On the Theory of Bodily Tides

2007 ◽  
Author(s):  
Michael Efroimsky ◽  
Valéry Lainey
Keyword(s):  
Bodily Tides

scholarly journals Why do warm Neptunes present nonzero eccentricity?

2020 ◽  
Vol 635 ◽  
pp. A37 ◽  
Author(s):  
A. C. M. Correia ◽  
V. Bourrier ◽  
J.-B. Delisle
Keyword(s):  
Planetary Systems ◽  
Atmospheric Tides ◽  
Tidal Dissipation ◽  
Bodily Tides ◽  
Orbital Periods

Most Neptune-mass planets in close-in orbits (orbital periods less than a few days) present nonzero eccentricity, typically around 0.15. This is somehow unexpected, as these planets undergo strong tidal dissipation that should circularize their orbits in a timescale shorter than the age of the system. In this paper we discuss some mechanisms that can oppose to bodily tides, namely, thermal atmospheric tides, evaporation of the atmosphere, and excitation from a distant companion. In the first two cases, the eccentricity can increase consistently, while in the last one, the eccentricity can only be excited for a limited amount of time (that may nevertheless exceed the age of the system). We show the limitations of these different mechanisms and how some of them could, depending on specific properties of the observed planetary systems, account for their presently observed eccentricities.

scholarly journals XIII. On the precession of a viscous spheroid, and on the remote history of the Earth

1879 ◽  
Vol 170 ◽  
pp. 447-538 ◽  
Keyword(s):  
Relative Motion ◽  
Mass Motion ◽  
The Sun ◽  
The Earth ◽  
Bodily Tides ◽  
History Of ◽  
The Subject ◽  
Theoretical Dynamics

The following paper contains the investigation of the mass-motion of viscous and imperfectly elastic spheroids, as modified by a relative motion of their parts, produced in them by the attraction of external disturbing bodies; it must be regarded as the continuation of my previous paper, where the theory of the bodily tides of such spheroids was given. The problem is one of theoretical dynamics, but the subject is so large and complex, th at I thought it best, in the first instance, to guide the direction of the speculation by considerations of applicability to the case of the earth, as disturbed by the sun and moon.

scholarly journals Bodily tides near spin–orbit resonances

2012 ◽  
Vol 112 (3) ◽  
pp. 283-330 ◽  
Author(s):  
Michael Efroimsky
Keyword(s):  
Spin Orbit ◽  
Bodily Tides

scholarly journals The Determination of Love's Number K from Tidal Variations of Rotation of a Compressible Earth

1972 ◽  
Vol 48 ◽  
pp. 234-234
Author(s):  
N. N. Pariisky ◽  
B. P. Pertsev
Keyword(s):  
Angular Speed ◽  
Long Period ◽  
The Past ◽  
The Earth ◽  
Bodily Tides ◽  
Tidal Variations ◽  
Near Future ◽  
Made In ◽  
Periodic Changes

Long period bodily tides (fortnightly and monthly) cause periodic changes of the Earth's moment of inertia and consequently the angular speed of its rotation.During the past few years the use of atomic clocks has made it possible to determine the amplitudes of these periodic variations of the Earth's rotation with high accuracy and has made this method very effective in determining Love's number K, which is dependent on the internal structure of the Earth (the most detailed studies were made in the U.S.S.R. – Pilnik and Gubanov).But up to now it was taken (Anderson, Woolard, Melchior, and others), that the formulae of Jeffreys and Woolard, which are used in this method, are valid only for incompressible Earth models.It is shown in this paper that the formulae are valid for the case of an actual compressible heterogeneous Earth. Thus, the method receives a real practical value. The use of lasers and radio methods in the near future will make this method even more effective.The full text of the paper will be published in the magazine Physics of the Earth in No. 3, 1972.

V. On the bodily tides of viscous and semi-elastic spheroids, and on the ocean tides on a yielding nucleus

1878 ◽  
Vol 27 (185-189) ◽  
pp. 419-424
Keyword(s):  
Viscous Fluid ◽  
Thin Shell ◽  
Elastic Solid ◽  
The State ◽  
Internal Strain ◽  
Incompressible Viscous Fluid ◽  
Elastic Sphere ◽  
Ocean Tides ◽  
The Earth ◽  
Bodily Tides

Sir W. Thomson’s investigation of the bodily tides of an elastic sphere has gone far to overthrow the idea of a semi-fluid interior to the earth, yet geologists are so strongly impressed by the fact that enormous masses of rock have been poured out of volcanic vents in the earth’s surface, that the belief is not yet extinct that we live on a thin shell over a sea of molten lava. It appeared to me, therefore, to be of interest to investigate the consequences which would arise from the supposition that the matter constituting the earth is of a viscous or imperfectly elastic nature. In this paper I follow out these hypo-theses, and it will be seen that the results are fully as hostile to the idea of any great mobility of the interior of the earth as are those of Sir W. Thomson. I begin by showing that the equations of flow of an incompressible viscous fluid have precisely the same form as those of strain of an incompressible elastic solid, at least when inertia is neglected. Hence, every problem about the strains of the latter has its analogue touching the flow of the former. This being so, the solution of Sir W. Thomson’s problem of the bodily tides of an elastic sphere may be adapted to give the bodily tides of a viscous spheroid. Sir W. Thomson, however, introduces the effects of the mutual gravitation of the parts of the sphere, by a synthetical method, after he has found the state of internal strain of an elastic sphere devoid of gravitational power The parallel synthetical method becomes, in the case of the viscous spheroid, somewhat complex, and I have preferred to adapt the solution analytically so as to include gravitation.

scholarly journals On the Effect of Ocean Tides on the Secular Retardation of the Earth's Rotation

1972 ◽  
Vol 48 ◽  
pp. 240-240 ◽  
Author(s):  
N. N. Pariisky ◽  
M. V. Kuznetsov ◽  
L. V. Kuznetsova
Keyword(s):  
World Ocean ◽  
Classical Problem ◽  
Earth’S Rotation ◽  
Earth's Rotation ◽  
Tidal Waves ◽  
Tidal Forces ◽  
The Earth ◽  
Secular Variations ◽  
Bodily Tides ◽  
Frictional Forces

The classical problem of determining the secular retardation of the Earth's rotation due to the effect of tides (oceanic and bodily) has an important geophysical value in determining the possible existence of processes inside the Earth, which lead to secular variations of rotation of the whole Earth or its external layers.Using new cotidal charts of the world ocean calculated by Bogdanov for the main tidal waves M2, S2, K1 and O1 and using the method of moments of tidal forces the retarding moment was found to be 8.3 × 1023 dyn cm. This is twice the amount of previous evaluations. (This method is superior to the method of calculating the dissipation of energy or the moments of frictional forces). This amount corresponds to a retardation of 3.8 μs/century in the speed of the Earth's rotation. But the observations of the Sun give only 1.9 μs/century for the retardation. Thus, there seem to be nontidal and probably internal processes, which accelerate the Earth's rotation by about 2 μs/century. And this is without taking account of additional smaller effects of bodily tides. The search for these processes is an important problem.The full text of the paper will be published in the magazine Physics of the Earth, No. 2, 1972.

scholarly journals II. On the precession of a viscous spheroid, and on the remote history of the Earth

1879 ◽  
Vol 28 (190-195) ◽  
pp. 184-194
Keyword(s):  
The Sun ◽  
Elastic Sphere ◽  
Rotating Body ◽  
The Earth ◽  
Time Harmonic ◽  
Bodily Tides ◽  
History Of ◽  
Direct Applicability

This paper is a continuation of a previous one on the bodily tides of homogeneous viscous spheroids (read on May 23rd), and it contains the investigation of the rotation of such a body as modified by the tides raised in it by external disturbing bodies. The earth is taken as the type of the rotating body, and the sun and moon as types of the disturbing ones; this plan not only affords a useful vocabulary, but permits an easy transition from questions of abstract dynamics to those of direct applicability to the physical history of the earth. In the paper on tides it was shown that, if the disturbing influence be expressed as a potential, which is expanded as a series of solid harmonics, each multiplied by a simple time harmonic, then each such term in the expansion corresponds with a tide in a viscous or imperfectly elastic sphere, which is independent of the tides corresponding to all other terms.

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