Tidal dissipation in the earth and planets

1968 ◽  
Vol 1 (7) ◽  
pp. 505-510 ◽  
Author(s):  
Peter L. Lagus ◽  
Don L. Anderson
Keyword(s):  
Tidal Dissipation ◽  
The Earth

scholarly journals Tidal interactions in rotating multiple stars and their impact on their evolution

2014 ◽  
Vol 9 (S307) ◽  
pp. 208-210
Author(s):  
P. Auclair-Desrotour ◽  
S. Mathis ◽  
C. Le Poncin-Lafitte
Keyword(s):  
Fluid Model ◽  
Orbital Evolution ◽  
Tidal Dissipation ◽  
Tidal Waves ◽  
Physical Mechanisms ◽  
Tidal Interactions ◽  
The Earth ◽  
Half Height ◽  
Multiple Stars ◽  
Stellar Interiors

AbstractTidal dissipation in stars is one of the key physical mechanisms that drive the evolution of binary and multiple stars. As in the Earth oceans, it corresponds to the resonant excitation of their eigenmodes of oscillation and their damping. Therefore, it strongly depends on the internal structure, rotation, and dissipative mechanisms in each component. In this work, we present a local analytical modeling of tidal gravito-inertial waves excited in stellar convective and radiative regions respectively. This model allows us to understand in details the properties of the resonant tidal dissipation as a function of the excitation frequencies, the rotation, the stratification, and the viscous and thermal properties of the studied fluid regions. Then, the frequencies, height, width at half-height, and number of resonances as well as the non-resonant equilibrium tide are derived analytically in asymptotic regimes that are relevant in stellar interiors. Finally, we demonstrate how viscous dissipation of tidal waves leads to a strongly erratic orbital evolution in the case of a coplanar binary system. We characterize such a non-regular dynamics as a function of the height and width of resonances, which have been previously characterized thanks to our local fluid model.

Geological constraints on tidal dissipation and dynamical ellipticity of the Earth over the past three million years

Nature ◽  
2001 ◽  
Vol 409 (6823) ◽  
pp. 1029-1033 ◽  
Author(s):  
Lucas J. Lourens ◽  
Rolf Wehausen ◽  
Hans J. Brumsack
Keyword(s):  
Tidal Dissipation ◽  
The Past ◽  
The Earth ◽  
Geological Constraints

scholarly journals Impact of Geophysical Fluids on UT1

2009 ◽  
Vol 5 (H15) ◽  
pp. 213-214
Author(s):  
Richard S. Gross
Keyword(s):  
Solid Earth ◽  
Secular Change ◽  
Length Of Day ◽  
Tidal Dissipation ◽  
The Earth ◽  
Fluid Core ◽  
Period Variations ◽  
Decadal Variations ◽  
Tidal Variations ◽  
Geophysical Fluids

AbstractGeophysical fluids have a major impact on the Earth's rotation. Tidal variations within the oceans are the predominant cause of subdaily length-of-day (lod) variations while those within the solid body of the Earth are a major source of longer period variations; tidal dissipation within the solid Earth and oceans cause a secular change in lod. Fluctuations of the atmospheric winds are the predominant cause of nontidal lod variations on sub-decadal time scales while decadal variations are caused by interactions between the fluid core and mantle.

Solution of the tidal equations for the M 2 and S 2 tides in the world oceans from a knowledge of the tidal potential alone

1978 ◽  
Vol 290 (1368) ◽  
pp. 235-266 ◽  
Keyword(s):  
Tidal Energy ◽  
Western Coast ◽  
Secondary Effects ◽  
Tidal Dissipation ◽  
The Earth ◽  
Tidal Potential ◽  
The Pacific ◽  
The World ◽  
Energy Incident ◽  
Tidal Loading

Laplace’s tidal equations are solved for the M 2 and S 2 tides in the world oceans on the basis of a knowledge of the tidal potential alone. Tidal dissipation was taken to be limited to the coastline, where a fraction of the tidal energy incident on the coast was assumed to be absorbed. The coast was assumed to be either vertical or to have a sloping shelf, the latter model yielding results in better agreement with observations. The main purpose of this investigation was to determine the effects of tidal self-attraction and of tidal loading. A fast iterative method was developed by which these secondary effects could be evaluated. The resulting change is of the order of 10%, and somewhat improves the agreement between the theoretical and observed tides. Tidal dissipation from the M 2 and S 2 tides totals 3.1 x 10 19 erg/s. The total retarding couple exerted by the M 2 and S 2 tides on the Earth comes out at 4.2 x 10 23 dyn cm, yielding a deceleration of the Earth’s rotation from these sources of 1080"/cy 2 . The theoretical tidal values were compared with observations on the northeastern and western coasts of the Pacific, on the western coast of the Atlantic, on New Zealand, and on islands. The theoretical tidal phases are generally within one hour of the observed values; the amplitudes are in reasonable agreement with observations except in zones where there is amplification by the fiord effect. A solution obtained for a ‘smoothed’ coastline showed little change.

scholarly journals Tidal heating and the habitability of the TRAPPIST-1 exoplanets

2019 ◽  
Vol 624 ◽  
pp. A2 ◽  
Author(s):  
Vera Dobos ◽  
Amy C. Barr ◽  
László L. Kiss
Keyword(s):  
Liquid Water ◽  
Weighted Average ◽  
Heat Fluxes ◽  
Tidal Dissipation ◽  
Water Ice ◽  
The Earth ◽  
Tidal Heating ◽  
The Masses ◽  
Viscoelastic Rheology ◽  
M Dwarf

Context. New estimates of the masses and radii of the seven planets orbiting the ultracool M-dwarf TRAPPIST-1 star permit improved modelling of their compositions, heating by tidal dissipation, and removal of tidal heat by solid-state convection. Aims. Here we compute the heat flux due to insolation and tidal heating for the inner four planets. Methods. We apply a Maxwell viscoelastic rheology to compute the tidal response of the planets using the volume-weighted average of the viscosities and rigidities of the metal, rock, high-pressure ice, and liquid water/ice I layers. Results. We show that TRAPPIST-1d and e can avoid entering a runaway greenhouse state. Planet e is the most likely to support a habitable environment, with Earth-like surface temperatures and possibly liquid water oceans. Planet d also avoids a runaway greenhouse, if its surface reflectance is at least as high as that of the Earth. Planets b and c, closer to the star, have heat fluxes high enough to trigger a runaway greenhouse and to support volcanism on the surfaces of their rock layers, rendering them too warm for life. Planets f, g, and h are too far from the star to experience significant tidal heating, and likely have solid ice surfaces with possible subsurface liquid water oceans.

Influence of some resonances on the inclination of a satellite

2020 ◽  
Author(s):  
Timothée Vaillant ◽  
Alexandre C. M. Correia
Keyword(s):  
Major Axis ◽  
The Moon ◽  
Semi Major Axis ◽  
Tidal Dissipation ◽  
The Earth ◽  
Hamiltonian Model ◽  
The Future ◽  
The Mean ◽  
Over Time ◽  
Probability Of Capture

<p align="justify">Knowing if the inclination of a satellite with respect to the equator of its planet is primordial can give hints on its origin and its formation. However, several mechanisms are able to modify its inclination during its evolution. The orbit of a satellite evolves over time and because of the tidal dissipation its semi-major axis can notably decrease or increase. Therefore the satellite can encounter several resonances in which it can potentially be captured. Some resonances are able to modify the equatorial inclination of a satellite. Touma and Wisdom (1998) noted that a resonance called ‘eviction’ between the mean motion of the Earth and the ascending node frequency of the Moon could increase by several degrees the equatorial inclination of the early Moon and could explain the present orientation of its orbit. Yokoyama (2002) studied these resonances for Phobos and Triton and observed that several resonances of this type can increase the equatorial inclination of Phobos in the future.</p> <p align="justify"> </p> <p align="justify">In this work, we study the different existing ‘eviction’ resonances to determine their possible influence on the equatorial inclination of a satellite. When a satellite goes through such a resonance, the capture is not certain and as noted by Yokoyama (2002), the probability of capture depends on several parameters as the obliquity of the planet and the interaction between other resonances. We consider the case of Phobos where we search to estimate the probability of a capture in an ‘eviction’ resonance by using an analytical Hamiltonian model and numerical simulations. This work will then notably estimate the probability that Phobos will be captured in the future in an ‘eviction’ resonance able to modify significantly its inclination and will measure the influence of the different parameters over the probability of capture.</p> <p align="justify"> </p> <p align="justify"><span lang="en-US">Acknowledgments: </span>The authors acknowledge support from project POCI-01-0145-FEDER-029932 (PTDC/FIS-AST/29932/2017), funded by FEDER through COMPETE 2020 (POCI) and FCT.</p> <p align="justify"> </p> <p align="justify">References:</p> <p align="justify"> </p> <p align="justify">Touma J. and Wisdom J., Resonances in the Early Evolution of the Earth-Moon System. <em>The Astronomical Journal</em>, 115:1653–1663, 1998.</p> <p align="justify">Yokoyama T., Possible effects of secular resonances in Phobos and Triton. <em>Planetary and Space Science</em>, 50:63–77, 2002.</p>

scholarly journals Extreme close encounters between proto-Mercury and proto-Venus in terrestrial planet formation

2020 ◽  
Vol 496 (3) ◽  
pp. 3781-3785
Author(s):  
Tong Fang ◽  
Hongping Deng
Keyword(s):  
Angular Momentum ◽  
Mass Fraction ◽  
Planet Formation ◽  
Orbital Motion ◽  
Terrestrial Planet ◽  
Small Mass ◽  
Tidal Dissipation ◽  
Hydrodynamic Simulations ◽  
Close Encounters ◽  
The Earth

ABSTRACT Modern models of terrestrial planet formation require solids depletion interior to 0.5–0.7 au in the planetesimal disc to explain the small mass of Mercury. The Earth and Venus analogues emerge after ∼100 Myr collisional growth, while Mercury forms in the diffusive tails of the planetesimal disc. We carried out 250 N-body simulations of planetesimal discs with mass confined to 0.7–1.0 au to study the statistics of close encounters that were recently proposed as an explanation for the high iron mass fraction in Mercury. We formed 39 Mercury analogues in total and all proto-Mercury analogues were scattered inwards by proto-Venus. Proto-Mercury typically experiences six extreme close encounters (closest approach smaller than six Venus radii) with Proto-Venus after Proto-Venus acquires 0.7 Venus Mass. At such close separation, the tidal interaction can already affect the orbital motion significantly such that the N-body treatment itself is invalid. More and closer encounters are expected should tidal dissipation of orbital angular momentum accounted. Hybrid N-body hydrodynamic simulations, treating orbital and encounter dynamics self-consistently, are desirable to evaluate the degree of tidal mantle stripping of proto-Mercury.

scholarly journals Scaling in global tidal dissipation of the Earth-Moon system

New Astronomy ◽  
2017 ◽  
Vol 54 ◽  
pp. 115-121 ◽  
Author(s):  
Maurice H.P.M. van Putten
Keyword(s):  
Tidal Dissipation ◽  
Moon System ◽  
The Earth

The motion of a lunar orbiter

1966 ◽  
Vol 25 ◽  
pp. 373
Author(s):  
Y. Kozai
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Artificial Satellite ◽  
Equations Of Motion ◽  
Triaxial Ellipsoid ◽  
The Moon ◽  
Secular Motion ◽  
The Earth ◽  
Close Satellite ◽  
The Mean

The motion of an artificial satellite around the Moon is much more complicated than that around the Earth, since the shape of the Moon is a triaxial ellipsoid and the effect of the Earth on the motion is very important even for a very close satellite.The differential equations of motion of the satellite are written in canonical form of three degrees of freedom with time depending Hamiltonian. By eliminating short-periodic terms depending on the mean longitude of the satellite and by assuming that the Earth is moving on the lunar equator, however, the equations are reduced to those of two degrees of freedom with an energy integral.Since the mean motion of the Earth around the Moon is more rapid than the secular motion of the argument of pericentre of the satellite by a factor of one order, the terms depending on the longitude of the Earth can be eliminated, and the degree of freedom is reduced to one.Then the motion can be discussed by drawing equi-energy curves in two-dimensional space. According to these figures satellites with high inclination have large possibilities of falling down to the lunar surface even if the initial eccentricities are very small.The principal properties of the motion are not changed even if plausible values ofJ3andJ4of the Moon are included.This paper has been published in Publ. astr. Soc.Japan15, 301, 1963.

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