Using wavelet approximation to study the influence of Jupiter on the orbital evolution of a distant satellite of Saturn

We suggest a nonstandard methodology for studying the influence of Jupiter on the secular orbital evolution of a distant satellite of Saturn. This influence is tangible only in short time spans near the times of the smallest separation between Jupiter and Saturn, i.e., when the heliocentric longitudes of the two planets coincide. These times are spaced about 20 years apart. To describe the jumplike behavior of perturbations, we suggest approximating the principal part of the perturbing function averaged over the satellite’s motion by a two-parameter exponential wavelet-type (burst) function. The subsequent averaging (smoothing) of the perturbing function allows us to eliminate the 20-year-period terms and obtain an approximate analytical solution in a special case of the problem. The results are illustrated by plots of the variations in the averaged perturbing function and the orbital eccentricity of Saturn’s outer satellite S/2000 S1, which is most strongly perturbed by Jupiter.     

Orbital evolution of Jupiter’s new outer satellites

Data on recently discovered outer satellites of Jupiter are used to analyze their long-period orbital evolution. We determine the extreme eccentricities and inclinations, as well as the circulation periods of the pericenter arguments and of the longitudes of the ascending nodes. The satellite orbital elements are plotted against time. The methods of analysis are identical to those that we used to analyze the orbital evolution of Uranus’s and Saturn’s new outer satellites.     

Final tidal evolution of orbit-orbit resonances

In this paper we describe a model for the tidal evolution of an orbit-orbit resonance between two satellites of the same planet. We let the system evolve till infinity or until the resonance is destroyed. We find that there are asymptotic values for the eccentricities and inclinations. We list the possible final stages that a resonance can achieve, we give a few examples, and finally we discuss the limitations of the model and its possible applications to real systems.     

Dynamical evolution of NEAs: Close encounters, secular perturbations and resonances

We discuss the main mechanisms affecting the dynamical evolution of Near-Earth Asteroids (NEAs) by analyzing the results of three numerical integrations over 1 Myr of the NEA (4179) Toutatis. In the first integration the only perturbing planet is the Earth. So the evolution is dominated by close encounters and looks like a random walk in semimajor axis and a correlated random walk in eccentricity, keeping almost constant the perihelion distance and the Tisserand invariant. In the second integration Jupiter and Saturn are present instead of the Earth, and the 3/1 (mean motion) and v ₆ (secular) resonances substantially change the eccentricity but not the semimajor axis. The third, most realistic, integration including all the three planets together shows a complex interplay of effects, with close encounters switching the orbit between different resonant states and no approximate conservation of the Tisserand invariant. This shows that simplified 3-body or 4-body models cannot be used to predict the typical evolution patterns and time scales of NEAs, and in particular that resonances provide some “fast-track” dynamical routes from low-eccentricity to very eccentric, planet-crossing orbits.     

Dynamical evolution of NEAs: Close encounters, secular perturbations and resonances

We discuss the main mechanisms affecting the dynamical evolution of Near-Earth Asteroids (NEAs) by analyzing the results of three numerical integrations over 1 Myr of the NEA (4179) Toutatis. In the first integration the only perturbing planet is the Earth. So the evolution is dominated by close encounters and looks like a random walk in semimajor axis and a correlated random walk in eccentricity, keeping almost constant the perihelion distance and the Tisserand invariant. In the second integration Jupiter and Saturn are present instead of the Earth, and the 3/1 (mean motion) and v ₆ (secular) resonances substantially change the eccentricity but not the semimajor axis. The third, most realistic, integration including all the three planets together shows a complex interplay of effects, with close encounters switching the orbit between different resonant states and no approximate conservation of the Tisserand invariant. This shows that simplified 3-body or 4-body models cannot be used to predict the typical evolution patterns and time scales of NEAs, and in particular that resonances provide some fast-track dynamical routes from low-eccentricity to very eccentric, planet-crossing orbits.On leave from the Department of Mathematics, University of Pisa, Via Buonarroti 2, 56127 Pisa, Italy, thanks to the G. Colombo fellowships of the European Space Agency.     

Numerical investigation on the orbital evolution of 1:2 resonant asteroids between Jupiter and Saturn

According to some investigations (Lecar and Franklin, 1973; Franklin et al., 1989; Soper et al., 1990) asteroids cannot remain for along time between Jupiter and Saturn. But as it is well known there is a near 5:2 commensurability between Jupiter and Saturn. So there might be a possibility that asteroids between Jupiter and Saturn could be trapped in a resonant relation.In order to investigate this possibility, the changes of orbital elements of an asteroid whose initial value of semi-major axis corresponds to that of a 1:2 resonant orbit were investigated by means of a double precision Cowell method. The integration routine was kindly supplied by Dr Yoshikawa.We considered first a planar restricted problem of three bodies, Sun-Jupiter-Asteroid, then a four body problem, Sun-Jupiter-Asteroid-Saturn. When integrating the equations of motion, short periodic terms were not eliminated and in the second test the interactions between Jupiter and Saturn were retained. Whether a close approach occured or not was not investigated. In every case a _j = 5.20, a _s = 9.54 and a = 8.26 were adopted as initial values of the semi-major axis of Jupiter, Saturn and Asteroid respectively.     

近地小行星轨道演化的数值研究与辛算法有效性的探讨

本文采用改进的显式辛算法（symplecticalgorithm）和嵌套的RKF7（8）积分器对43颗已命名（或编号）的近地小行星的轨道演化进行数值研究．在力学模型上,除考虑各大行星的引力振动外,还增加了后牛顿效应,而在算法上则着重探索辛算法在近地小行星轨道演化研究中的应用前景,特别是当小行星与某一大行星靠近时辛算法的有效性．本文的结果可为了解近地小行星的轨道演化状况和对它们进行监测提供可靠的信息．     

Recent orbital evolution and the internal structures of Enceladus and Dione

We study the orbital behavior of Saturn’s satellites Enceladus and Dione during their passage through the 2:1 mean-motion resonances to constrain their interior structures, parameterized by the quantity k₂/Q (assumed constant). Enceladus’ evolution after escape from the second-order e-Enceladus e-Dione resonance requires that (k₂/Q)_Enceladus<8×10^-4, for that Q_Saturn>18,000. This result is in agreement with [Meyer, J., Wisdom, J., 2008b. Icarus 193, 213-223]. The present-day libration amplitude of Enceladus requires that (k₂/Q)_Enceladus>1.2×10^-4, assuming that Q_Saturn<10⁵. Dione’s present-day eccentricity indicates that (k₂/Q)_Dione?3×10^-4 for Q_Saturn>18,000. Assuming Maxwellian viscoelastic behavior, we find that for Enceladus a convective ice shell overlying an ocean is too dissipative to match the orbital constraints. We conclude that a conductive shell overlying an ocean is more likely, and discuss the implications of this result. Dione’s ice shell is also likely to be conductive, but our results are less constraining.     

Orbital evolution of the distant satellites of the giant planets

We study the evolution of several distant satellite orbits. These are the orbits (including the improved ones)of the recently discovered Neptunian satellites S/2002 N1, N2, N3, N4; S/2003 N1 and the orbits of Jovian, Saturnian, and Uranian satellites with librational variations in the argument of the pericenter: S/2001 J10 (Euporie), S/2003 J20; S/2000 S5 (Kiviuq), S/2000 S6 (Ijiraq), and S/2003 U3. The study is performed using mainly an approximate numerical-analytical method. We determine the extreme eccentricities and inclinations as well as the periods of the variations in the arguments of pericenters and longitudes of the ascending nodes on time intervals ～10⁵?10⁶ yr. We compare our results with those obtained by numerically integrating the rigorous equations of satellite motion on time intervals of the order of the circulation periods of the longitudes of the ascending nodes (10²?10³ yr).     

Orbital evolution of new distant Neptunian satellites and ω-librators in the satellite systems of Saturn and Jupiter

We used data on the recently discovered three outer Neptunian satellites to analyze the long-period evolution of their orbits. We estimated the ranges of eccentricities and inclinations as well as approximate circulation periods of the pericenter arguments and the longitudes of the ascending nodes. The results were mainly obtained by using two different versions of the averaged Hill problem. Plane sections of the phase space of satellite orbital elements are given. We discuss the peculiarity of the evolution of several satellite orbits related to the librational variation of the pericenter argument ω. The ω-librators of Saturn’s system were found to qualitatively differ from the libration orbit in the system of Jupiter.     

Asteroids in three-body mean-motion resonances with Jupiter and Mars

We identify the asteroids in three-body mean-motion resonances with Jupiter and Mars on the set of all known on April 2016 numbered asteroids (467308 objects). The resonant objects are identified by the direct analysis of the behavior (libration/circulation) of the resonant arguments on 100000 yrs. All essential perturbations during the integration of the equations of the motion are taken into account. The number of the asteroids in different resonances has been calculated for all possible resonances with the order less or equal 6.     

The orbital resonance amongst the Galilean satellites of Jupiter

The resonance amongst three of the Galilean satellites is described in a way intended to demonstrate the similarities it has to the normal two-satellite resonance. The hypothesis that the resonance was formed by the action of tidal forces is discussed. The problem is too complicated to reach any firm conclusions, but the tidal hypothesis does not seem to be a satisfactory explanation.

     

The Kozai resonance in the outer solar system and the dynamics of long-period comets

We consider the secular evolution of the orbits of bodies in the Outer Solar System under the perturbations of the jovian planets assumed on coplanar and circular orbits. Through the approach used for asteroidal belt by Yoshihide Kozai in 1962, we obtain that the Kozai resonance do not affect the behavior of bodies belonging to the Kuiper belt but concerns the long-timescale evolution of long-period comets. In particular this resonance appears as a process contributing to produce Sun-grazer comets.     

The space distribution and orbital resonances of asteroids

We have made a detailed numerical analysis of the various orbital resonances of the asteroids and examined the variation in the distribution of trajectories near the equilibrium points in the phase plane, and hence arrived at a preliminary explanation of the features (gaps and clusters) in their distribution in space.     

Effect of the high-order resonances on the orbital evolution of objects near geostationary orbit

The area-to-mass ratio of high-orbit space objects is estimated on the basis of positional observations from the SBG telescope at the Kourovka astronomical observatory of the Ural Federal University. The properties of regions where high-order resonances are located are analyzed. The position and sizes of the resonance zones depending on the area-to-mass ratio of objects are determined on the basis of numerical modeling. It is shown that a system transits through the high-order resonances due to secular perturbations of the semimajor axis under the Poynting-Robertson effect. The high-order resonances weakly influence the formation of the stochastic trajectories. The stochastic properties are mostly manifested in evolution of the semimajor axis of the orbit.     

Spectral observations of 19 weathered and 23 fresh NEAs and their correlations with orbital parameters

Results of our visible to near-infrared spectrophotometric observations of 41 near-Earth asteroids (NEAs) are reported. These moderate-resolution spectra, along with 14 previously published spectra from our earlier survey [Hicks, M.D., Fink, U., Grundy, W.M., 1998. Icarus 133, 69-78] show a preponderance of spectra consistent with ordinary chondrites (23 NEAs with this type of spectrum, along with 19 S-types and 13 in other taxonomic groups). There exists statistically significant evidence for orbit-dependent trends in our data. While S-type NEAs from our survey reside primarily in (1) Amor orbits or (2) Aten or Apollo orbits which do not cross the asteroid main-belt, the majority of objects with spectra consistent with ordinary chondrites in our survey are in highly eccentric Apollo orbits which enter the asteroid main-belt. This trend toward fresh, relatively unweathered NEAs with ordinary chondrite type spectra in highly eccentric Apollo orbits is attributed to one or a combination of three possible causes: (1) the chaotic nature of NEA orbits can easily result in high eccentricity orbits/large aphelion distances so that they can enter the collisionally enhanced environment in the main-belt, exposing fresh surfaces, (2) they have recently been injected into such orbits after a collision in the main-belt, or (3) such objects cross the orbits of several terrestrial planets, causing tidal disruption events that expose fresh surfaces.     

Structure and evolution of the Jupiter family

Both physical and dynamical issues are important in order to judge the origin and evolution of the Jupiter family of short-period comets. The steady-state condition for maintaining this structure at its present size by captures from the classical Oort cloud is reviewed on the basis of recent results concerning the absolute number of Jupiter family comets as a function of perihelion distance as well as the coupled physical and dynamical evolutions that evidently occur. Like in most earlier investigations, a clear shortage is found in the classical Oort cloud source. The shortage seems, however, less extreme than sometimes assumed. Monte Carlo simulations are envisaged as a way to shed further light on the fate of Jupiter family comets.     

主带小行星的动力学模拟

采用接近真实太阳系的动力学模型,对主带小行星的动力学演化进行了数值模拟。计算的起始时间是儒略日JD=2.4540005×10~6,计算的时间长度为100万年。力学模型采用n+m体模型,计算程序基于小行星轨道演化的软件Orbit9。对演化结果进行分析可以发现测试粒子与木星的平运动共振对测试粒子稳定性的不同作用,以及在2:3、3:4共振处不同初始ω值对测试粒子演化结果的影响。     

Orbital evolution of giant comet-like objects

We investigated by numerical integrations the long-term orbital evolution of four giant comets or comet-like objects. They are Chiron, P/Schwassmann-Wachmann 1 (SW1), Hidalgo, and 1992AD (5145), and their orbits were traced for 100–200 thousand years (kyr) toward both the past and the future. For each object, 13 orbits were calculated, one for the nominal orbital elements and other 12 with slightly modified elements based on the rms residual of the orbit determination and on the number of observations. As past studies indicate, their orbital evolution is found to be very chaotic, and thus can be described only in terms of probability. Plots of the semi-major axis (a) and perihelion distance (q) of the objects treated here seem to cross each other frequently, suggesting a possibility of their common evolutionary paths. About a half of all the calculated orbits showedq- ora-decreasing evolution. This indicates that, at least on the time scale in question, the giant comet-like objects are possibly on a dynamical track that can lead to capture from the outer solar system. We could hardly find the orbits with perihelia far outside the orbit of Saturn (q>15 AU). This is perhaps because the evolution of the orbits beyond Saturn is so slow that substantial orbital changes do not take place within 100–200 kyr.