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1.
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2.
Ramon Brasser  Kevin J. Walsh 《Icarus》2011,213(1):423-427
We performed numerical simulations of the obliquity evolution of Mars during the Noachian era, at which time the giant planets were on drastically different orbits than today. For the preferred primordial configuration of the planets we find that there are two large zones where the martian obliquity is stable and oscillates with an amplitude lower than 20°. These zones occur at obliquities below 30° and above 60°; intermediate values show either resonant or chaotic behaviour depending on the primordial orbits of the terrestrial planets.  相似文献   

3.
Integrability, one of the classic issues in galactic dynamics and in general in celestial mechanics, is here revisited in a Riemannian geometric framework, where Newtonian motions are seen as geodesics of suitable -mechanical- manifolds. The existence of constants of motion that entail integrability is associated with the existence of Killing tensor fields on the mechanical manifolds. Such tensor fields correspond to hidden symmetries of non-Noetherian kind. Explicit expressions for Killing tensor fields are given for the N = 2 Toda model, and for a modified Hénon-Heiles model, recovering the already known analytic expressions of the second conserved quantity besides energy for each model respectively.  相似文献   

4.
An infinite family of axially symmetric thin discs of finite radius is presented. The family of discs is obtained by means of a method developed by Hunter and contains, as its first member, the Kalnajs disc. The surface densities of the discs present a maximum at the centre of the disc and then decrease smoothly to zero at the edge, in such a way that the mass distribution of the higher members of the family is more concentrated at the centre. The first member of the family has a circular velocity proportional to the radius, thus representing a uniformly rotating disc. On the other hand, the circular velocities of the other members of the family increase from a value of zero at the centre of the discs to a maximum and then decrease smoothly to a finite value at the edge of the discs, in such a way that, for the higher members of the family, the maximum value of the circular velocity is attained nearest the centre of the discs.  相似文献   

5.
This paper summarises a numerical investigation of phase mixing in time-independent Hamiltonian systems that admit a coexistence of regular and chaotic phase space regions, allowing also for low amplitude perturbations idealised as periodic driving, friction, and/or white and coloured noise. The evolution of initially localised ensembles of orbits was probed through lower order moments and coarse-grained distribution functions. In the absence of time-dependent perturbations, regular ensembles disperse initially as a power law in time and only exhibit a coarse-grained approach towards an invariant equilibrium over comparatively long times. Chaotic ensembles generally diverge exponentially fast on a time scale related to a typical finite time Lyapunov exponent, but can exhibit complex behaviour if they are impacted by the effects of cantori or the Arnold web. Viewed over somewhat longer times, chaotic ensembles typical converge exponentially towards an invariant or near-invariant equilibrium. This, however, need not correspond to a true equilibrium, which may only be approached over very long time scales. Time-dependent perturbations can dramatically increase the efficiency of phase mixing, both by accelerating the approach towards a near-equilibrium and by facilitating diffusion through cantori or along the Arnold web so as to accelerate the approach towards a true equilibrium. The efficacy of such perturbations typically scales logarithmically in amplitude, but is comparatively insensitive to most other details, a conclusion which reinforces the interpretation that the perturbations act via a resonant coupling.  相似文献   

6.
We are conducting a systematic study of a carefully selected sampleof nearby E/S0 galaxies and Sa bulges using the unique panoramic integral-fieldspectrograph SAURON, mounted at the WHT. The goal of the SAURON projectis to fully map the gaseous/stellar kinematics and the stellar populations of a representative sample of 80 early-type galaxies up to 1 Re,probing different environments (clusters, field). These data, used in combination with existing ground-based and HST observations, and fed to the theoretical machinery we have developed, will allow to determine theintrinsic dynamical structure of the galaxies. We will also measure the masses of central black holes, relate the internal dynamics to the ageand metallicity of the stellar populations, and establish the historyof metal enrichment as a function of Hubble type and environment. Some brief results on two targets observed during the SAURON campaign will serve as an illustration of the unique and high quality data we are currently gathering. This revised version was published online in September 2006 with corrections to the Cover Date.  相似文献   

7.
Bruce G. Bills  Francis Nimmo 《Icarus》2011,214(1):351-355
Estimates of the moments of inertia of Titan, as separately deduced from its gravitational field and spin pole orientation, are quite different. This discrepancy can be resolved if Titan is either not precessing as a rigid body (e.g. if the shell is decoupled from the interior by an ocean), or if the spin pole is not fully damped (e.g. due to atmospheric excitation). By the end of the Cassini mission, continued monitoring of the changing spin pole orientation, by Cassini radar observations, will determine which effect dominates.  相似文献   

8.
We consider a differentially rotating, 2D stellar disc perturbed by two steady-state spiral density waves moving at different pattern speeds. Our investigation is based on direct numerical integration of initially circular test-particle orbits. We examine a range of spiral strengths and spiral speeds and show that stars in this time-dependent gravitational field can be heated (their random motions increased). This is particularly noticeable in the simultaneous propagation of a two-armed spiral density wave near the corotation resonance (CR), and a weak four-armed one near the inner and outer 4:1 Lindblad resonances. In simulations with two spiral waves moving at different pattern speeds, we find: (i) the variance of the radial velocity,  σ2 R   , exceeds the sum of the variances measured from simulations with each individual pattern; (ii)  σ2 R   can grow with time throughout the entire simulation; (iii)  σ2 R   is increased over a wider range of radii compared to that seen with one spiral pattern; and (iv) particles diffuse radially in real space, whereas they do not when only one spiral density wave is present. Near the CR with the stronger, two-armed pattern, test-particles are observed to migrate radially. These effects take place at or near resonances of both spirals, so we interpret them as the result of stochastic motions. This provides a possible new mechanism for increasing the stellar velocity dispersion in galactic discs. If multiple spiral patterns are present in the Galaxy, we predict that there should be large variations in the stellar velocity dispersion as a function of radius.  相似文献   

9.
The shaking of Mercury’s orbit by the planets forces librations in longitude in addition to those at harmonics of the orbital period that have been used to detect Mercury’s molten core. We extend the analytical formulation of Peale et al. (Peale, S.J., Margot, J.L., Yseboodt, M. [2009]. Icarus 199, 1-8) in order to provide a convenient means of determining the amplitudes and phases of the forced librations without resorting to numerical calculations. We derive an explicit relation between the amplitude of each forced libration and the moment of inertia parameter (B-A)/Cm. Far from resonance with the free libration period, the libration amplitudes are directly proportional to (B-A)/Cm. Librations with periods close to the free libration period of ∼12 years may have measurable (∼arcsec) amplitudes. If the free libration period is sufficiently close to Jupiter’s orbital period of 11.86 years, the amplitude of the forced libration at Jupiter’s period could exceed the 35 arcsec amplitude of the 88-day forced libration. We also show that the planetary perturbations of the mean anomaly and the longitude of pericenter of Mercury’s orbit completely determine the libration amplitudes.While these signatures do not affect spin rate at a detectable level (as currently measured by Earth-based radar), they have a much larger impact on rotational phase (affecting imaging, altimetry, and gravity sensors). Therefore, it may be important to consider planetary perturbations when interpreting future spacecraft observations of the librations.  相似文献   

10.
We investigate planetary fly-bys of asteroids using an approximate volume-averaged method that offers a relatively simple, but very flexible, approach to study the rotational dynamics of ellipsoids. The asteroid is considered to be a deformable, prolate ellipsoid, with its interior being modeled as a rigid-granular material. Effects due to the asteroid's rotation, its self-gravity and gravitational interaction with the planet are included. Using a simplified approach allows us to explore in detail the mechanics of asteroid's deformations and disruptions during planetary encounters. We also compare our results with those obtained by Richardson et al. [Richardson, D.C., Bottke Jr., W.F., Love, S.G., 1998. Icarus 134, 47-76] who used a large numerical code. We find that many of the features reported by them can indeed be captured by our rather simple methodology, and we discuss the reasons why some of our results differ from theirs.  相似文献   

11.
The Cassini Imaging Science Subsystem (ISS) and Composite Infrared Spectrometer (CIRS) reported a North Equatorial Belt (NEB) wave in Jupiter's atmosphere from optical images [Porco, C.C., and 23 colleagues, 2003. Science 299, 1541-1547] and thermal maps [Flasar, F.M., and 39 colleagues, 2004. Nature 427, 132-135], respectively. The connection between the two waves remained uncertain because the two observations were not simultaneous. Here we report on simultaneous ISS images and CIRS thermal maps that confirm that the NEB wave shown in the ISS ultraviolet (UV1) and strong methane band (MT3) images is correlated with the thermal wave in the CIRS temperature maps, with low temperatures in the CIRS maps (upwelling) corresponding to dark regions in the UV1 images (UV-absorbing particles) and bright regions in the MT3 images (high clouds and haze). The long period of the NEB wave suggests that it is a planetary (Rossby) wave. The combined observations from the ISS and CIRS are utilized to discuss the vertical and meridional propagation of the NEB wave, which offers a possible explanation for why the NEB wave is confined to specific latitudes and altitudes. Further, the ISS UV1 images reveal a circumpolar wave centered at 48.5° S (planetocentric) and probably located in the stratosphere, as suggested by the ISS and CIRS observations. The simultaneous comparison between the ISS and CIRS also implies that the large dark oval in the polar stratosphere of Jupiter discovered in the ISS UV1 images [Porco, C.C., and 23 colleagues, 2003. Science 299, 1541-1547] is the same feature as the warm regions at high northern latitudes in the CIRS 1-mbar temperature maps [Flasar, F.M., and 39 colleagues, 2004. Nature 427, 132-135]. This comparison supports a previous suggestion that the dark oval in the ISS UV1 images is linked to auroral precipitation and heating [Porco, C.C., and 23 colleagues, 2003. Science 299, 1541-1547].  相似文献   

12.
We investigate the possibility of discriminating between modified Newtonian dynamics (MOND) and Newtonian gravity with dark matter, by studying the vertical dynamics of disc galaxies. We consider models with the same circular velocity in the equatorial plane (purely baryonic discs in MOND and the same discs in Newtonian gravity embedded in spherical dark matter haloes), and we construct their intrinsic and projected kinematical fields by solving the Jeans equations under the assumption of a two-integral distribution function. We find that the vertical velocity dispersion of deep MOND discs can be much larger than in the equivalent spherical Newtonian models. However, in the more realistic case of high surface density discs, this effect is significantly reduced, casting doubt on the possibility of discriminating between MOND and Newtonian gravity with dark matter by using current observations.  相似文献   

13.
We have tested a previous analytical estimate of the dynamical friction time-scale in modified Newtonian dynamics (MOND) with fully non-linear N -body simulations. The simulations confirm that the dynamical friction time-scale is significantly shorter in MOND than in equivalent Newtonian systems, i.e. systems with the same phase-space distribution of baryons and additional dark matter. An apparent conflict between this result and the long time-scales determined for bars to slow and mergers to be completed in previous N -body simulations of MOND systems is explained. The confirmation of the short dynamical-friction time-scale in MOND underlines the challenge that the Fornax dwarf spheroidal poses to the viability of MOND.  相似文献   

14.
We have developed a model of the response of the outer Oort cloud of comets to simultaneous tidal perturbations of the adiabatic galactic force and a stellar impulse. The six-dimensional phase space of near-parabolic comet orbital elements has been subdivided into cells. A mapping of the evolution of these elements from beyond the loss cylinder boundary into the inner planetary region over the course of a single orbit is possible. This is done by treating each perturbation separately, and in combination, during a time interval of 5 Myr. We then obtain the time dependence of a wide range of observable comet flux characteristics, which provides a fingerprint of the dynamics. These include the flux distributions of energy, perihelion distance, major axis orientation, and angular momentum orientation. Correlations between these variables are also determined. We show that substantive errors occur if one superposes the separately obtained flux results of the galactic tide and the stellar impulse rather than superposing the tidal and impulsive perturbations in a single analysis. Detailed illustrations are given for an example case where the stellar mass and relative velocity have the ratio M∗/Vrel=0.043 M⊙/km s−1 and the solar impact parameter is 45,000 AU. This case has features similar to the impending Gliese 710 impulse with the impact parameter selected to be close to the low end of the predicted range. We find that the peak in the observable comet flux exceeds that due to the galactic tide alone by ≈41%. We also present results for the time dependence of the flux enhancements and for the mean encounter frequency of weak stellar impulse events as functions of M∗/Vrel and solar impact parameter.  相似文献   

15.
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   

16.
We obtain the size and orbital distributions of near-Earth asteroids (NEAs) that are expected to be in the 1 : 1 mean motion resonance with the Earth in a steady state scenario. We predict that the number of such objects with absolute magnitudes H<18 and H<22 is 0.65±0.12 and 16.3±3.0, respectively. We also map the distribution in the sky of these Earth coorbital NEAs and conclude that these objects are not easily observed as they are distributed over a large sky area and spend most of their time away from opposition where most of them are too faint to be detected.  相似文献   

17.
The pumping up of orbital inclinations of asteroids caused by sweeping secular resonances associated with depletion of a protoplanetary disk is discussed, focusing on the dependence on the disk inclinations and surface density distribution. The asteroids have large mean inclinations that cannot be explained by present planetary perturbations alone. It has been suggested that the sweeping secular resonances caused by disk depletion are responsible for these high inclinations. Nagasawa et al. (2000, Astron. J.119, 1480-1497) showed that the inclinations of asteroids are pumped up if the disk is depleted in an inside-out manner on a time scale longer than 3×105 years. Their assumed disk midplane is not on the invariant plane. However, it should be affected by the inclination of the disk plane. Here we investigate the dependence on the disk inclinations. We assume a disk depletion model in which the disk inside the jovian orbit has been removed and the residual outer disk is uniformly depleted. We calculate the locations of the secular resonances and the excitation magnitude of the inclinations with analytical methods. We found that the inclinations are pumped up to the observational level for a depletion time scale longer than 106 years in the case of the disk plane that coincides with the invariant plane. The required time scale is longest (3×106 years) if the disk plane coincides with the jovian orbital plane. However, it is still within the observationally inferred depletion time scale. We also studied dependence on a disk surface density gradient and found that the results do not change significantly as long as the inner disk depletion is faster than the outer disk one.  相似文献   

18.
We investigate the relevance of the Yarkovsky effect for the origin of kilometer and multikilometer near-Earth asteroids (NEAs). The Yarkovsky effect causes a slow migration in semimajor axis of main belt asteroids, some of which are therefore captured into powerful resonances and transported to the NEA space. With an innovative simulation scheme, we determine that in the current steady-state situation 100-160 bodies with H < 18 (roughly larger than 1 km) enter the 3/1 resonance per million years and 40-60 enter the ν6 resonance. The ranges are due to uncertainties on relevant simulation parameters such as the time scales for collisional disruption and reorientation, their size dependence, and the strength of the Yarkovsky and YORP effects. These flux rates to the resonances are consistent with those independently derived by Bottke et al. (2002, Icarus 156, 399-433) with considerations based only on the NEA orbital distribution and dynamical lifetime. Our results have been obtained assuming that the main belt contains 1,300,000 asteroids with H < 18 and linearly scale with this number. Assuming that the cumulative magnitude distribution of main belt asteroids is N(< H) ∝ 10γ′H with γ′ = 0.25 in the 15.5 < H < 18 range (consistent with the results of the SDSS survey), we obtain that the bodies captured into the resonances should have a similar magnitude distribution, but with exponent coefficient γ = 0.33-0.40. The lowest value is obtained taking into account the YORP effect, while higher values correspond to a weakened YORP or to YORP-less cases. These values of γ are all compatible with the debiased magnitude distributions of the NEAs according to Rabinowitz et al. (2000, Nature 403, 165-166), Bottke et al. (2000b, Science 288, 2190-2194), and Stuart (2001, Science 294, 1691-1693). Hence the Yarkovsky and YORP effects allow us to understand why the magnitude distribution of NEAs is only moderately steeper than that of the main belt population. The steepest main belt distribution that would still be compatible with the NEA distribution has exponent coefficient γ′ ∼ 0.3.  相似文献   

19.
Pawe? Wajer 《Icarus》2009,200(1):147-153
We study the dynamical evolution of Asteroid 2002 AA29. This object moves in the co-orbital region of the Earth and is the first known asteroid which experiences recurrent horseshoe-quasi-satellite transitions. The transitions between the HS and QS states are unique among other known Earth co-orbital asteroids and in the QS state 2002 AA29 remains very close to Earth (within 0.2 AU for several decades [Connors, M., Chodas, P., Mikkola, S., Wiegert, P., Veillet, C., Innanen, K., 2002. Meteorit. Planet. Sci. 37, 1435-1441]). Based on results obtained analytically by Brasser et al. [Brasser, R., Heggie, D.C., Mikkola, S., 2004b. Celest. Mech. Dynam. Astron. 88, 123-152] we developed a simple analytical method to describe and analyze the motion of 2002 AA29. We distinguish a few moments in time crucial for understanding its dynamics. Near 2400 and 2500 this object will be close to going through the maxima of the averaged disturbing function and it will either change its co-orbital regime by transition from the HS into QS state, or leave the librating mode. These approaches generate instability in the motion of 2002 AA29. By means of 66 observations, covering a two-year interval, we extend the analysis of the long term evolution of this object presented by Connors et al. [Connors, M., Chodas, P., Mikkola, S., Wiegert, P., Veillet, C., Innanen, K., 2002. Meteorit. Planet. Sci. 37, 1435-1441] and Brasser et al. [Brasser, R., Innanen, K.A., Connors, M., Veillet, C., Wiegert, P., Mikkola, S., Chodas, P.W., 2004a. Icarus 171, 102-109]. Our analysis is based on a sample of 100 cloned orbits. We show that the motion of 2002 AA29 is predictable in the time interval [−2600,7100] and outside of this interval the past and future orbital history can be studied using statistical methods.  相似文献   

20.
We analyze the dynamical evolution of Jupiter-family (JF) comets and near-Earth asteroids (NEAs) with aphelion distances Q>3.5 AU, paying special attention to the problem of mixing of both populations, such that inactive comets may be disguised as NEAs. From numerical integrations for 2×106 years we find that the half lifetime (where the lifetime is defined against hyperbolic ejection or collision with the Sun or the planets) of near-Earth JF comets (perihelion distances q<1.3 AU) is about 1.5×105 years but that they spend only a small fraction of this time (∼ a few 103 years) with q<1.3 AU. From numerical integrations for 5×106 years we find that the half lifetime of NEAs in “cometary” orbits (defined as those with aphelion distances Q>4.5 AU, i.e., that approach or cross Jupiter's orbit) is 4.2×105 years, i.e., about three times longer than that for near-Earth JF comets. We also analyze the problem of decoupling JF comets from Jupiter to produce Encke-type comets. To this end we simulate the dynamical evolution of the sample of observed JF comets with the inclusion of nongravitational forces. While decoupling occurs very seldom when a purely gravitational motion is considered, the action of nongravitational forces (as strong as or greater than those acting on Encke) can produce a few Enckes. Furthermore, a few JF comets are transferred to low-eccentricity orbits entirely within the main asteroid belt (Q<4 AU and q>2 AU). The population of NEAs in cometary orbits is found to be adequately replenished with NEAs of smaller Q's diffusing outward, from which we can set an upper limit of ∼20% for the putative component of deactivated JF comets needed to maintain such a population in steady state. From this analysis, the upper limit for the average time that a JF comet in near-Earth orbit can spend as a dormant, asteroid-looking body can be estimated to be about 40% of the time spent as an active comet. More likely, JF comets in near-Earth orbits will disintegrate once (or shortly after) they end their active phases.  相似文献   

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