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1.
The recent numerical simulations of Tittemore and Wisdom (1988, 1989, 1990) and Dermottet al. (1988), Malhotra and Dermott (1990) concerning the tidal evolution through resonances of some pairs of Uranian satellites have revealed interesting dynamical phenomena related to the interactions between close-by resonances. These interactions produce chaotic layers and strong secondary resonances. The slow evolution of the satellite orbits in this dynamical landscape is responsible for temporary capture into resonance, enhancement of eccentricity or inclination and subsequent escape from resonance. The present contribution aims at developing analytical tools for predicting the location and size of chaotic layers and secondary resonances. The problem of the 3:1 inclination resonance between Miranda and Umbriel is analysed. 相似文献
2.
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
3.
The origin of Neptune’s large, circular but retrograde satellite Triton has remained largely unexplained. There is an apparent consensus that its origin lies in it being captured, but until recently no successful capture mechanism has been found. Agnor and Hamilton (Agnor, C.B., Hamilton, D.P. [2006]. Nature 441, 192-194) demonstrated that the disruption of a trans-neptunian binary object which had Triton as a member, and which underwent a very close encounter with Neptune, was an effective mechanism to capture Triton while its former partner continued on a hyperbolic orbit. The subsequent evolution of Triton’s post-capture orbit to its current one could have proceeded through gravitational tides (Correia, A.C.M. [2009]. Astrophys. J. 704, L1-L4), during which time Triton was most likely semi-molten (McKinnon, W.B. [1984]. Nature 311, 355-358). However, to date, no study has been performed that considered both the capture and the subsequent tidal evolution. Thus it is attempted here with the use of numerical simulations. The study by Agnor and Hamilton (Agnor, C.B., Hamilton, D.P. [2006]. Nature 441, 192-194) is repeated in the framework of the Nice model (Tsiganis, K., Gomes, R., Morbidelli, A., Levison, H.F. [2005]. Nature 435, 459-461) to determine the post-capture orbit of Triton. After capture Triton is then subjected to tidal evolution using the model of Mignard (Mignard, F. [1979]. Moon Planets 20, 301-315; Mignard, F. [1980]. Moon Planets 23, 185-201). The perturbations from the Sun and the figure of Neptune are included. The perturbations from the Sun acting on Triton just after its capture cause it to spend a long time in its high-eccentricity phase, usually of the order of 10 Myr, while the typical time to circularise to its current orbit is some 200 Myr, consistent with earlier studies. The current orbit of Triton is consistent with an origin through binary capture and tidal evolution, even though the model prefers Triton to be closer to Neptune than it is today. The probability of capturing Triton in this manner is approximately 0.7%. Since the capture of Triton was at most a 50% event - since only Neptune has one, but Uranus does not - we deduce that in the primordial trans-neptunian disc there were some 100 binaries with at least one Triton-sized member. Morbidelli et al. (Morbidelli, A., Levison, H.F., Bottke, W.F., Dones, L., Nesvorný, D. [2009]. Icarus 202, 310-315) concludes there were some 1000 Triton-sized bodies in the trans-neptunian proto-planetary disc, so the primordial binary fraction with at least one Triton-sized member is 10%. This value is consistent with theoretical predictions, but at the low end. If Triton was captured at the same time as Neptune’s irregular satellites, the far majority of these, including Nereid, would be lost. This suggests either that Triton was captured on an orbit with a small semi-major axisa ? 50RN (a rare event), or that it was captured before the dynamical instability of the Nice model, or that some other mechanism was at play. The issue of keeping the irregular satellites remains unresolved. 相似文献
4.
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
5.
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
6.
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
7.
The three-dimensional secular behavior of a system composed of a central star and two massive planets is modeled semi-analytically in the frame of the general three-body problem. The main dynamical features of the system are presented in geometrical pictures allowing us to investigate a large domain of the phase space of this problem without time-expensive numerical integrations of the equations of motion and without any restriction on the magnitude of the planetary eccentricities, inclinations and mutual distance. Several regimes of motion of the system are observed. With respect to the secular angle Δ?, possible motions are circulations, oscillations (around 0° and 180°), and high-eccentricity/inclination librations in secular resonances. With respect to the arguments of pericenter, ω1 and ω2, possible motions are direct circulation and high-inclination libration around ±90° in the Lidov-Kozai resonance. The regions of transition between domains of different regimes of motion are characterized by chaotic behavior. We apply the analysis to the case of the two outer planets of the υ Andromedae system, observed edge-on. The topology of the 3-D phase space of this system is investigated in detail by means of surfaces of section, periodic orbits and dynamical spectra, mapping techniques and numerical simulations. We obtain the general structure of the phase space, and the boundaries of the spatial secular stability. We find that this system is secularly stable in a large domain of eccentricities and inclinations. 相似文献
8.
Harrington and Van Flandern (1979, Icarus39, 131–136) suggests that the irregular features of the Neptunian satellite system and Pluto's escape were caused by an encounter with a massive external body. They rule out the alternative mechanism based on the capture of Triton (which seems more plausible because it does not appeal to any unobserved object) on the basis of an incorrect deduction from McCord's (1966, Astron. J.71, 585–590) analysis on the tidal decay of Triton's orbit. As a matter of fact, many recent results show that satellite captures are possible, and in the case of Triton several arguments support this interpretation. 相似文献
9.
G. Voyatzis K. I. Antoniadou K. Tsiganis 《Celestial Mechanics and Dynamical Astronomy》2014,119(3-4):221-235
We consider a two-planet system migrating under the influence of dissipative forces that mimic the effects of gas-driven (Type II) migration. It has been shown that, in the planar case, migration leads to resonant capture after an evolution that forces the system to follow families of periodic orbits. Starting with planets that differ slightly from a coplanar configuration, capture can, also, occur and, additionally, excitation of planetary inclinations has been observed in some cases. We show that excitation of inclinations occurs, when the planar families of periodic orbits, which are followed during the initial stages of planetary migration, become vertically unstable. At these points, vertical critical orbits may give rise to generating stable families of \(3D\) periodic orbits, which drive the evolution of the migrating planets to non-coplanar motion. We have computed and present here the vertical critical orbits of the \(2/1\) and \(3/1\) resonances, for various values of the planetary mass ratio. Moreover, we determine the limiting values of eccentricity for which the “inclination resonance” occurs. 相似文献
10.
We investigate the orbital history of the small neptunian satellites discovered by Voyager 2. Over the age of the Solar System, tidal forces have caused the satellites to migrate radially, bringing them through mean-motion resonances with one another. In this paper, we extend our study of the largest satellites Proteus and Larissa [Zhang, K., Hamilton, D.P., 2007. Icarus 188, 386-399] by adding in mid-sized Galatea and Despina. We test the hypothesis that these moons all formed with zero inclinations, and that orbital resonances excited their tilts during tidal migration. We find that the current orbital inclinations of Proteus, Galatea, and Despina are consistent with resonant excitation if they have a common density . Larissa's inclination, however, is too large to have been caused by resonant kicks between these four satellites; we suggest that a prior resonant capture event involving either Naiad or Thalassa is responsible. Our solution requires at least three past resonances with Proteus, which helps constrain the tidal migration timescale and thus Neptune's tidal quality factor: 9000<QN<36,000. We also improve our determination of Qs for Proteus and Larissa, finding 36<QP<700 and 18<QL<200. Finally, we derive a more general resonant capture condition, and work out a resonant overlap criterion relevant to satellite orbital evolution around an oblate primary. 相似文献
11.
Bálint Érdi Emese Forgács-Dajka Imre Nagy Renáta Rajnai 《Celestial Mechanics and Dynamical Astronomy》2009,104(1-2):145-158
The size of the stable region around the Lagrangian point L 4 in the elliptic restricted three-body problem is determined by numerical integration as a function of the mass parameter and eccentricity of the primaries. The size distribution of the stable regions in the mass parameter-eccentricity plane shows minima at certain places that are identified with resonances between the librational frequencies of motions around L 4. These are computed from an approximate analytical equation of Rabe relating the frequency, mass parameter and eccentricity. Solutions of this equation are determined numerically and the global behaviour of the frequencies depending on the mass parameter and eccentricity is shown and discussed. The minimum sizes of the stable regions around L 4 change along the resonances and the relative strength of the resonances is analysed. Applications to possible Trojan exoplanets are indicated. Escape from L 4 is also investigated. 相似文献
12.
This paper is third in a series, studying the optical properties of a sample of Seyfert galaxies. Here we present a homoge neous set of global (ellipticity, position angle, inclination, and total magnitude) and isophotal (semi‐major axis and colour indices at 24V mag arcsec–2) parameters of the galaxy sample. We find the following median corrected isophotal colour indices: (B – IC)(0)24 = 1.9 mag arcsec–2 and (V – IC)(0)24 = 1.1 mag arcsec–2. A set of bar parameters (ellipticity, position angle, semi‐major axis corresponding to the ellipticity maximum in the bar region, and length) are also reported; deprojection has been applied to the bar ellipticity, length, and relative length in terms of galaxy isophotal semi‐major axis. Regarding bar length estimation, we use a method, based on the relation between the behaviour of the profiles and orbit analysis. The so estimated bar length tightly correlates with the semi‐major axis, corresponding to the ellipticity maximum with a median ratio of the former to the latter of 1.22. The median of the deprojected bar ellipticity, length, and relative length are 0.39, 5.44 kpc, and 0.44, respectively. There is a correlation between the deprojected bar length and the corrected isophotal semi‐major axis at 24V mag arcsec–2. Three of the 17 large‐scale bars appear strong, based on the deprojected bar ellipticity as a first‐order approximation of bar strength. The deprojected relative bar length does not appear to correlate with the bar ellipticity (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
13.
This paper investigates the combined effect of small perturbations ε,ε′ in the Coriolis and centrifugal forces, radiation pressure q i , and changing oblateness of the primaries A i (t) (i=1,2) on the stability of equilibrium points in the restricted three body problem in which the primaries is a supergiant eclipsing binary system which consists of a pair of bright oblate stars having the appearance of a giant peanut in space and their masses assumed to vary with time in the absence of reactive forces. The equations of motion are derived and the equilibrium points are obtained. For the autonomized system, it is seen that there are more than a pair of the triangular points as κ→∞; κ being the arbitrary sum of the masses of the primaries. In the case of the collinear points, two additional equilibrium points exist on the line joining the primaries when simultaneously κ+ε′<0 and both primaries are oblate, i.e., 0<α i ?1. So there are five collinear equilibrium points in this case. Two non-planar equilibrium points exist for κ>1. Hence, there are at least nine equilibrium points of the system. The stability of these points is explored analytically and numerically. It is seen that the collinear and triangular points are stable with respect to certain conditions controlled by κ while the non-planar equilibrium points are unstable. 相似文献
14.
Rodney S. Gomes 《Icarus》2011,215(2):661-668
Numerical integrations of the equations of motion of the giant planets and scattering particles show that there is a possible orbital itinerary that a particle may follow from a scattering mode up to a stable position near the orbit of 2004 XR190. This orbital evolution requires that the particle gets trapped in a mean motion resonance with Neptune coupled with the Kozai resonance. Imposing migration on Neptune while a particle is experiencing both resonances can entail an escape from resonance at a low particle’s eccentricity. This eccentricity and the associated inclination are always similar to those of 2004 XR190. I conclude that 2004 XR190 was most likely a scattered object that went through those resonance processes and was eventually deposited at its current position. By the same argument, it is expected that there must exist several other objects with similar semimajor axis, eccentricity and inclination as those of 2004 XR190. 相似文献
15.
N. Delsate 《Planetary and Space Science》2011,59(13):1372-1383
The aim of Dawn mission is the acquisition of data from orbits around two bodies (4) Vesta and (1) Ceres, the two most massive asteroids.Due to the low thrust propulsion, Dawn will slowly cross and transit through ground-track resonances, where the perturbations on Dawn orbit may be significant. In this context, to safety go the Dawn mission from the approach orbit to the lowest science orbit, it is essential to know the properties of the crossed resonances.This paper analytically investigates the properties of the major ground-track resonances (1:1, 1:2, 2:3 and 3:2) appearing for Vesta orbiters: location of the equilibria, aperture of the resonances and period at the stable equilibria. We develop a general method using an averaged Hamiltonian formulation with a spherical harmonic approximation of the gravity field. If the values of the gravity field coefficient change, our method stays correct and applicable. We also discuss the effect of one uncertainty on the C20 and C22 coefficients on the properties of the 1:1 resonance. These results are checked by numerical tests. We determine that the increase of the eccentricity appearing in the 2:3 resonance is due to the C22 and S22 coefficients.Our method can be easily adapted to missions similar to Dawn because, contrarily to the numerical results, the analytical formalism stays the same and is valid for a wide range of physical parameters of the asteroid (namely the shape and the mass) as well as for different spacecraft orbits.Finally we numerically study the probability of the capture in resonance 1:1. Our paper reproduces, explains and supplements the results of Tricarico and Sykes (2010). 相似文献
16.
In this paper, we investigate analytically the level space of the imaginary part of quasinormal frequencies for a black hole with a deficit solid angle and quintessence-like matter by the Padmanabhan’s method (Padmanabhan in Class. Quantum Gravity 21:L1, 2004). Padmanabhan presented a method to study analytically the imaginary part of quasinormal frequencies for a class of spherically symmetric spacetimes including Schwarzschild-de Sitter black holes which has an evenly spaced structure. The results show that the level space of scalar and gravitational quasinormal frequencies for this kind of black holes only depend on the surface gravity of black-hole horizon in the range of $-1<w<-\frac{1}{3}$ , respectively. We also extend the range of w to w≤?1, the results of which are similar to that in $-1<w<-\frac{1}{3}$ case. Particularly, a black hole with a deficit solid angle in accelerating universe will be a Schwarzschild-de Sitter black hole, fixing w=?1 and ε 2=0. And a black hole with a deficit solid angle in the accelerating universe will be a Schwarzschild black hole,when ρ 0=0 and ε 2=0. In this paper, w is the parameter of state equation, ε 2 is a parameter relating to a deficit solid angle and ρ 0 is the density of static spherically symmetrical quintessence-like matter at r=1. 相似文献
17.
Understanding the evolution of asteroid spin states is challenging work, in part because asteroids have a variety of orbits, shapes, spin states, and collisional histories but also because they are strongly influenced by gravitational and non-gravitational (YORP) torques. Using efficient numerical models designed to investigate asteroid orbit and spin dynamics, we study here how several individual asteroids have had their spin states modified over time in response to these torques (i.e., 951 Gaspra, 60 Echo, 32 Pomona, 230 Athamantis, 105 Artemis). These test cases which sample semimajor axis and inclination space in the inner main belt, were chosen as probes into the large parameter space described above. The ultimate goal is to use these data to statistically characterize how all asteroids in the main belt population have reached their present-day spin states. We found that the spin dynamics of prograde-rotating asteroids in the inner main belt is generally less regular than that of the retrograde-rotating ones because of numerous overlapping secular spin-orbit resonances. These resonances strongly affect the spin histories of all bodies, while those of small asteroids (?40 km) are additionally influenced by YORP torques. In most cases, gravitational and non-gravitational torques cause asteroid spin axis orientations to vary widely over short (?1 My) timescales. Our results show that (951) Gaspra has a highly chaotic rotation state induced by an overlap of the s and s6 spin-orbit resonances. This hinders our ability to investigate its past evolution and infer whether thermal torques have acted on Gaspra's spin axis since its origin. 相似文献
18.
B. Novaković K. Tsiganis Z. Knežević 《Celestial Mechanics and Dynamical Astronomy》2010,107(1-2):35-49
In this paper we present a comprehensive analysis of the dynamics in the region of the (3556) Lixiaohua asteroid family. The family lies in a particularly interesting region of the phase space, crossed by several two-body and three-body mean motion resonances. Also, members of this family can have close encounters with large asteroids, such as Ceres. We have identified the mean motion resonances which contribute to the long-term dynamical evolution of the family and our results confirm that the members of this family can be classified into a number of groups, exhibiting different dynamical behavior. We show for the first time that in the Lixiaohua region, apart from the chaotic diffusion in proper eccentricity and inclination (e p and I p ), there is at least one extended chaotic zone where several resonances overlap, thus giving rise to chaotic diffusion in proper semi-major axis (a p ) as well. Using a code of Monte Carlo type, we simulate the evolution of the family, according to the model which combines the chaotic diffusion (in a p , e p and I p ), Yarkovsky/YORP thermal effect and random walk in a p due to the close encounters with massive asteroids. These simulations show that all these effects should be taken into account in order to accurately explain the observed distribution of family members in the space of proper elements, although a “minimal” model that accounts for chaotic diffusion in (e p , I p ), Yarkovsky-induced drift in a p and random walk in a p due to the close encounters with the most massive asteroids is enough to grossly characterize the shape of the family. 相似文献
19.
S.I. Akasofu 《Planetary and Space Science》1985,33(1):81-87
We examine time variations of the total magnetospheric output UT and the two geomagnetic indices AE and Dst during the magnetospheric storm of 31 December 1967–1 January 1968. A unique feature of this particular storm is that the solar-wind magnetosphere dynamo power ε was nearly constant for about 24 h by maintaining a high value of ～1019 erg s?1. It is found that UT was also nearly constant during that period, indicating that the magnetosphere is primarily a directly driven system. However, during an early epoch of the storm, the electrojet intensity levelled off, while the ring current began to grow during the same epoch. Subsequently, there occurred a sudden surge of the electrojet intensity, while the growth of the ring-current levelled off. Later variations of both the AE and Dst indices were very complex. After the surge, the AE index continued to decline and became as low as ~250 nT during the maximum epoch of this major storm (when the Dst decrease attained the maximum values). This trend can also be seen in many other major storms, but is often masked by changes of ε. One possible cause for such features for ε ? 1019erg/s?1 is that the neutral wind is generated by the motion in the lower ionosphere, reducing the electrojet intensity and enhancing the ring-current particle-injection rate. 相似文献
20.
Simulations of Titan's atmospheric transmission and surface reflectivity have been developed in order to estimate how Titan's atmosphere and surface properties could affect performances of the Cassini radar experiment. In this paper we present a selection of models for Titan's haze, vertical rain distribution, and surface composition implemented in our simulations. We collected dielectric constant values for the Cassini radar wavelength (∼2.2 cm) for materials of interest for Titan: liquid methane, liquid mixture of methane-ethane, water ice, and light hydrocarbon ices. Due to the lack of permittivity values for Titan's haze particles in the microwave range, we performed dielectric constant (εr) measurements around 2.2 cm on tholins synthesized in laboratory. We obtained a real part of εr in the range of 2-2.5 and a loss tangent between 10−3 and 5×10−2. By combining aerosol distribution models (with hypothetical condensation at low altitudes) to surface models, we find the following results: (1) Aerosol-only atmospheres should cause no loss and are essentially transparent for Cassini radar, as expected by former analysis. (2) However, if clouds are present, some atmospheric models generate significant attenuation that can reach −50 dB, well below the sensitivity threshold of the receiver. In such cases, a 13.78 GHz radar would not be able to measure echoes coming from the surface. We thus warn about possible risks of misinterpretation if a “wet atmosphere” is not taken into account. (3) Rough surface scattering leads to a typical response of ∼−17 dB. These results will have important implications on future Cassini radar data analysis. 相似文献