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1.
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2.
Spin-orbit coupling is often described in an approach known as ??the MacDonald torque??, which has long become the textbook standard due to its apparent simplicity. Within this method, a concise expression for the additional tidal potential, derived by MacDonald (Rev Geophys 2:467?C541, 1994), is combined with a convenient assumption that the quality factor Q is frequency-independent (or, equivalently, that the geometric lag angle is constant in time). This makes the treatment unphysical because MacDonald??s derivation of the said formula was, very implicitly, based on keeping the time lag frequency-independent, which is equivalent to setting Q scale as the inverse tidal frequency. This contradiction requires the entire MacDonald treatment of both non-resonant and resonant rotation to be rewritten. The non-resonant case was reconsidered by Efroimsky and Williams (Cel Mech Dyn Astron 104:257?C289, 2009), in application to spin modes distant from the major commensurabilities. In the current paper, we continue this work by introducing the necessary alterations into the MacDonald-torque-based model of falling into a 1-to-1 resonance. (The original version of this model was offered by Goldreich (Astron J 71:1?C7, 1996). Although the MacDonald torque, both in its original formulation and in its corrected version, is incompatible with realistic rheologies of minerals and mantles, it remains a useful toy model, which enables one to obtain, in some situations, qualitatively meaningful results without resorting to the more rigorous (and complicated) theory of Darwin and Kaula. We first address this simplified model in application to an oblate primary body, with tides raised on it by an orbiting zero-inclination secondary. (Here the role of the tidally-perturbed primary can be played by a satellite, the perturbing secondary being its host planet. A planet may as well be the perturbed primary, its host star acting as the tide-raising secondary). We then extend the model to a triaxial primary body experiencing both a tidal and a permanent-figure torque exerted by an orbiting secondary. We consider the effect of the triaxiality on both circulating and librating rotation near the synchronous state. Circulating rotation may evolve toward the libration region or toward a spin faster than synchronous (the so-called pseudosynchronous spin). Which behaviour depends on the orbit eccentricity, the triaxial figure of the primary, and the mass ratio of the secondary and primary bodies. The spin evolution will always stall for the oblate case. For libration with a small amplitude, expressions are derived for the libration frequency, damping rate, and average orientation. Importantly, the stability of pseudosynchronous spin hinges upon the dissipation model. Makarove and Efroimsky (Astrophys J, 2012) have found that a more realistic tidal dissipation model than the corrected MacDonald torque makes pseudosynchronous spin unstable. Besides, for a sufficiently large triaxiality, pseudosynchronism is impossible, no matter what dissipation model is used.  相似文献   

3.
We explore a possible origin for the puzzling anti-correlation between the formation epoch of galactic dark-matter haloes and their environment density. This correlation has been revealed from cosmological N -body simulations and is in conflict with the extended Press–Schechter model of halo clustering. Using similar simulations, we first quantify the straightforward association of an early formation epoch with a reduced mass-growth rate at late times. We then find that a primary driver of suppressed growth, by accretion and mergers, is tidal effects dominated by a neighbouring massive halo. The tidal effects range from a slowdown of the assembly of haloes due to the shear along the large-scale filaments that feed the massive halo to actual mass loss in haloes that pass through the massive halo. Using the restricted three-body problem, we show that haloes are prone to tidal mass loss within 1.5 virial radii of a larger halo. Our results suggest that the dependence of the formation epoch on environment density is a secondary effect induced by the enhanced density of haloes in filaments near massive haloes where the tides are strong. Our measures of assembly rate are particularly correlated with the tidal field at high redshifts   z ∼ 1  .  相似文献   

4.
The locations of the fully despun, double synchronous end states of tidal evolution, where the rotation rates of both the primary and secondary components in a binary system synchronize with the mean motion about the center of mass, are derived for spherical components. For a given amount of scaled angular momentum J/J′, the tidal end states are over-plotted on a tidal evolution diagram in terms of mass ratio of the system and the component separation (semimajor axis in units of primary radii). Fully synchronous orbits may not exist for every combination of mass ratio and angular momentum; for example, equal-mass binary systems require J/J′ > 0.44. When fully synchronous orbits exist for prograde systems, tidal evolution naturally expands the orbit to the stable outer synchronous solution. The location of the unstable inner synchronous orbit is typically within two primary radii and often within the radius of the primary itself. With the exception of nearly equal-mass binaries, binary asteroid systems are in the midst of lengthy tidal evolutions, far from their fully synchronous tidal end states. Of those systems with unequal-mass components, few have even reached the stability limit that splits the fully synchronous orbit curves into unstable inner and stable outer solutions.Calculations of material strength based on limiting the tidal evolution time to the age of the Solar System indicate that binary asteroids in the main belt with 100-km-scale primary components are consistent with being made of monolithic or fractured rock as expected for binaries likely formed from sub-catastrophic impacts in the early Solar System. To tidally evolve in their dynamical lifetime, near-Earth binaries with km-scale primaries or smaller created via a spin-up mechanism must be much weaker mechanically than their main-belt counterparts even if formed in the main belt prior to injection into the near-Earth region. Small main-belt binaries, those having primary components less than 10 km in diameter, could bridge the gap between the large main-belt binaries and the near-Earth binaries, as, depending on the age of the systems, small main-belt binaries could either be as strong as the large main-belt binaries or as weak as the near-Earth binaries. The inherent uncertainty in the age of a binary system is the leading source of error in calculation of material properties, capable of affecting the product of rigidity μ and tidal dissipation function Q by orders of magnitude. Several other issues affecting the calculation of μQ are considered, though these typically affect the calculation by no more than a factor of two. We also find indirect evidence within all three groups of binary asteroids that the semimajor axis of the mutual orbit in a binary system may evolve via another mechanism (or mechanisms) in addition to tides with the binary YORP effect being a likely candidate.  相似文献   

5.
We present numerical simulations of near-Earth asteroid (NEA) tidal disruption resulting in bound, mutually orbiting systems. Using a rubble pile model we have constrained the relative likelihoods for possible physical and dynamical properties of the binaries created. Overall 110,500 simulations were run, with each body consisting of ∼1000 particles. The encounter parameters of close approach distance and velocity were varied, as were the bodies' spin, elongation and spin axis direction. The binary production rate increases for closer encounters, at lower speeds, for more elongated bodies, and for bodies with greater spin. The semimajor axes for resultant binaries are peaked between 5 to 20 primary radii, and there is an overall trend for high eccentricity, with 97% of binaries having e > 0.1. The secondary-to-primary size ratios of the simulated binaries are peaked between 0.1 and 0.2, similar to trends among observed asteroid binaries. The spin rates of the primary bodies are narrowly distributed between 3.5- and 6-h periods, whereas the secondaries' periods are more evenly distributed and can exceed 15-h periods. The spin axes of the primary bodies are very closely aligned with the angular momenta of the binary orbits, whereas the secondary spin axes are nearly random. The shapes of the primaries show a large distribution of axis ratios, where those with low elongation (ratio of long and short axis) are both oblate and prolate, and nearly all with large elongation are prolate. This work presents results that suggest tidal disruption of gravitational aggregates can make binaries physically similar to those currently observed in the NEA population. As well, tidal disruption may create an equal number of binaries with qualities different from those observed, mostly binaries with large separation and with elongated primaries.  相似文献   

6.
The classical Kepler Problem consists in the determination of the relative orbital motion of a secondary body (planet) with respect to the primary body (Sun), for a given time. However, any natural system tends to have minimum energy and is subjected to differential gravitational or tidal forces (called into play mainly due to the finite size and deformability of the secondary body). We formulate the Kepler Problem taking into account the finite size of the secondary body and consider an approximation which tends towards minimum energy orbits, by increasing the dimensionality of the problem. This formulation leads to a conceivable natural explanation of the fact that the planetary orbits are characterized by small eccentricities.  相似文献   

7.
The angle between planetary spin and the normal direction of an orbital plane is supposed to reveal a range of information about the associated planetary formation and evolution. Since the orbit's eccentricity and inclination oscillate periodically in a hierarchical triple body and tidal friction makes the spin parallel to the normal orientation of the orbital plane with a short timescale in an isolated binary system, we focus on the comprehensive effect of third body perturbation and tidal mechanism on the angle. Firstly, we extend the Hut tidal model(1981) to the general spatial case, adopting the equilibrium tide and weak friction hypothesis with constant delay time, which is suitable for arbitrary eccentricity and any angle ? between the planetary spin and normal orientation of the orbital plane. Furthermore, under the constraint of angular momentum conservation, the equations of orbital and ratational motion are given. Secondly, considering the coupled effects of tidal dissipation and third body perturbation, and adopting the quadrupole approximation as the third body perturbation effect, a comprehensive model is established by this work. Finally, we find that the ultimate evolution depends on the timescales of the third body and tidal friction. When the timescale of the third body is much shorter than that of tidal friction, the angle ? will oscillate for a long time,even over the whole evolution; when the timescale of the third body is observably larger than that of the tidal friction, the system may enter stable states, with the angle ? decaying to zero ultimately, and some cases may have a stable inclination beyond the critical value of Lidov-Kozai resonance. In addition, these dynamical evolutions depend on the initial values of the orbital elements and may aid in understanding the characteristics of the orbits of exoplanets.  相似文献   

8.
The aim of the present paper will be to derive an equation of dissipation of energy for a rotating body of arbitrary viscosity distorted by tides, which arise from the gravitational field of its companion in a close pair of such bodies.By a transformation of the fundamental equation of energy dissipation in terms of velocity of tidal deformation (Section 2), the dissipation function is constructed for a tidally-distorted body (Section 3). From this equation, the rate of dissipation of tidal energy is formulated for a nearly-spherical rotating body distorted by second harmonic longitudinal tides (Section 4); the coefficients of viscosity (or the bulk modulus) are treated as arbitrary functions of spatial coordinates. Finally (Section 5), expressions for the total energy dissipation within the orbital cycle are given for axial rotation of the distorted body, provided its angular velocity is constant (for example, with the Keplerian angular velocity).Research financed in part by the Division of Scientific Research and Development of Ministry of Sciences and Culture of Greece.  相似文献   

9.
Abstract— 1996 FG3 is a binary near‐Earth object (NEO) that was likely formed during a tidal disruption event. Our results indicate that the formation of this binary object was unlikely to have occurred when the progenitor had a encounter velocity with the Earth significantly smaller than its current value (10.7 km/s); The formation of the binary object on an orbit similar to the present one is possible, and the survival of the satellite constrains this to have happened less than 1.6 Ma ago. However, the binary object could also have been formed when the progenitor's encounter velocity with Earth was >12 km/s, and in this case we cannot constrain its formation age. Our results indicate that tidal disruptions occurring among NEOs with low velocity encounters with Earth are unlikely to produce long‐lasting NEO binaries. Thus, tidal disruption may not be able to completely re‐supply the observed population. This would imply that a significant fraction of the observed NEO binaries evolved out of the main asteroid belt. Overall, our results suggest to us that the CM2 meteorites having cosmic ray exposure (CRE) ages of ?200,000 yr were likely liberated by the tidal disruption of a primitive NEO with a relative velocity with the Earth significantly smaller than that of 1996 FG3. We propose a list of such objects, although as far as we know, none of the candidates is a binary for the reasons described above.  相似文献   

10.
This is an exploration of dynamic tides on elastic bodies. The body is thought of as a dynamical system described by its modes of oscillation. The dynamics of these modes are governed by differential equations that depend on the rheology. The modes are damped by dissipation. Tidal friction occurs as exterior bodies excite the modes and the modes act back on the tide raising body. The whole process is governed by a closed set of differential equations. Standard results from tidal theory are recovered in a two-timescale approximation to the solution of these differential equations.  相似文献   

11.
We study the tidal effects of a deeply penetrating collision between two spherical galaxies, one twice massive but less dense than the other, by numerical simulations. We consider the relative motion of the galaxies to be initially in a hyperbolic orbit. The collision parameters are so chosen that the primary (bigger) galaxy is just below the limit of disruption and the relative velocity of the pair is slightly in excess of the escape limit and the primary suffer greater tidal damage than the secondary. The primary develops a core halo structure and shows over all expansion while the secondary while the secondary shows contraction in the inner region and less significant expansion in the outer parts. The initially hyperbolic orbit is transformed into a parabolic orbit as a result of the collision. The result also indicate that the tidal interaction does not induce appreciable rotation in hyperbolic collision. We calculate the angle of deflection of the orbit and compare it with that computed using analytical work. The numerical work shows larger angle of deflection which is attributed to the large tidal effects of the bigger galaxy in the interpenetrating collision. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

12.
The aim of the present paper will be to investigate the circumstances under which an irreversible dissipation of the kinetic energy into heat is generated by the dynamical tides in close binary systems if (a) their orbit is eccentric; (b) the axial rotation of the components is not synchronized with the revolution; or (c) the equatorial planes are inclined to that of the orbit.In Section 2 the explicit form of the viscous dissipation function will be set up in terms of the velocity-components of spheroidal deformation arising from the tides; in Section 3, the principal partial tides contributing to the dissipation will be detailed; Section 4 will be devoted to a determination of the extent of stellar viscosity — both gas and radiative; while in the concluding Section 5 quantitative estimates will be given of the actual rate at which the kinetic energy of dynamical tides gets dissipated into heat by viscous friction in stellar plasma.The results disclose that the amount of heat produced per unit time by tidal interaction between components of actual close binaries equals only about 10–10th part of their nuclear energy production; and cannot, therefore, affect the internal structure of evolution of the constituent stars to any appreciable extent. Moreover, it is shown that the kinetic energy of their axial rotation can be influenced by tidal friction only on a nuclear, rather than gravitational (Kelvin) time-scale — as long as plasma or radiative viscosity constitute the sole sources of dissipation. However, the emergence of turbulent viscosity in secondary components of late spectral types, which have evolved away from the Main Sequence, can accelerate the dissipation 105–106 times, and thus give rise to appreciable changes in the elements of the system (particularly, in the orbital periods) over time intervals of the order of 105–106 years. Lastly, it is pointed out that, in close binary systems consisting of a pair of white dwarfs, a dissipation of the kinetic energy through viscous tides in degenerate fermion-gas could produce enough heat to account, by itself, for the observed luminosity of such objects.  相似文献   

13.
The Darwin-Kaula theory of bodily tides is intended for celestial bodies rotating without libration. We demonstrate that this theory, in its customary form, is inapplicable to a librating body. Specifically, in the presence of libration in longitude, the actual spectrum of Fourier tidal modes differs from the conventional spectrum rendered by the Darwin–Kaula theory for a nonlibrating celestial object. This necessitates derivation of formulae for the tidal torque and the tidal heating rate, that are applicable under libration. We derive the tidal spectrum for longitudinal forced libration with one and two main frequencies, generalisation to more main frequencies being straightforward. (By main frequencies we understand those emerging due to the triaxiality of the librating body.) Separately, we consider a case of free libration at one frequency (once again, generalisation to more frequencies being straightforward). We also calculate the tidal torque. This torque provides correction to the triaxiality-caused physical libration. Our theory is not self-consistent: we assume that the tidal torque is much smaller than the permanent-triaxiality-caused torque, so the additional libration due to tides is much weaker than the main libration due to the permanent triaxiality. Finally, we calculate the tidal dissipation rate in a body experiencing forced libration at the main mode, or free libration at one frequency, or superimposed forced and free librations.  相似文献   

14.
天文潮汐与地震   总被引：6，自引：0，他引：6  
从三个方面综述了天文潮汐与地震关纱的研究，内容包括，日、月、地球的相对位置与地震，天文潮汐的周期，相位与地震，天文潮汐应力与地震，日、月、地球的相对位置与地震和天文潮汐周期与地城的研究均属于从体积力的角度考虑问题，主要是从宏观角度揭示地震发生时的日月位置分布有何规律性，揭示地震发生时间丛集在潮汐周期变化过程中的相位或时段以及地城牟潮汐周期，天文潮汐应力与震的研究从引潮力在地震内部地震源处产生的潮汐应力角度出发，着重研究不同类型性质的发震断层与潮汐应力触发的关系，从物理意义上讲，该研究较深 次地切入了问题的实质，分析了采用某些方法和样本研究结果不一致性的原因，并提出了进一步研究的方向。  相似文献   

15.
This report is a review of Darwin’s classical theory of bodily tides in which we present the analytical expressions for the orbital and rotational evolution of the bodies and for the energy dissipation rates due to their tidal interaction. General formulas are given which do not depend on any assumption linking the tidal lags to the frequencies of the corresponding tidal waves (except that equal frequency harmonics are assumed to span equal lags). Emphasis is given to the cases of companions having reached one of the two possible final states: (1) the super-synchronous stationary rotation resulting from the vanishing of the average tidal torque; (2) capture into the 1:1 spin-orbit resonance (true synchronization). In these cases, the energy dissipation is controlled by the tidal harmonic with period equal to the orbital period (instead of the semi-diurnal tide) and the singularity due to the vanishing of the geometric phase lag does not exist. It is also shown that the true synchronization with non-zero eccentricity is only possible if an extra torque exists opposite to the tidal torque. The theory is developed assuming that this additional torque is produced by an equatorial permanent asymmetry in the companion. The results are model-dependent and the theory is developed only to the second degree in eccentricity and inclination (obliquity). It can easily be extended to higher orders, but formal accuracy will not be a real improvement as long as the physics of the processes leading to tidal lags is not better known.  相似文献   

16.
Wegener concluded that the Earth's surface has suffered regionally variable westward displacement. Modern data support Wegener's conclusion, but a causative mechanism has not been evident. The retarding torque is too small to distort the viscous Earth. At the same time difficulty has been experienced in explaining the large value of the astronomically detected tidal dissipation. We have examined the effect of the secular rotational strain imposed by tidal bulge formation on convection in the mantle of arbitrary origin. The dissipation as measured by the lag in the bodily tides appears adequate to explain the missing part of the dissipation, some 8.5 × 1026 erg yr–1, without recourse to an unidentified mechanism in the seas. The convection must itself be influenced by the external force system. The effect to be expected is that circulation resulting in westward displacement at surface must be fostered at the expense of circulation in other directions. The history of the tidal couple, if this is based on dissipation in the mantle, is likely to differ greatly from that of a couple based on dissipation in the seas.  相似文献   

17.
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   

18.
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19.
The main goal of this paper is to compare the relative importance of destruction by tides vs. destruction by mergers, in order to assess if tidal destruction of galaxies in clusters is a viable scenario for explaining the origin of intracluster stars. We have designed a simple algorithm for simulating the evolution of isolated clusters. The distribution of galaxies in the cluster is evolved using a direct gravitational N-body algorithm combined with a subgrid treatment of physical processes such as mergers, tidal disruption, and galaxy harassment. Using this algorithm, we have performed a total of 148 simulations. Our main results are:
–  destruction of dwarf galaxies by mergers dominates over destruction by tides, and
–  the destruction of galaxies by tides is sufficient to explain the observed intracluster light in clusters.
  相似文献   

20.
Joseph A. Burns 《Icarus》1976,28(4):453-458
Mercury, currently rotating very slowly, probably rotated faster in the past. If Mercury's rotation period had been near 8 hours initially, similar to that of most solar system bodies today, it would have been flattened by a few percent. As Mercury was slowed by solar tides, craters which were circular when they were emplaced would have been distorted by the same few percent. Substantial surface stresses, well above the fracture stress, would have been produced unless stress relief occurred; these stresses should have produced tensional fractures near the poles and two intersecting sets of shear planes in equatorial regions. Satellite orbits about the slowly spinning Mercury have been shown to collapse onto its surface: the impact craters resulting from these hypothetical lost satellites should be elongated along the orbit paths, which probably lie near the equator. However, none of these features has been found on the Mariner 10 images. They may be obscured by the effects of tidal heating that should cause an overall internal temperature increase of about 100°K although the increase would be substantially more in certain regions. Radial tides, sometimes called push-pull tides, are important at the present time because Mercury's large orbital eccentricity causes the planet to undergo significant tidal flexing each orbital period; the contemporary tidal heating due to this mechanism is estimated at more than 1016 erg/sec.  相似文献   

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