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1.
《Icarus》1987,70(2):334-347
The Laplace resonance among the inner three Galilean satellites (mean motions n1 − 3n2 + 2n3 = 0) has stable configurations in “deep resonance,” i.e., where mean motions taken by pairs are in ratios very close to 2:1. The present satellite configuration, with the resonance variable φ ≡ λ1 − 3λ2 + 2λ3 stable at 180°, is unstable near this exact commensurability. But there is a continuous path of stable conditions branching from φ = 180° to higher and lower values of φ and toward very deep resonance, according to a theory extended to third order in orbital eccentricity. This path provides a track for tidal evolution of the system. Thus, scenarios involving evolution (probably episodic) from deep resonance are viable, and eliminate the requirement by the alternative equilibrium hypothesis for rapid tidal dissipation in Jupiter. Evolution out from deep resonance is consistent with the free eccentricity of Ganymede, the free libration of φ, and observational constraints on Io's secular acceleration. Also, the relatively large forced eccentricities in deep resonance may have controlled geophysical processes in the satellites by much greater tidal heating and global stress than at present. 相似文献
2.
Tidal evolution of Mimas, Enceladus, and Dione 总被引：2，自引：0，他引：2
The tidal evolution through several resonances involving Mimas, Enceladus, and/or Dione is studied numerically with an averaged resonance model. We find that, in the Enceladus-Dione 2:1 e-Enceladus type resonance, Enceladus evolves chaotically in the future for some values of k2/Q. Past evolution of the system is marked by temporary capture into the Enceladus-Dione 4:2 ee′-mixed resonance. We find that the free libration of the Enceladus-Dione 2:1 e-Enceladus resonance angle of 1.5° can be explained by a recent passage of the system through a secondary resonance. In simulations with passage through the secondary resonance, the system enters the current Enceladus-Dione resonance close to tidal equilibrium and thus the equilibrium value of tidal heating of 1.1(18,000/QS) GW applies. We find that the current anomalously large eccentricity of Mimas can be explained by passage through several past resonances. In all cases, escape from the resonance occurs by unstable growth of the libration angle, sometimes with the help of a secondary resonance. Explanation of the current eccentricity of Mimas by evolution through these resonances implies that the Q of Saturn is below 100,000. Though the eccentricity of Enceladus can be excited to moderate values by capture in the Mimas-Enceladus 3:2 e-Enceladus resonance, the libration amplitude damps and the system does not escape. Thus past occupancy of this resonance and consequent tidal heating of Enceladus is excluded. The construction of a coherent history places constraints on the allowed values of k2/Q for the satellites. 相似文献
3.
The tectonically and cryovolcanically resurfaced terrains of Ganymede attest to the satellite's turbulent geologic history. Yet, the ultimate cause of its geologic violence remains unknown. One plausible scenario suggests that the Galilean satellites passed through one or more Laplace-like resonances before evolving into the current Laplace resonance. Passage through such a resonance can excite Ganymede's eccentricity, leading to tidal dissipation within the ice shell. To evaluate the effects of resonance passage on Ganymede's thermal history we model the coupled orbital-thermal evolution of Ganymede both with and without passage through a Laplace-like resonance. In the absence of tidal dissipation, radiogenic heating alone is capable of creating large internal oceans within Ganymede if the ice grain size is 1 mm or greater. For larger grain sizes, oceans will exist into the present epoch. The inclusion of tidal dissipation significantly alters Ganymede's thermal history, and for some parameters (e.g. ice grain size, tidal Q of Jupiter) a thin ice shell (5 to 20 km) can be maintained throughout the period of resonance passage. The pulse of tidal heating that accompanies Laplace-like resonance capture can cause up to 2.5% volumetric expansion of the satellite and contemporaneous formation of near surface partial melt. The presence of a thin ice shell and high satellite orbital eccentricity would generate moderate diurnal tidal stresses in Ganymede's ice shell. Larger stresses result if the ice shell rotates non-synchronously. The combined effects of satellite expansion, its associated tensile stress, rapid formation of near surface partial melt, and tidal stress due to an eccentric orbit may be responsible for creating Ganymede's unique surface features. 相似文献
4.
Milan Burša 《Earth, Moon, and Planets》1991,54(3):241-255
It has been demonstrated that dynamically the Saturnian system is analogous to the Jovian system; however, it is not an analogue of the Solar system as a whole. The departures in the figure parameters of the tri-axial Saturnian satellites orbiting in 1 : 1 resonance, from equilibrium figure parameters are not large in general, and the tidal and centrifugal distorting forces can be supposed to be responsible for the actual figures. The estimates for different dynamical parameters of the system support the hypothesis that the tri-axial satellites in 1 : 1 resonance were formed from the same protoplanetary nebula that gave rise to Saturn. 相似文献
5.
The present work is a critical revision of the hypothesis of the planetary tidal influence on solar activity published by Abreu et al. (Astron. Astrophys. 548, A88, 2012; called A12 here). A12 describes the hypothesis that planets can have an impact on the solar tachocline and therefore on solar activity. We checked the procedure and results of A12, namely the algorithm of planetary tidal torque calculation and the wavelet coherence between torque and heliospheric modulation potential. We found that the claimed peaks in long-period range of the torque spectrum are artefacts caused by the calculation algorithm (viz. aliasing effect). Also the statistical significance of the results of the wavelet coherence is found to be overestimated by an incorrect choice of the background assumption of red noise. Using a more conservative non-parametric random-phase method, we found that the long-period coherence between planetary torque and heliospheric modulation potential becomes insignificant. Thus we conclude that the considered hypothesis of planetary tidal influence on solar activity is not based on a solid ground. 相似文献
6.
S.J. Peale 《Icarus》1978,36(2):240-244
If Hyperion's radius is near the upper limit of recent estimates, and tidal dissipation in Hyperion is reasonably well represented by a frequency-independent Q ? 2–300, finding Hyperion rotating in the 3:2 spin-orbit resonance like Mercury would imply a primordial origin for the Titan-Hyperion 4:3 orbital resonance. Independent of this test, observation of Hyperion's spin rate will place an upper bound on the average tidal effective Q for the satellite as a function of its assumed initial angular velocity. 相似文献
7.
A planar, fixed-orbit model of the rotation of the planet Mercury is analyzed. The model includes only the solar torques on the planet's permanent asymmetry and its solar tidal bulge. For this model, it is shown that the zero of the averaged tidal torque corresponds to an asymptotically stable periodic solution of the second kind which, for two tidal torque representations, is close to the asymptotically stable equilibrium point corresponding to an exact 32 spin-orbit resonance. A conjecture that the current rotation state of Mercury is due to transfer from capture by the zero of the averaged tidal torque to 32 resonance capture with changes in the eccentricity of the planet's orbit is discussed briefly. 相似文献
8.
Charles F. Yoder 《Icarus》1982,49(3):327-346
The Martian satellites Phobos and Deimos move along nearly circular coplanar, stable orbits and have created surfaces older than ～ 109 years. The accretion hypothesis suggests that their primordial orbits were also very regular. However, tides raised on Mars and Phobos can substantially alter the semimajor axis a of Phobos' orbit over time. The effect of the Martian tidal torque alone on Phobos' orbit implies that the primordial e was ～0.1 to 0.2 about 4.6 × 109 years ago if the present observed e = 0.015 is naively interpreted as a tidally damped remnant. Significant tidal friction in Phobos reduces the time scale for Phobos to achieve a crossing orbit with Deimos to less than 109 years and permits the primodial e to approach unity. The consequences of orbital intersections cannot easily be resolved by assuming either a catastrophic origin for both satellites (namely, that both are fragments of a common parent body fractured by an impact) or that they were captured sequentially by Mars. Either hypothesis is difficult to accept, given that Deimos' orbit, which is only slightly affected by tides, is now so regular. An alternative scenario is proposed in this paper in which the observed e of Phobos results from several gravitational resonance excitations within the last 109 years, assuming tidal friction in Phobos has had only a small effect on its orbit. In facr, both the primordial e and the inclination i may have been much smaller than presently observed. The constraints imposed on tidal friction in Phobos by both the apparent age of Phobos' surface (> 109yrs) and the above scenario can be satisfied only of μQ > 1012dynes/cm2. Since the Q factor is ～102, the rigidity μ > 1010dynes/cm2. Thus Phobos should have substantial internal strength. 相似文献
9.
Richard Greenberg 《Icarus》1981,46(3):415-423
The Laplace resonance among the Galilean satellites Io, Europa, and Ganymede is traditionally reduced to a pendulum-like dynamical problem by neglecting short-period variations of several orbital elements. However, some of these variations that can now be neglected may once have had longer periods, comparable to the “pendulum” period, if the system was formerly in deep resonance (pairs of periods even closer to the ratio 2:1 than they are now). In that case, the dynamical system cannot be reduced to fewer than nine dimensions. The nine-dimensional system is linearized here in order to study small variations about equilibrium. When tidal effects are included, the resulting evolution is substantially the same as was indicated by the pendulum approach, except that evolution out of deep resonance is found to be somewhat slower than suggested by extrapolation of the pendulum results. This slower rate helps support my hypothesis that the system may have evolved from deep resonance, although other factors still need to be considered to determine whether that hypothesis is quantitatively viable. 相似文献
10.
A. T. Sinclair 《Celestial Mechanics and Dynamical Astronomy》1973,8(2):221-221
The five types of resonance possible between a pair of satellites at a 21 commensurability are described. By a modification of the method usually used in the restricted three-body problem, phase-plane diagrams are constructed for these resonances for the more general case where both satellite masses are non-zero. These phase-plane diagrams are used to discuss the different types of motion possible at the five resonances.It is shown that tidal forces can drive a pair of satellites towards a commensurability, and at the 21 commensurability it is possible for the satellites to be captured into a libration at any of the five resonances, the probability of capture depending on the eccentricities, inclinations, and masses of the satellites. The tidal hypothesis provides a reasonable explanation of the origin of the commensurabilities between Mimas and Tethys, and between Enceladus and Dione, in the satellite system of Saturn.Presented at the Conference on Celestial Mechanics, Oberwolfach, Germany, August 27–September 2, 1972. 相似文献
11.
Matija ?uk 《Icarus》2011,211(1):97-100
The Moon has long been known to have an overall shape not consistent with expected past tidal forces. It has recently been suggested (Garrick-Bethell, I., Wisdom, J., Zuber, M.T. [2006]. Science 313, 652-655) that the present lunar moments of inertia indicate a past high-eccentricity orbit and, possibly, a past non-synchronous spin-orbit resonance. Here I show that the match between the lunar shape and the proposed orbital and spin states is much less conclusive than initially proposed. Garrick-Bethell et al. (Garrick-Bethell, I., Wisdom, J., Zuber, M.T. [2006]. Science 313, 652-655) spin and shape evolution scenarios also completely ignore the physics of the capture into such resonances, which require prior permanent deformation, as well as tidal despinning to the relevant resonance. If the early lunar orbit was eccentric, the Moon would have been rotating at an equilibrium non-synchronous rate determined by it eccentricity. This equilibrium supersynchronous rotation would be much too fast to allow a synchronous spin-orbit lock at e = 0.49, while the capture into the 3:2 resonance is possible only for a very constrained lunar eccentricity history and assuming some early permanent lunar tri-axiality. Here I show that large impacts in the early history of the Moon would have frequently disrupted this putative resonant rotation, making the rotation and eccentricity solutions of Garrick-Bethell et al. (Garrick-Bethell, I., Wisdom, J., Zuber, M.T. [2006]. Science 313, 652-655) unstable. I conclude that the present lunar shape cannot be used to support the hypothesis of an early eccentric lunar orbit. 相似文献
12.
It is shown that emission lines, first of all the ultraviolet resonance doublet 2800 Mgii, can be used to decipher the internal dynamic structure of QSOs and active galactic nuclei. The electron temperatures of the emission regions of these objects are determined. A hypothesis is proposed explaining the observed broad profiles of the 2800 Mgii line as a summary effect of emission clouds with a Maxwellian velocity distribution. The main physical parameters of emission clouds in QSOs are obtained. A mechanism of formation of emission clouds is suggested: namely, tidal disruption of stars near to a massive compact object. 相似文献
13.
In a previous work (Callegari and Yokoyama, Celest. Mech. Dyn. Astr. 98:5–30, 2007), the main features of the motion of the
pair Enceladus–Dione were analyzed in the frozen regime, i.e., without considering the tidal evolution. Here, the results
of a great deal of numerical simulations of a pair of satellites similar to Enceladus and Dione crossing the 2:1 mean-motion
resonance are shown. The resonance crossing is modeled with a linear tidal theory, considering a two-degrees-of-freedom model
written in the framework of the general three-body planar problem. The main regimes of motion of the system during the passage
through resonance are studied in detail. We discuss our results comparing them with classical scenarios of tidal evolution
of the system. We show new scenarios of evolution of the Enceladus–Dione system through resonance not shown in previous approaches
of the problem. 相似文献
14.
Michael Efroimsky 《Celestial Mechanics and Dynamical Astronomy》2012,112(3):283-330
Spin–orbit coupling can be described in two approaches. The first method, known as the “MacDonald torque”, is often combined with a convenient assumption that the quality factor Q is frequency-independent. This makes the method inconsistent, because derivation of the expression for the MacDonald torque
tacitly fixes the rheology of the mantle by making Q scale as the inverse tidal frequency. Spin–orbit coupling can be treated also in an approach called “the Darwin torque”. While this theory is general enough to accommodate an arbitrary frequency-dependence of Q, this advantage has not yet been fully exploited in the literature, where Q is often assumed constant or is set to scale as inverse tidal frequency, the latter assertion making the Darwin torque equivalent
to a corrected version of the MacDonald torque. However neither a constant nor an inverse-frequency Q reflect the properties of realistic mantles and crusts, because the actual frequency-dependence is more complex. Hence it
is necessary to enrich the theory of spin–orbit interaction with the right frequency-dependence. We accomplish this programme
for the Darwin-torque-based model near resonances. We derive the frequency-dependence of the tidal torque from the first principles
of solid-state mechanics, i.e., from the expression for the mantle’s compliance in the time domain. We also explain that the
tidal torque includes not only the customary, secular part, but also an oscillating part. We demonstrate that the lmpq term of the Darwin–Kaula expansion for the tidal torque smoothly passes zero, when the secondary traverses the lmpq resonance (e.g., the principal tidal torque smoothly goes through nil as the secondary crosses the synchronous orbit). Thus,
we prepare a foundation for modeling entrapment of a despinning primary into a resonance with its secondary. The roles of
the primary and secondary may be played, e.g., by Mercury and the Sun, correspondingly, or by an icy moon and a Jovian planet.
We also offer a possible explanation for the “improper” frequency-dependence of the tidal dissipation rate in the Moon, discovered
by LLR. 相似文献
15.
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
16.
Paolo Farinella Andrea Milani Anna M. Nobili Giovanni B. Valsecchi 《Earth, Moon, and Planets》1979,20(4):415-421
We analyze the system formed by Pluto and its satellite Charon from the point of view of the theory of tidal evolution. The singular feature of the system, i.e. the configuration of complete synchronism which has been suggested by the available data, is found to represent the stable end-product of the evolution. The time needed for the synchronization is shown to be less than the age of the solar system, provided that Pluto's tidal dissipation function is smaller than 104–105. Moreover, the initial orbital radius of the system could not be largerthan two or three times the present radius, so that Charon has been always a close satellite.Finally, we discuss Lyttleton's hypothesis that Pluto is an escaped satellite of Neptune, suggesting that a possible mechanism of Pluto's ejection could be connected with a retrograde capture of Triton by Neptune or with the subsequent tidal evolution of Triton's orbit. 相似文献
17.
József Vanyó Bruno Escribano Julyan H. E. Cartwright Diego L. González Oreste Piro Tamás Tél 《Celestial Mechanics and Dynamical Astronomy》2011,109(2):181-200
We study tidal synchronization and orbit circularization in a minimal model that takes into account only the essential ingredients
of tidal deformation and dissipation in the secondary body. In previous work we introduced the model (Escribano et al. in
Phys. Rev. E, 78:036216, 2008); here we investigate in depth the complex dynamics that can arise from this simplest model of tidal synchronization and
orbit circularization. We model an extended secondary body of mass m by two point masses of mass m/2 connected with a damped spring. This composite body moves in the gravitational field of a primary of mass M ≫ m located at the origin. In this simplest case oscillation and rotation of the secondary are assumed to take place in the plane
of the Keplerian orbit. The gravitational interactions of both point masses with the primary are taken into account, but that
between the point masses is neglected. We perform a Taylor expansion on the exact equations of motion to isolate and identify
the different effects of tidal interactions. We compare both sets of equations and study the applicability of the approximations,
in the presence of chaos. We introduce the resonance function as a resource to identify resonant states. The approximate equations
of motion can account for both synchronization into the 1:1 spin-orbit resonance and the circularization of the orbit as the
only true asymptotic attractors, together with the existence of relatively long-lived metastable orbits with the secondary
in p:q (p and q being co-prime integers) synchronous rotation. 相似文献
18.
We investigate the orbital resonant history of Proteus and Larissa, the two largest inner neptunian satellites discovered by Voyager 2. Due to tidal migration, these two satellites probably passed through their 2:1 mean-motion resonance a few hundred million years ago. We explore this resonance passage as a method to excite orbital eccentricities and inclinations, and find interesting constraints on the satellites' mean density () and their tidal dissipation parameters (Qs>10). Through numerical study of this mean-motion resonance passage, we identify a new type of three-body resonance between the satellite pair and Triton. These new resonances occur near the traditional two-body resonances between the small satellites and, surprisingly, are much stronger than their two-body counterparts due to Triton's large mass and orbital inclination. We determine the relevant resonant arguments and derive a mathematical framework for analyzing resonances in this special system. 相似文献
19.
G. I.Ogilvie 《Monthly notices of the Royal Astronomical Society》2002,330(4):937-949
The non-axisymmetric features observed in the discs of dwarf novae in outburst are usually considered to be spiral shocks, which are the non-linear relatives of tidally excited waves. This interpretation suffers from a number of problems. For example, the natural site of wave excitation lies outside the Roche lobe, the disc must be especially hot, and most treatments of wave propagation do not take into account the vertical structure of the disc.
In this paper I construct a detailed semi-analytical model of the non-linear tidal distortion of a thin, three-dimensional accretion disc by a binary companion on a circular orbit. The analysis presented here allows for vertical motion and radiative energy transport, and introduces a simple model for the turbulent magnetic stress. The m =2 inner vertical resonance has an important influence on the amplitude and phase of the tidal distortion. I show that the observed patterns find a natural explanation if the emission is associated with the tidally thickened sectors of the outer disc, which may be irradiated from the centre. According to this hypothesis, it may be possible to constrain the physical parameters of the disc through future observations. 相似文献
In this paper I construct a detailed semi-analytical model of the non-linear tidal distortion of a thin, three-dimensional accretion disc by a binary companion on a circular orbit. The analysis presented here allows for vertical motion and radiative energy transport, and introduces a simple model for the turbulent magnetic stress. The m =2 inner vertical resonance has an important influence on the amplitude and phase of the tidal distortion. I show that the observed patterns find a natural explanation if the emission is associated with the tidally thickened sectors of the outer disc, which may be irradiated from the centre. According to this hypothesis, it may be possible to constrain the physical parameters of the disc through future observations. 相似文献
20.
One of the great discoveries of NASA's Galileo mission was the presence of an intrinsically produced magnetic field at Ganymede. Generation of the relatively strong (750 nT) field likely requires dynamo action in Ganymede's metallic core, but how such a dynamo has been maintained into the present epoch remains uncertain. Using a one-dimensional, three layer thermal model of Ganymede, we find that magnetic field generation can only occur if the sulfur mass fraction in Ganymede's core is very low (?3%) or very high (?21%), and the silicate mantle can cool rapidly (i.e. it has a viscosity like wet olivine). However, these requirements are not necessarily compatible with cosmochemical and physical models of the satellite. We therefore investigate an alternative scenario for producing Ganymede's magnetic field in which passage through an eccentricity pumping Laplace-like resonance in Ganymede's past enables present day dynamo action in the metallic core. If sufficient tidal dissipation occurs in Ganymede's silicate mantle during resonance passage, silicate temperatures can undergo a runaway which prevents the core from cooling until the resonance passage ends. The rapid silicate and core cooling that follows resonance escape triggers dynamo action via thermal and/or compositional convection. To test the feasibility of this mechanism we couple our thermal model with an orbital evolution model to examine the effects of resonance passage on Ganymede's silicate mantle and metallic core. We find that, contrary to expectations, there are no physically plausible scenarios in which tidal heating in the silicates is sufficient to cause the thermal runaway necessary to prevent core cooling. These findings are robust to variations in the silicate rheology, tidal dissipation factor of Jupiter (QJ), structure of the ice shell, and the inclusion of partial melting in the silicate mantle. Resonance passage therefore appears unlikely to explain Ganymede's magnetic field and we must appeal to the special conditions described above to explain the presence of the field. 相似文献