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1.
Recent analytical and numerical modelling has demonstrated the possibility that impulsively-stimulated compressional hydromagnetic cavity resonances can drive local field-line resonances in the magnetosphere. This paper extends the modelling to include axisymmetric plasmapause structures with realistic radial variation in the magnetospheric cavity. The results show that: (a) the plasmapause plays an important rôle in determining which cavity resonances are dominant; (b) when the wave fields are significantly non-axisymmetric, additional cavity resonances are evident which are at least partly trapped within the plasmasphere; (c) the position of the plasmapause determines where (and whether) cavity resonances couple significantly to field-line resonances; (d) for the small “azimuthal” wavenumber chosen, there is no evidence of a compressional surface wave on the plasmapause.  相似文献   

2.
Our aim is to identify and classify mean‐motion resonances (MMRs) for the coplanar circular restricted three‐body problem (CR3BP) for mass ratios between 0.10 and 0.50. Our methods include the maximum Lyapunov exponent, which is used as an indicator for the location of the resonances, the Fast Fourier Transform (FFT) used for determining what kind of resonances are present, and the inspection of the orbital elements to classify the periodicity. We show that the 2:1 resonance occurs the most frequently. Among other resonances, the 3:1 resonance is the second most common, and furthermore both 3:2 and 5:3 resonances occur more often than the 4:1 resonance. Moreover, the resonances in the coplanar CR3BP are classified based on the behaviour of the orbits. We show that orbital stability is ensured for high values of resonance (i.e., high ratios) where only a single resonance is present. The resonances attained are consistent with the previously established resonances for the solar system, i.e., specifically, in regards to the asteroid belt. Previous work employed digital filtering and Lyapunov characteristic exponents to determine stochasticity of the eccentricity, which is found to be consistent with our usage of Lyapunov exponents as an alternate approach based on varying the mass ratio instead of the eccentricity. Our results are expected to be of principal interest to future studies, including augmentations to observed or proposed resonances, of extra‐solar planets in binary stellar systems (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

3.
We present a global view of the resonant structure of the phase space of a planetary system with two planets, moving in the same plane, as obtained from the set of the families of periodic orbits. An important tool to understand the topology of the phase space is to determine the position and the stability character of the families of periodic orbits. The region of the phase space close to a stable periodic orbit corresponds to stable, quasi periodic librations. In these regions it is possible for an extrasolar planetary system to exist, or to be trapped following a migration process due to dissipative forces. The mean motion resonances are associated with periodic orbits in a rotating frame, which means that the relative configuration is repeated in space. We start the study with the family of symmetric periodic orbits with nearly circular orbits of the two planets. Along this family the ratio of the periods of the two planets varies, and passes through rational values, which correspond to resonances. At these resonant points we have bifurcations of families of resonant elliptic periodic orbits. There are three topologically different resonances: (1) the resonances (n + 1):n, (2:1, 3:2, ...), (2) the resonances (2n + 1):(2n-1), (3:1, 5:3, ...) and (3) all other resonances. The topology at each one of the above three types of resonances is studied, for different values of the sum and of the ratio of the planetary masses. Both symmetric and asymmetric resonant elliptic periodic orbits exist. In general, the symmetric elliptic families bifurcate from the circular family, and the asymmetric elliptic families bifurcate from the symmetric elliptic families. The results are compared with the position of some observed extrasolar planetary systems. In some cases (e.g., Gliese 876) the observed system lies, with a very good accuracy, on the stable part of a family of resonant periodic orbits.  相似文献   

4.
The system of Saturn's inner satellites is saturated with many resonances. Its structure should be strongly affected by tidal forces driving the satellites through several orbit–orbit resonances. The evolution of these satellites is investigated using analytic and numerical methods. We show that the pair of satellites Prometheus and Pandora has a particularly short lifetime (<20 Myr) if the orbits of the satellites converge without capture into a resonance. The capture of Pandora into a resonance with Prometheus increases the lifetime of the couple by a few tens of Myr. However, resonances of the system are not well separated, and capture results in a chaotic motion. Secondary resonances also disrupt the resonant configurations. In all cases, the converging orbits of these two satellites result in a close encounter. The implications for the origin of Saturn's rings are discussed.  相似文献   

5.
An essential role in the asteroidal dynamics is played by the mean motion resonances. Two-body planet–asteroid resonances are widely known, due to the Kirkwood gaps. Besides, so-called three-body mean motion resonances exist, in which an asteroid and two planets participate. Identification of asteroids in three-body (namely, Jupiter–Saturn–asteroid) resonances was initially accomplished by Nesvorný and Morbidelli (Nesvorný D., Morbidelli, A. [1998]. Astron. J. 116, 3029–3037), who, by means of visual analysis of the time behaviour of resonant arguments, found 255 asteroids to reside in such resonances. We develop specialized algorithms and software for massive automatic identification of asteroids in the three-body, as well as two-body, resonances of arbitrary order, by means of automatic analysis of the time behaviour of resonant arguments. In the computation of orbits, all essential perturbations are taken into account. We integrate the asteroidal orbits on the time interval of 100,000 yr and identify main-belt asteroids in the three-body Jupiter–Saturn–asteroid resonances up to the 6th order inclusive, and in the two-body Jupiter–asteroid resonances up to the 9th order inclusive, in the set of ～250,000 objects from the “Asteroids – Dynamic Site” (AstDyS) database. The percentages of resonant objects, including extrapolations for higher-order resonances, are determined. In particular, the observed fraction of pure-resonant asteroids (those exhibiting resonant libration on the whole interval of integration) in the three-body resonances up to the 6th order inclusive is ≈0.9% of the whole set; and, using a higher-order extrapolation, the actual total fraction of pure-resonant asteroids in the three-body resonances of all orders is estimated as ≈1.1% of the whole set.  相似文献   

6.
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   

7.
The twenty most chaotic objects found among first hundred of numbered asteroids are studied. Lyapunov time calculated with and without inner planets indicates that for eleven of those asteroids the strongest chaotic effect results from the resonances with Mars. The filtered semimajor axis displays an abrupt variation only when a close approach to Mars takes place. The study of the behaviour of the critical argument for candidate resonances can reveal which is responsible for the semimajor axis variation. We have determined these resonances for the asteroids in question. For the asteroids chaotic even without the inner planets we have determined the most important resonances with Jupiter, or three-body resonances. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

8.
Third and fourth order mean motion resonances are studied in the model of the restricted three-body problem by numerical methods for mass parameters corresponding approximately to the Sun?CJupiter and Sun?CNeptune systems. In the case of inner resonances, it is shown that there are two regions of libration in the 8:5 and 7:4 resonances, one at low, the other at high eccentricities. In the 9:5 and 7:3 resonances libration can exist only in one region at high eccentricities. The 5:2 and 4:1 resonances are very regular, with one librational zone existing for all eccentricities. There is no visible region of libration at any eccentricities in the 5:1 resonance, the transition between the regions of direct and retrograde circulation is very sharp. In the case of outer resonances, the 8:5 and 7:4 resonances have also two regions of libration, but the 9:5 resonance has three, the 7:3 resonance two librational zones. The 5:2 resonance is again very regular, but it is parted for two regions of libration at high eccentricities. Libration is possible in the 4:1 resonance only at high eccentricities. The 5:1 resonance is very symmetric. In the case of outer resonances, a comparison is made with trans-Neptunian objects (TNO) in higher order mean motion resonances. Several new librating TNOs are identified.  相似文献   

9.
We have shown, in previous publications, that stable chaos is associated with medium/high-order mean motion resonances with Jupiter, for which there exist no resonant periodic orbits in the framework of the elliptic restricted three-body problem. This topological “defect” results in the absence of the most efficient mechanism of eccentricity transport (i.e., large-amplitude modulation on a short time scale) in three-body models. Thus, chaotic diffusion of the orbital elements can be quite slow, while there can also exist a nonnegligible set of chaotic orbits which are semiconfined (stable chaos) by “quasi-barriers” in the phase space. In the present paper we extend our study to all mean motion resonances of order q≤9 in the inner main belt (1.9-3.3 AU) and q≤7 in the outer belt (3.3-3.9 AU). We find that, out of the 34 resonances studied, only 8 possess resonant periodic orbits that are continued from the circular to the elliptic three-body problem (regular families), namely, the 2/1, 3/1, 4/1, and 5/2 in the inner belt and the 7/4, 5/3, 11/7, and 3/2 in the outer belt. Numerical results indicate that the 7/3 resonance also carries periodic orbits but, unlike the aforementioned resonances, 7/3-periodic orbits belong to an irregular family. Note that the five inner-belt resonances that carry periodic orbits correspond to the location of the main Kirkwood gaps, while the three outer-belt resonances correspond to gaps in the distribution of outer-belt asteroids noted by Holman and Murray (1996, Astron. J.112, 1278-1293), except for the 3/2 case where the Hildas reside. Fast, intermittent eccentricity increase is found in resonances possessing periodic orbits. In the remaining resonances the time-averaged elements of chaotic orbits are, in general, quite stable, at least for times t∼250 Myr. This slow diffusion picture does not change qualitatively, even if more perturbing planets are included in the model.  相似文献   

10.
A procedure is shown for extracting weak resonances from the responses of electromagnetic systems excited by electric discharges. The procedure, based on analysis of the late-time system response, is first checked using an analytical function and later with the data for the electric field generated by the computational simulation of Titan's atmosphere using the Transmission Line Matrix (TLM) method. Finally, the low frequency spectrum of the natural electric field in Titan's atmosphere sent by the mutual impedance sensor (MIP) included in the Huygens probe is analyzed employing this technique. The MIP sensor was initially designed to measure the horizontal component of the electric field during a quiet descent. Fortunately, the swinging that occurred during the descent allowed the MIP to measure the radial component of the electric field mixed with the horizontal one. Application of the late-time analysis technique shown in this paper confirms the signature of lightning reported by preliminary data observations, bringing out the expected eigenfrequencies of the Titan-ionosphere electromagnetic cavity, known as Schumann resonances. These resonances are the resonant frequencies of the lower TMr (transverse magnetic to r) modes, which are quasi-transverse electromagnetic modes because they present vertical or radial components of the electric field two orders of magnitude higher than the associated horizontal, azimuthal and zenithal, components. The sequence of Schumann resonances is unique for each celestial body with an ionosphere, since these resonances are fully determined by the dimensions of the planet or satellite and the corresponding atmospheric conductivity profile. Detecting these frequencies in an atmosphere is clear proof of electrical activity, since it implies the existence of an electromagnetic-energy source, which is essential to create and maintain them.  相似文献   

11.
In the last three years we have carried out numerical and semi-analytical studies on the secular dynamical mechanisms in the region (semimajor axis a < 2 AU) where the NEA orbits evolve. Our numerical integrations (over a time span of a few Myr) have shown that: (i) the linear secular resonances with both the inner and the outer planets may play an important role in the dynamical evolution of NEAs; (ii) the apsidal secular resonance with Mars could provide an important dynamical transport mechanism by which asteroids in the Mars-crossing region eventually achieve Earth-crossing orbits; (iii) in this region, due to the interaction with the terrestrial planets, the Kozai resonance can occur at small inclinations, with the argument of perihelion ω librating around 0° or 180°, providing a temporary protection mechanism against close approaches to the planets. The location of the linear secular resonances in this zone has also been obtained by an automatic procedure using a semi-numerical method valid for all values of the inclinations and eccentricities of the small bodies, and also in the case of libration of the argument of perihelion. A map of the secular resonances in the (a, i) plane shows — in agreement with the numerical integrations — that all the resonances with the terrestrial and giant planets are present, and also that some of them overlap. Thus the way is now open to fully take into account secular resonances in modelling the dynamical evolution of NEAs. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

12.
In extending the analysis of the four secular resonances between close orbits in Li and Christou (Celest Mech Dyn Astron 125:133–160, 2016) (Paper I), we generalise the semianalytical model so that it applies to both prograde and retrograde orbits with a one-to-one map between the resonances in the two regimes. We propose the general form of the critical angle to be a linear combination of apsidal and nodal differences between the two orbits \( b_1 \Delta \varpi + b_2 \Delta \varOmega \), forming a collection of secular resonances in which the ones studied in Paper I are among the strongest. Test of the model in the orbital vicinity of massive satellites with physical and orbital parameters similar to those of the irregular satellites Himalia at Jupiter and Phoebe at Saturn shows that \({>}20\) and \({>}40\%\) of phase space is affected by these resonances, respectively. The survivability of the resonances is confirmed using numerical integration of the full Newtonian equations of motion. We observe that the lowest order resonances with \(b_1+|b_2|\le 3\) persist, while even higher-order resonances, up to \(b_1+|b_2|\ge 7\), survive. Depending on the mass, between 10 and 60% of the integrated test particles are captured in these secular resonances, in agreement with the phase space analysis in the semianalytical model.  相似文献   

13.
We study the excitation of density and bending waves and the associated angular momentum transfer in gaseous discs with finite thickness by a rotating external potential. The disc is assumed to be isothermal in the vertical direction and has no self-gravity. The disc perturbations are decomposed into different modes, each characterized by the azimuthal index m and the vertical index n , which specifies the nodal number of the density perturbation along the disc normal direction. The   n = 0  modes correspond to the two-dimensional density waves previously studied by Goldreich & Tremaine and others. In a three-dimensional disc, waves can be excited at both Lindblad resonances (LRs; for modes with   n = 0, 1, 2, …  ) and vertical resonances (VRs; for the   n ≥ 1  modes only). The torque on the disc is positive for waves excited at outer Lindblad/vertical resonances and negative at inner Lindblad/vertical resonances. While the   n = 0  modes are evanescent around corotation, the   n ≥ 1  modes can propagate into the corotation region where they are damped and deposit their angular momenta. We have derived analytical expressions for the amplitudes of different wave modes excited at LRs and/or VRs and the resulting torques on the disc. It is found that for   n ≥ 1  , angular momentum transfer through VRs is much more efficient than LRs. This implies that in some situations (e.g. a circumstellar disc perturbed by a planet in an inclined orbit), VRs may be an important channel of angular momentum transfer between the disc and the external potential. We have also derived new formulae for the angular momentum deposition at corotation and studied wave excitations at disc boundaries.  相似文献   

14.
Lunisolar resonances arise in the artificial satellite problem without short-periodic terms. The basic model including the Earth's J 2and a Hill-type model for the Sun or the Moon admits 20 different periodic terms which may lead to a resonance involving the satellite's perigee, node and the longitude of the perturbing body. Some of the resonances have been studied separately since 1960s. The present paper reviews all single resonances, attaching an appropriate fundamental model to each case. Only a part of resonances match known fundamental models. An extended fundamental model is proposed to account for some complicated phenomena. Most of the double resonance cases still remain unexplored.  相似文献   

15.
The general theory exposed in the first part of this paper is applied to the following resonances with Jupiter's motion : 3/2, 2/1, 5/2, 3/1, 7/2, 4/1; these are the most relevant resonances for the asteroids. The whole analysis is performed in the framework of the spatial problem of three bodies, both in the circular and in the elliptic case. The results are also compared with the observed distribution of the asteroids.  相似文献   

16.
In a previous paper (Gayon and Bois 2008a), we have shown the general efficiency of retrograde resonances for stabilizing compact planetary systems. Such retrograde resonances can be found when two-planets of a three-body planetary system are both in mean motion resonance and revolve in opposite directions. For a particular two-planet system, we have also obtained a new orbital fit involving such a counter-revolving configuration and consistent with the observational data. In the present paper, we analytically investigate the three-body problem in this particular case of retrograde resonances. We therefore define a new set of canonical variables allowing to express correctly the resonance angles and obtain the Hamiltonian of a system harboring planets revolving in opposite directions. The acquiring of an analytical “rail” may notably contribute to a deeper understanding of our numerical investigation and provides the major structures related to the stability properties. A comparison between our analytical and numerical results is also carried out.  相似文献   

17.
The temporary capture of the dust grains in the exterior resonances with planets is studied in the frames of the planar circular three-body problem with Poynting-Robertson (PR) drag. For the Earth and particles ~ 10 Μm the resonances 4/5, 5/6, 6/7, 7/8 are shown to be most effective. The capture is only temporary (of order 105 years) and the position of resonance may be calculated from semi-analytical model using averaged disturbing function. These semi-analytical results are confirmed by numerical integration. For various planet this picture changes as with increasing planetary mass the more exterior resonances become more important. We showed that for Jupiter (at least in the space between Jupiter and Saturn) the resonance 1/2 plays the dominant role. The capture time is here several myr but again eccentricity is evolving to eccentricity e 0 ~ 0.48 of libration point for this resonance.  相似文献   

18.
This paper presents a comparative analysis of the 2/1 and 3/2 asteroidal resonances based on several analytical and numerical tools. The frequency map analysis was used to obtain a refined estimation of the chaotic transport. Fourier and wavelet analyses were used to construct the web of inner resonances and showed that they are the seat of the strongly unstable motion observed in the numerical simulations. The most regular regions in both resonances were classified. A fast symplectic mapping allowed a number of direct runs over 108 years of the orbits initially in these regions. The stability of orbits over the age of the solar system was discussed and compared to the distribution of the observed asteroids in both resonances.  相似文献   

19.
We have investigated the pericentric resonances through which Miranda and Umbriel are believed to have passed when, due to tidal evolution, their orbital mean motions reached a 3 : 1 commensurability. Our investigation is based upon a perturbative treatment. The predictions of this theory are in good agreement with the results of numerical integrations concerning both the extend of the chaotic layers generated by the separatrices of the primary resonances and the location of the secondary resonances. The effect of tidal evolution is discussed on the bases of the adiatatic invariant theory and its extension to separatrix crossing. We recover qualitatively the mean features of the numerical experiments of Tittermore and Wisdom (1988–1989), Dermott et al (1988) and Malhotra and Dermott (1989).  相似文献   

20.
In preparation for the Rosetta mission, the location and widths of gravitational resonances surrounding a regularly shaped and possibly complex rotating body are mapped following the second fundamental model of resonance. It is found that for uniaxial rotation of the central body, the surrounding resonances are widest for prograde orbits. If the figure axis is tilted with respect to the spin axis of the central body, an additional number of wide resonances appear with a preference for prograde and inclined orbits, and the occurrence of initial conditions which lie in the globally connected chaotic web is significantly increased. For larger rotational excitations, it is seen how these new additional resonances overlap internally at low eccentricity for very large semi-major axes. However, with exceptions for some excited short-axis rotational modes of the central body, it is argued that most resonances vanish for retrograde orbits lying in the plane normal to the body spin, and that resonant or non-resonant stability therefore can be expected for a wide range of mean orbit eccentricities.  相似文献   

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