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1.
In papers (Godziewski and Maciejewski, 1998a, b, 1999), we investigate unrestricted, planar problem of a dynamically symmetric rigid body and a sphere. Following the original statement of the problem by Kokoriev and Kirpichnikov (1988), we assume that the potential of the rigid body is approximated by the gravitational field of a dumb-bell. The model is described in terms of a 2D Hamiltonian depending on three parameters.In this paper, we investigate the stability of triangular equilibria permissible by the dynamics of the model, under the assumption of low-order resonances. We analyze all resonances of order smaller than four, and we examine the stability with application of theorems by Markeev and Sokolsky. These are the possible following cases: the non-diagonal resonance of the first order with two null characteristic frequencies (unstable); resonances of the first order with one nonzero frequency (diagonal and non-diagonal, stable and unstable); the second-order resonance, which is non-diagonal and stable, and the third-order resonance which is generically unstable, except for three points in the parameters' space, corresponding to stable equilibria.We discuss a perturbed version of Kokoriev and Kirpichnikov model, and we find that if the perturbation is small and depends on the coordinates only, the triangular equilibria persist, except if for the unperturbed equilibria the first-order resonance occurs. We show that the resonances of the order higher than two are also preserved if the perturbation acts.  相似文献   

2.
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3.
Tabaré Gallardo 《Icarus》2006,184(1):29-38
The aim of this work is to present a systematic survey of the strength of the mean motion resonances (MMRs) in the Solar System. We know by applying simple formulas where the resonances with the planets are located but there is no indication of the strength that these resonances have. We propose a numerical method for the calculation of this strength and we present an atlas of the MMRs constructed with this method. We found there exist several resonances unexpectedly strong and we look and find in the small bodies population several bodies captured in these resonances. In particular in the inner Solar System we find one asteroid in the resonance 6:5 with Venus, five asteroids in resonance 1:2 with Venus, three asteroids in resonance 1:2 with Earth and six asteroids in resonance 2:5 with Earth. We find some new possible co-orbitals of Earth, Mars, Saturn, Uranus and Neptune. We also present a discussion about the behavior of the resonant disturbing function and where the stable equilibrium points can be found at low and high inclination resonant orbits.  相似文献   

4.
We resume and consistently extend our previous researches concerning the Gyldén‐type problem (a two‐body problem with time‐dependent equivalent gravitational parameter). To approach most of the concrete astronomical situations to be modelled in this way, we consider a periodic small perturbation. For the nonresonant case, we present a second‐order analytical solution. For the resonant case, we adopt the most realistic astronomical situation: only one dominant term of the Hamiltonian. In this case we point out a fundamental model of resonance, common to every resonant situation, and, moreover, identical to the first fundamental model of resonance . Considering the simplest model of periodic change of the equivalent gravitational parameter, we .nd that all possible resonances are con.ned to the first fundamental model. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

5.
Planets form in active protoplanetary disks that sustain stellar jets. Momentum loss from the jet system may excite the planets’ orbital eccentricity and inclination (Namouni in Astron. J. 130:280, 2005). Evaluating quantitatively the effects of such excitation requires a realistic modeling of the momentum loss profiles associated with stellar jets. In this work, we model linear momentum loss as a time-variable stochastic process that results in a zero mean stellar acceleration. Momentum loss may involve periodic or random polarity reversals. We characterize orbital excitation as a function of the variability timescale and identify a novel excitation resonance between a planet’s orbital period and the jet’s variability timescale where the former equals twice the latter. For constant variability timescales, resonance is efficient for both periodic and random polarity reversals, the latter being stronger than the former. For a time variable variability timescale, resonance crossing is a more efficient excitation mechanism when polarity reversals are periodic. Each polarity reversal type has distinct features that may help constrain the magnetic history of the star through the observation of its planetary companions. For instance, outward planet migration to large distances from parent stars is one of the natural outcomes of periodic polarity reversal excitation if resonance crossing is sufficiently slow. Applying the excitation mechanism to the solar system, we find that the planet-jet variability resonance with periodic polarity reversal momentum loss is a possible origin for the hitherto unexplained inclination of Jupiter’s orbit by 6° with respect to the Sun’s equator.  相似文献   

6.
In the resonance model, high‐frequency quasi‐periodic oscillations (QPOs) are supposed to be a consequence of nonlinear resonance between modes of oscillations occurring within the innermost parts of an accretion disk. Several models with a prescribed mode–mode interaction were proposed in order to explain the characteristic properties of the resonance in QPO sources. In this paper, we examine nonlinear oscillations of a system having a quadratic nonlinearity and we show that this case is particularly relevant for QPOs. We present a very convenient way how to study autoparametric resonances of a fully general system using the method of multiple scales. We concentrate to conservative systems and discuss their behavior near the 3:2 parametric resonance. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

7.
A stochastic model of the Earth-Moon tidal evolution taking into account fluctuating effects of the continental drift is described. The above effects caused by alternation of periods of consolidation and disintegration of continents are specified as a combination of cyclic variations and superimposed random perturbations of the ocean eigenoscillation spectrum. The solution is found with use of one-mode and multi-mode resonance approximations. In other words, we assume that the ocean response to the Moon's forcing is due to one or several resonant modes predominant over all other ocean eigenoscillations. For the multi-mode resonance approximation, the model ensures a proper time scale of the Earth-Moon tidal evolution and qualitative agreement of predicted changes in the number of solar days and synodic months per year with paleontological and sedimentological data. Moreover, it makes possible fitting of model estimates of tidal energy dissipation to those derived from global paleotide models for different periods of the Phanerozoic.  相似文献   

8.
We present a symplectic mapping model to study the evolution of a small body at the 3/4 exterior resonance with Neptune, for planar and for three dimensional motion. The mapping is based on the averaged Hamiltonian close to this resonance and is constructed in such a way that the topology of its phase space is similar to that of the Poincaré map of the elliptic restricted three-body problem. Using this model we study the evolution of a small object near the 3/4 resonance. Both chaotic and regular motions are found, and it is shown that the initial phase of the object plays an important role on the appearance of chaos. In the planar case, objects that are phase-protected from close encounters with Neptune have regular orbits even at eccentricities up to 0.44. On the other hand objects that are not phase protected show chaotic behaviour even at low eccentricities. The introduction of the inclination to our model affects the stable areas around the 3/4 mean motion resonance, which now become thinner and thinner and finally at is=10° the whole resonant region becomes chaotic. This may justify the absence of a large population of objects at this resonance.  相似文献   

9.
Jiang & Yeh proposed gas-drag-induced resonant capture as a mechanism able to explain the dominant 3:2 resonance observed in the trans-Neptunian belt. Using a model of a disc–star–planet system they concluded that gaseous drag in a protoplanetary disc can trap trans-Neptunian object (TNO) embryos into the 3:2 resonance rather easily although it could not trap objects into the 2:1 resonance. Here we further investigate this scenario using numerical simulations within the context of the planar restricted four-body problem by including both present-day Uranus and Neptune. Our results show that mean motion and corotation resonances are possible and trapping into both the 3:2 and 2:1 resonances as well as other resonances is observed. The associated corotation centres may easily form larger planetesimals from smaller ones. Corotation resonances evolve into pure Lindblad resonances in a time-scale of 0.5 Myr. The non-linear corotation and mean motion resonances produced are very size selective. The 3:2 resonance is dominant for submetric particles but for larger particles the 2:1 resonance is stronger. In summary, our calculations show that confined chaotic motion around the resonances not only increases trapping efficiency but also the orbital eccentricities of the trapped material, modifying the relative abundance of trapped particles in different resonances. If we assume a more compact planetary system, instead of using the present-day values of the orbital elements of Uranus and Neptune, our results remain largely unchanged.  相似文献   

10.
We found a hydrodynamic pulsation model of yellow supergiants under subharmonic resonance. It is confirmed that the feature of pulsation by the resonance is long-lived in the model by performing the hydrodynamical simulation for a long time.  相似文献   

11.
By studying orbits of asteroids potentially in 3:2 exterior mean motion resonance with Earth, Venus, and Mars, we have found plutino analogs. We identify at least 27 objects in the inner Solar System dynamically protected from encounter through this resonance. These are four objects associated with Venus, six with Earth, and seventeen with Mars. Bodies in the 3:2 exterior resonance (including those in the plutino resonance associated with Neptune) orbit the Sun twice for every three orbits of the associated planet, in such a way that with sufficiently low libration amplitude close approaches to the planet are impossible. As many as 15% of Kuiper Belt objects share the 3:2 resonance, but are poorly observed. One of several resonance sweeping mechanisms during planetary migration is likely needed to explain the origin and properties of 3:2 resonant Kuiper Belt objects. Such a mechanism likely did not operate in the inner Solar System. We suggest that scattering by the next planet out allows entry to, and exit from, 3:2 resonance for objects associated with Venus or Earth. 3:2 resonators of Mars, on the other hand, do not cross the paths of other planets, and have a long lifetime. There may exist some objects trapped in the 3:2 Mars resonance which are primordial, with our tests on the most promising objects known to date indicating lifetimes of at least tens of millions of years. Identifying 3:2 resonant systems in the inner Solar System permits this resonance to be studied on shorter timescales and with better determined orbits than has been possible to date, and introduces new mechanisms for entry into the resonant configuration.  相似文献   

12.
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   

13.
We have looked for and found a possible spatial correlation between the present pulsar distribution and the estimated locations of the spiral arms at earlier epochs. Through a detailed statistical analysis we find a significant correlation between the present distribution of pulsars and the mass distribution (in the spiral arms) expected about 60 Myr ago for a corotation resonance radius of 14kpc. We discuss the implications of this correlation for the minimum mass of the progenitors of pulsars. Interpreting the spread in the locations of pulsars with respect to the past locations of the spiral arms as predominantly due to their space velocities, we derive an average velocity for the pulsar population.  相似文献   

14.
In order to understand the observed oscillations in sunspots we present a new method for calculating the resonant response of a realistic semi-empirical model of the sunspot umbral atmosphere and subphotosphere to magneto-atmospheric waves in a vertical magnetic field. The depth dependence of both the adiabatic coefficient and the turbulent pressure is taken into account. This requires an extension of the wave equations by Ferraro & Plumpton (1958). We compare the coefficients of wave transmission, re flection, and conversion between fast mode and slow mode waves for different assumptions, compare the results with those from earlier modelling efforts, and point out possible sources of mistakes. The depth dependence of the adiabatic coefficient strongly influences the resulting spectrum of resonance frequencies. The condition of a conservation of wave flux is violated if the depth dependence of the turbulent pressure is not properly considered.  相似文献   

15.
On the basis of a high-order (order 12) expansion of the perturbative potential in powers of the eccentricities and the inclinations, we analyze the secular interactions of two non-coplanar planets which are not in mean-motion resonance. The model is based on the planetary three-body problem which can be reduced to two degrees of freedom by the well-known elimination of the nodes [Jacobi, C.G.J., 1842. Astron. Nachr. XX, 81-102]. We introduce non-singular canonical variables which bring forward the symmetries of the problem. The main dynamical features depend on the location and stability of the equilibria which are easily found with our analytical model. We find that there exists an equilibrium when both eccentricities are zero. When the mutual inclination is small, this equilibrium is stable, but for larger mutual inclination it becomes unstable, generating a large chaotic zone and, by bifurcation, two regular regions, the so-called Kozai resonances. This analytical study which depends on only two parameters (the ratio of the semi-major axes and the mass ratio of the planets) makes possible a large survey of the problem and enables us to identify and quantify its main dynamical features, periodic orbits, regular and chaotic zones, etc. The results of our analytical model are illustrated and confirmed by numerical integrations.  相似文献   

16.
We carry out simulations to investigate the dynamics of the HD 82943 planetary system with two resonant Jupiter-like planets, and to reveal possible stabilizing mechanism for the system. By following different coplanar configurations in the neighborhood of the best-fit orbits, we find that all the stable cases are involved in the 2:1 mean motion resonance and that the alignment of the periastra of the two planets also plays important part in the secular orbital evolution, indicating that these two kinds of mechanisms could be responsible for the dynamics of the system under study.  相似文献   

17.
A Hamiltonian model is constructed for the spin axis of a planet perturbed by a nearby planet with both planets in orbit about a star. We expand the planet–planet gravitational potential perturbation to first order in orbital inclinations and eccentricities, finding terms describing spin resonances involving the spin precession rate and the two planetary mean motions. Convergent planetary migration allows the spinning planet to be captured into spin resonance. With initial obliquity near zero, the spin resonance can lift the planet’s obliquity to near 90\(^\circ \) or 180\(^\circ \) depending upon whether the spin resonance is first or zeroth order in inclination. Past capture of Uranus into such a spin resonance could give an alternative non-collisional scenario accounting for Uranus’s high obliquity. However, we find that the time spent in spin resonance must be so long that this scenario cannot be responsible for Uranus’s high obliquity. Our model can be used to study spin resonance in satellite systems. Our Hamiltonian model explains how Styx and Nix can be tilted to high obliquity via outward migration of Charon, a phenomenon previously seen in numerical simulations.  相似文献   

18.
F. MarzariH. Scholl 《Icarus》2002,159(2):328-338
We have numerically explored the mechanisms that destabilize Jupiter's Trojan orbits outside the stability region defined by Levison et al. (1997, Nature385, 42-44). Different models have been exploited to test various possible sources of instability on timescales on the order of ∼108 years.In the restricted three-body model, only a few Trojan orbits become unstable within 108 years. This intrinsic instability contributes only marginally to the overall instability found by Levison et al.In a model where the orbital parameters of both Jupiter and Saturn are fixed, we have investigated the role of Saturn and its gravitational influence. We find that a large fraction of Trojan orbits become unstable because of the direct nonresonant perturbations by Saturn. By shifting its semimajor axis at constant intervals around its present value we find that the near 5:2 mean motion resonance between the two giant planets (the Great Inequality) is not responsible for the gross instability of Jupiter's Trojans since short-term perturbations by Saturn destabilize Trojans, even when the two planets are far out of the resonance.Secular resonances are an additional source of instability. In the full six-body model with the four major planets included in the numerical integration, we have analyzed the effects of secular resonances with the node of the planets. Trojan asteroids have relevant inclinations, and nodal secular resonances play an important role. When a Trojan orbit becomes unstable, in most cases the libration amplitude of the critical argument of the 1:1 mean motion resonance grows until the asteroid encounters the planet. Libration amplitude, eccentricity, and nodal rate are linked for Trojan orbits by an algebraic relation so that when one of the three parameters is perturbed, the other two are affected as well. There are numerous secular resonances with the nodal rate of Jupiter that fall inside the region of instability and contribute to destabilize Trojans, in particular the ν16. Indeed, in the full model the escape rate over 50 Myr is higher compared to the fixed model.Some secular resonances even cross the stability region delimited by Levison et al. and cause instability. This is the case of the 3:2 and 1:2 nodal resonances with Jupiter. In particular the 1:2 is responsible for the instability of some clones of the L4 Trojan (3540) Protesilaos.  相似文献   

19.
We consider the application of the statistical method of phase mixing to the approximate Poincaré solution to resonant motion. The two Poincaré integrals of the motion for the restricted problem of three bodies are introduced to first order in the eccentricity. The theory of the phase mixing of an initialad hoc distribution of particles is then developed for this dynamical system, and the absence of significant evolution of the system far from resonance is verified.A selection of results is given for the 21, 31, and 52 resonances, which show in general a peak on the low side of exact resonance and a gap on the high side. The amplitudes of both the peak and the gap decrease, and their relative separation increases as the resonance order increases, or as the initial distribution is shifted to higher eccentricities. Comparison with large numbers of numerically integrated orbits gives good agreement with the model, at least for small eccentricities. However, the model is unable to exhibit the clean gaps shown by the real asteroid belt. Hence, a purely statistical model of the Kirkwood gaps is ruled out, and we must search for an additional mechanism. Some speculation on possible additional mechanisms is offered.  相似文献   

20.
Generalization of the escape probability method introduced by Sobolev allows us to study the transfer of spectral line radiation for a resonance doublet in rapidly expanding envelopes.For the cases of outward-accelerating (or equivalently inward-decelerating) and outward-decelerating (or equivalently inward-accelerating) envelopes we derive, in the frame of a three-level atom model, the expressions for the spectral radiation fieldsJ 12 andJ 13, for the resulting radiative force FRE exerted per atom and for the resonance doublet profileE(X)/C c; we take into account the complex radiative coupling, in both resonance transitions 12 and 13, between distant parts of the atmosphere.For various physical and geometrical conditions prevailing in the expanding media, we illustrate and discuss the behaviours of those quantities as well as their dependence on the parameters of the model. Namely, we deduce criteria under which resonance doublet profiles formed in outward-accelerating and/or outward-decelerating envelopes would appear to be resolved into double P Cygni profiles.We also stress the importance of treating a resonance doublet as being formed by two distinct resonance transitions when evaluating the resulting radiative force FRE acting on an atom. It is indeed shown that if we use a two-level atom model to represent a resonance doublet-i.e., assigning to it an oscillator strength equal to the sum of the oscillator strengths of both resonance transitions-the amplitude of the resulting radiative force can be underestimated by factors reaching 100% and more in the regions of the expanding envelope which are optically thick to the spectral line radiation. In this context, it would be essential to revise the previous models of radiation-driven winds developed for early-type stars in which the lines belonging to any multiplet were treated as a single line.Also, Aspirant au Fonds National de la Recherche Scientifique (Belgium).  相似文献   

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