in semi-major axis and eccentricity. The estimations of diffusion were obtained using the Melnikov integral, a Hadjidemetriou-type sympletic map and numerical integrations for times up to 108 years.Facultad de Ciencias Astronómicas y GeofísicasInstituto de Astrofísica de La Plat

Chirikov diffusion in the asteroidal three-body resonance (5, −2, −2)

The theory of diffusion in many-dimensional Hamiltonian system is applied to asteroidal dynamics. The general formulation developed by Chirikov is applied to the Nesvorný-Morbidelli analytic model of three-body (three-orbit) mean-motion resonances (Jupiter-Saturn-asteroid). In particular, we investigate the diffusion along and across the separatrices of the (5, −2, −2) resonance of the (490) Veritas asteroidal family and their relationship to diffusion in semi-major axis and eccentricity. The estimations of diffusion were obtained using the Melnikov integral, a Hadjidemetriou-type sympletic map and numerical integrations for times up to 108 years.Facultad de Ciencias Astronómicas y GeofísicasInstituto de Astrofísica de La Plat