A celestial-mechanical model for the tidal evolution of the Earth-Moon system treated as a double planet

Zlenko, A. A.

doi:10.1134/s1063772915010096

Cited by 18 publications

(4 citation statements)

References 21 publications

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“…There are several simplified tide models which are not explicitly parameterized by Love numbers (see, for instance Mignard (1979), Efroimsky and Williams (2009), Zlenko (2014), Celletti (1990), Antognini et al (2014), Bambusi and Haus (2015), Ferraz-Mello (2013), Correia et al (2014), Boué et al (2016), Wisdom and Meyer (2016), Ragazzo and Ruiz (2015), Ragazzo and Ruiz (2017)), two of them will be important in this paper: the first presented in Boué et al (2016) after previous work in Ferraz-Mello (2013) and Correia et al (2014), and the second presented in Ragazzo and Ruiz (2017) after previous work in Ragazzo and Ruiz (2015).…”

Section: Introductionmentioning

confidence: 99%

The effects of deformation inertia (kinetic energy) in the orbital and spin evolution of close-in bodies

Correia

Ragazzo

Ruiz

2018

Celest Mech Dyn Astr

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The purpose of this work is to evaluate the effect of deformation inertia on tide dynamics, particularly within the context of the tide response equations proposed independently by Boué et al (2016) and Ragazzo and Ruiz (2017). The singular limit as the inertia tends to zero is analysed and equations for the small inertia regime are proposed. The analysis of Love numbers shows that, independently of the rheology, deformation inertia can be neglected if the tide forcing-frequency is much smaller than the frequency of small oscillations of an ideal body made of a perfect (inviscid) fluid with the same inertial and gravitational properties of the original body. Finally, numerical integration of the full set of equations, which couples tide, spin and orbit, is used to evaluate the effect of inertia on the overall motion. The results are consistent with those obtained from the Love number analysis. The conclusion is that, from the point of view of orbital evolution of celestial bodies, deformation inertia can be safely neglected (exceptions may occur when a higher order harmonic of the tide-forcing has a high amplitude).

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Section: Introductionmentioning

confidence: 99%

The effects of deformation inertia (kinetic energy) in the orbital and spin evolution of close-in bodies

Correia

Ragazzo

Ruiz

2018

Celest Mech Dyn Astr

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“…This is more evident in the study of two-body systems, which we will pursue in a future work. Finally, due to its Lagrangian formulation our model can be used as a building block in the study of many-body systems without any further assumptions (compare to the study of a planar two body system in Zlenko (2015). (1 + λ) −2 − (1 + λ) −1 dλTr (B 2 ) = 8 15 γ Tr (B 2 ).…”

Section: Theorem 5 Suppose That the Zero Solution Of (55) Is Stable mentioning

confidence: 99%

Dynamics of an isolated, viscoelastic, self-gravitating body

Ragazzo

Ruiz

2015

Celest Mech Dyn Astr

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This paper is devoted to an alternative model for a rotating, isolated, selfgravitating, viscoelastic body. The initial approach is quite similar to the classical one, present in the works of Dirichlet, Riemann, Chandrasekhar, among others. Our main contribution is to present a simplified model for the motion of an almost spherical body. The Lagrangian function L and the dissipation function D of the simplified model are:where ω is the angular velocity vector, Q is the quadrupole moment tensor, I = I • Id − Q/3 is the usual moment of inertia tensor with I • equal to the moment of inertia of the spherical body at rest, γ is an elastic constant, and ν is a damping coefficient. The angular momentum Iω transformed to an inertial reference frame is conserved. The constants γ and ν must be determined experimentally. We believe this to be the simplest model one can get without loosing the symmetries and the conserved quantities of the original problem. This model can be used as a building block for the study of many-body planetary systems.

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“…The dynamics of satellites and space debris in external resonances focus on the 1:2, 1:3, and 2:3 resonances by the Hamiltonian approach. Zlenko (2015) [30] has determined a celestial-mechanical model for the tidal evolution of the Earth-Moon system of two viscoelastic spheres in the gravitational field using the Kelvin-Voigt model. Gallardo et al (2016) [10] have investigated three-body mean motion resonances for planetary and satellite by the semi-analytical method.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of Resonant Curves of Earth-Moon system under the influence of Resistive Force using Unperturbed Solution

Yadav

Kumar

Aggarwal

et al. 2023

Preprint

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This work investigates the dynamical behavior of the resonant curves in the motion of the Earth-Moon system under the influence of resistive force. In this study, the resonance arises in this motion due to the rate of change of Earth’s equatorial ellipticity (EEE) (˙ γ), the Moon’s angular velocity (˙ θmo) around the Earth, and angular velocity of barycenter (˙ α0) around the Sun, including the coefficient of resistive force (b). The configuration and equations of motion are expressed in a spherical coordinate system using the Earth’s potential. Applying the unperturbed solution reduces and simplifies the system into a second-order ODE and obtains a particular solution. It is observe that the commensurability occur between the frequencies: (i) ˙ γ and ˙ θm0, (ii) ˙ θm0 and ˙ α0 with the coefficient of resistive force. Finally, we analyze the dynamical behavior of the resonant curves for the orbital elements and the coefficient of resistive force.

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A celestial-mechanical model for the tidal evolution of the Earth-Moon system treated as a double planet

Cited by 18 publications

References 21 publications

The effects of deformation inertia (kinetic energy) in the orbital and spin evolution of close-in bodies

The effects of deformation inertia (kinetic energy) in the orbital and spin evolution of close-in bodies

Dynamics of an isolated, viscoelastic, self-gravitating body

Dynamics of Resonant Curves of Earth-Moon system under the influence of Resistive Force using Unperturbed Solution

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