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1.
The discussion of tidal friction in the Earth-Moon system given in successive editions ofThe Earth by Jeffreys is shown to contain a serious dynamical error. When the treatment is corrected, it shows that the moment of inertia of the Earth must be changing. The apparent secular accelerations of the Moon and Sun require a diminishing moment of inertia, and the rate is in agreement with the phase-change hypothesis for the nature of the core.Paper presented at the European Workshop on Planetary Sciences, organised by the Laboratorio di Astrofisica Spaziale di Frascati, and held between April 23–27, 1979, at the Accademia Nazionale del Lincei in Rome, Italy. 相似文献
2.
R. A. Lyttleton 《Earth, Moon, and Planets》1976,16(1):41-58
The tidal theory of the evolution of the lunar orbit has remained inconsistent with the observational values of the apparent secular accelerations of the Sun and Moon since it was first developed by Jeffreys in 1920. Allowance for a changing moment of inertia of the Earth enables the discrepancy to be completely removed if a decrease is occurring at a rate of just about the amount already required by the phase-change theory of the nature of the terrestrial core. The agreement of the resulting theory with the latest determinations of the lunar acceleration increases confidence in the phase-change hypothesis. On the other hand the theory renders it most unlikely that a changing constant of gravitation will prove necessary to account for the observations. On the present theory of itself the Moon would have been extremely close to the Earth only about 109 yr ago which suggests that some additional process may at times have influenced the lunar orbit. 相似文献
3.
L. V. Morrison 《Earth, Moon, and Planets》1972,5(3-4):253-264
The results and methods of determining the secular accelerations of the Moon's orbital motion and the Earth's rotation from astronomical observations are critically reviewed. In particular, the effect on these results is considered should Spencer Jones' value for the secular acceleration of the Moon be revised. General relationships are deduced between these accelerations, the rate of dissipation of energy in the Earth and the fractional change in the rate of rotation of the Earth. It is shown that the theory of tidal torques alone does not completely account forany of the wide range of results for the retardation of the Earth deduced from astronomical observations.Presented to the NATO Advanced Study Institute on Lunar Studies, Patras, Greece, September 1971. 相似文献
4.
In two previous papers (Zafiropoulos and Kopal, 1983a, b; hereafter referred to as Papers I and II) we have investigated the effects of rotational and tidal distortion (for non-lagging tides) on the orbital elements of a close binary system. The present paper deals with secular and periodic perturbations caused by dynamical tides. The componentsR, S, andW of disturbing accelerations for tidal lag have been substituted in the Gaussian form of Lagrange's planetary equations to give the first-order approximation. The results obtained have been expressed by means of Hansen coefficients and include the effects produced by the second, third and fourth harmonic dynamical tides. 相似文献
5.
B. Zafiropoulos 《Astrophysics and Space Science》1987,137(1):139-149
The aim of this investigation is to present the periodic and secular perturbations of the orbital elements of close binary systems due to tidal lag in latitude. The variational equations of the problem of plane motion will be set up in terms of the rectengular componentsR, S, andW of the disturbing accelerations. These equations are highly nonlinear with respect to the orbital elements and we present analytic approximations to the effects produced by the perturbing acceleration due to dynamical tides lagging in latitude. The perturbed elements of the orbit have been expressed by means of Hansen coefficients in the compact form of summations. 相似文献
6.
G. A. Krasinsky 《Celestial Mechanics and Dynamical Astronomy》2006,96(3-4):169-217
Improved differential equations of the rotation of the deformable Earth with the two-layer fluid core are developed. The equations describe both the precession-nutational motion and the axial rotation (i.e. variations of the Universal Time UT). Poincaré’s method of modeling the dynamical effects of the fluid core, and Sasao’s approach for calculating the tidal interaction between the core and mantle in terms of the dynamical Love number are generalized for the case of the two-layer fluid core. Some important perturbations ignored in the currently adopted theory of the Earth’s rotation are considered. In particular, these are the perturbing torques induced by redistribution of the density within the Earth due to the tidal deformations of the Earth and its core (including the effects of the dissipative cross interaction of the lunar tides with the Sun and the solar tides with the Moon). Perturbations of this kind could not be accounted for in the adopted Nutation IAU 2000, in which the tidal variations of the moments of inertia of the mantle and core are the only body tide effects taken into consideration. The equations explicitly depend on the three tidal phase lags δ, δ
c, δ
i responsible for dissipation of energy in the Earth as a whole, and in its external and inner cores, respectively. Apart from the tidal effects, the differential equations account for the non-tidal interaction between the mantle and external core near their boundary. The equations are presented in a simple close form suitable for numerical integration. Such integration has been carried out with subsequent fitting the constructed numerical theory to the VLBI-based Celestial Pole positions and variations of UT for the time span 1984–2005. Details of the fitting are given in the second part of this work presented as a separate paper (Krasinsky and Vasilyev 2006) hereafter referred to as Paper 2. The resulting Weighted Root Mean Square (WRMS) errors of the residuals dθ, sin θd for the angles of nutation θ and precession are 0.136 mas and 0.129 mas, respectively. They are significantly less than the corresponding values 0.172 and 0.165 mas for IAU 2000 theory. The WRMS error of the UT residuals is 18 ms. 相似文献
7.
In this paper, the expressions of variations of the dynamical ellipticity and the principal moments of inertia due to the
deformations produced by the zonal part of the tidal potential are obtained. Starting from these expressions, we have studied
from equations related to Hamiltonian theory, their effects on the nutation and finally we have evaluated numerically such
influences, with a level of truncation at 0.1 μas. Thus we have shown that some coefficients are quite large with respect
to the usual accuracy of up-to-date observations.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
8.
The search for asteroids that maintain stable motion in the zone between the Earth and Mars has been performed. The near-Earth object 2013 RB6, which has avoided close encounters with the planets for a long period of time, has been found. Integration of the equations of motion of the object shows that its dynamical lifetime in the zone between the Earth and Mars significantly exceeds 100 Myr. 2013 RB6 moves away from orbital resonances with the planets, but is in the secular resonance ν5. Solving the question of its origin requires further observations. 相似文献
9.
10.
It is known that the observed secular accelerations of the Sun and Moon are not consistent with the tidal interactions of the Earth with the Sun and Moon. Following Dicke, the hypothesis of variable constant of gravity is adopted and expressions for the accelerations are derived. It is shown that if the theoretical ratio of the acceleration is equated the observed one, a unique value for —/G can be calculated. Adopting the accelerations obtained by Fotheringham, Newton, Muller and Stephenson, and Stephenson, it is found that — /G ranges from 1.4 × 10–11 to 3.3 × 10–11 yr–1. This estimate is consistent with the one based upon the comparison of the lunar accelerations measured with respect to atomic and ephemis times. 相似文献
11.
D.J. Scheeres 《Icarus》2007,188(2):430-450
A detailed derivation is given of the effect of solar radiation on the rotational dynamics of asteroids, commonly called the YORP effect. The current derivation goes beyond previous discussions published in the literature and provides a comprehensive secular dynamical analysis of the effect of solar radiation torques acting on a uniformly rotating body, and the evolution of its rotation state over time. Our predicted model has the global radiation properties of the asteroid as explicit parameters, and hence can be specified independent of these parameters. The resulting secular equations for the rotation rate and rotation pole are characterized by three parameters of the body's shape and explicitly includes the effect of thermal inertia on the evolution of these rotation state parameters. With this detailed model, in conjunction with estimated asteroid shapes and poles, we compute the expected YORP torques and dynamic response of several asteroids and the change in rotation rate for specific shapes as a function of obliquity. Finally, we define a convenient dimensionless parameter that is only a function of the body geometry and that can be used to characterize the effects of YORP. 相似文献
12.
13.
The motion of a particle about a non-rotating 2nd degree and order-gravity field is investigated. Averaging conditions are applied to the particle motion and a qualitative analysis which reveals the general character of motion in this system is given. It is shown that the orbit plane will either be stationary or precess about the body's axis of minimum or maximum moment of inertia. It is also shown that the secular equations for this system can be integrated in terms of trigonometric, hyperbolic or elliptic functions. The explicit solutions are derived in all cases of interest.This revised version was published online in October 2005 with corrections to the Cover Date. 相似文献
14.
Zhennian Gu 《Astrophysics and Space Science》1998,259(4):427-432
The long period variation of the earth rotation is generally explained by the tidal friction. The tidal friction, however,
is not the only source to influence the earth rotation in long term. In this paper, by means of the interaction between the
solar wind and the magnetosphere of the earth, the additional magnetic pressure will exist in the magnetic tail due to the
crowding and sparseness of the magnetic lines in the consideration of the earth rotation, which could be considered as a source
of effecting the long term variation of the earth rotation. It is shown in this paper that this mechanism can produce angular
deceleration of the Earth rotation in the magnitude of ω = −1.7 × 10-22 s-2. This result might be a prompt to search for other
sources in the secular variation of the rate of the Earth rotation variation further in order to regulate the observed result
with the theoretical one.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
15.
One of the possible early states of the Earth-Moon system was a system of several large satellites around the Earth. The dynamical
evolution of coplanar three-body systems is studied; a planet (Earth) and two massive satellites (proto-moons) with geocentric
orbits of slightly different radii. Such configurations may arise in multiple satellite systems receding from a planet due
to tidal friction. The numerical integration of the equations of motion shows that initially circular Keplerian orbits are
soon transformed into disturbed elliptic orbits which are intersecting. The life-time of such a coplanar system between two
probable physical collisions of satellites is roughly from one day to one year for satellite systems with radii less than
20R⊕, and may reach 100 yr for three-dimensional systems. This time-scale is short in comparison with the duration of the removal
of satellites due to tides raised on the planet, which is estimated as 106–108 yr for the same orbital dimensions. Therefore, the life-time of a system of several proto-moons is mainly determined by their
tidal interactions with the Earth. For conditions which we have considered, the most probable result of the evolution was
coalescence of satellites as the consequence of the collisions. 相似文献
16.
The secular effect of YORP torque on the rotational dynamics of an asteroid in non-principal axis rotation is studied. The
general rotational equations of motion are derived and approximated with an illumination function expanded up to second order.
The resulting equations of motion can be averaged over the fast rotation angles to yield secular equations for the angular
momentum, dynamic inertia and obliquity. We study the properties of these secular equations and compare results to previous
research. Finally, an application to several real asteroid shapes is made, in particular we study the predicted rotational
dynamics of the asteroid Toutatis, which is known to be in a non-principal axis state. 相似文献
17.
Gwenaël Boué Alexandre C. M. Correia Jacques Laskar 《Celestial Mechanics and Dynamical Astronomy》2016,126(1-3):31-60
In this paper, we present a formalism designed to model tidal interaction with a viscoelastic body made of Maxwell material. Our approach remains regular for any spin rate and orientation, and for any orbital configuration including high eccentricities and close encounters. The method is to integrate simultaneously the rotation and the position of the planet as well as its deformation. We provide the equations of motion both in the body frame and in the inertial frame. With this study, we generalize preexisting models to the spatial case and to arbitrary multipole orders using a formalism taken from quantum theory. We also provide the vectorial expression of the secular tidal torque expanded in Fourier series. Applying this model to close-in exoplanets, we observe that if the relaxation time is longer than the revolution period, the phase space of the system is characterized by the presence of several spin-orbit resonances, even in the circular case. As the system evolves, the planet spin can visit different spin-orbit configurations. The obliquity is decreasing along most of these resonances, but we observe a case where the planet tilt is instead growing. These conclusions derived from the secular torque are successfully tested with numerical integrations of the instantaneous equations of motion on HD 80606 b. Our formalism is also well adapted to close-in super-Earths in multiplanet systems which are known to have non-zero mutual inclinations. 相似文献
18.
The chaotic behaviour of the motion of the planets in our Solar System is well established. In this work to model a hypothetical extrasolar planetary system our Solar System was modified in such a way that we replaced the Earth by a more massive planet and let the other planets and all the orbital elements unchanged. The major result of former numerical experiments with a modified Solar System was the appearance of a chaotic window at κ E ∈ (4, 6), where the dynamical state of the system was highly chaotic and even the body with the smallest mass escaped in some cases. On the contrary for very large values of the mass of the Earth, even greater than that of Jupiter regular dynamical behaviour was observed. In this paper the investigations are extended to the complete Solar System and showed, that this chaotic window does still exist. Tests in different ‘Solar Systems’ clarified that including only Jupiter and Saturn with their actual masses together with a more ‘massive’ Earth (4 < κ E < 6) perturbs the orbit of Mars so that it can even be ejected from the system. Using the results of the Laplace‐Lagrange secular theory we found secular resonances acting between the motions of the nodes of Mars, Jupiter and Saturn. These secular resonances give rise to strong chaos, which is the cause of the appearance of the instability window. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
19.
20.
B.A. Conway 《Icarus》1982,51(3):610-622
A frequency-dependent model of tidal friction is used in the determination of the time rate of change of the lunar orbital elements and the angular velocity of the Earth. The variational equations consider eccentricity, the solar tide on the Earth, Earth oblateness, and higher-order terms in the Earth's tidal potential. A linearized solution of the equations governing the precission of the Earth's rotational angular momentum and the lunar ascending node is found. This allows the analytical averaging of the variational equations over the period of relative precession which, though large, is necessarily small in comparison to the time step of the numerical integrator that yields the system history over geological time. Results for this history are presented and are identified as consistent with origin of the Moon by capture. This model may be applied to any planet-satellite system where evolution under tidal friction is of interest. 相似文献