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 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.     

Peculiarities of Uranus’s satellite system

The absence of Uranus’s equatorial satellites in the region of approximately equal influence of its oblateness and solar perturbations is explained in terms of an improved physical model. This model is more complete than the previously studied case of an integrable averaged problem. The model improvement stems from the fact that the inclination of Uranus’s equator to the ecliptic differs by 90° and that the orbital evolution of Uranus due to secular planetary perturbations is taken into account. The lifetime of Uranus’s hypothetical satellites in orbits with semimajor axes 1.3–7 million km can be estimated by numerically integrating the evolution equations to be ～10⁴ yr. This is the time scale on which the evolution of the orbits leads to their intersection with the orbits of inner satellites.     

A numerical-analytical method for studying the orbital evolution of distant planetary satellites

We describe an approximate numerical-analytical method for calculating the perturbations of the elements of distant satellite orbits. The model for the motion of a distant satellite includes the solar attraction and the eccentricity and ecliptic inclination of the orbit of the central planet. In addition, we take into account the variations in planetary orbital elements with time due to secular perturbations. Our work is based on Zeipel’s method for constructing the canonical transformations that relate osculating satellite orbital elements to the mean ones. The corresponding transformation of the Hamiltonian is used to construct an evolution system of equations for mean elements. The numerical solution of this system free from rapidly oscillating functions and the inverse transformation from the mean to osculating elements allows the evolution of distant satellite orbits to be studied on long time scales on the order of several hundred or thousand satellite orbital periods.     

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).     

现代天王星卫星运动定量理论的研究和发展

1986年“旅行者2号”飞越天于星期间，由空间无线电和光学观测获得的卫星资料首次给出天王星5颗主要卫星质量的可靠估计，从而推动了现代天王星卫星运动定量理论的建立。Laskar于1986年建立了第一个相对完整的天王星主要卫星的(半）分析理论——GUST86，其高精度已被许多学者的实算证实。之后，对理论的改进作出贡献的学者有：Malhotra等人(1989）、Lazzaro等人(1987，1991)分析研究了天王星卫星系统中近共振项对长期摄动解的影响；Taylor(1998)采用数值积分拟合观测资料，以更精确地测定卫星质量；Christou和Murray(1997)则将一个2阶Laplace—Lagrange理论应用于天王星卫星系统。对这些学者的工作作一概述。     

Dynamical evolution of the Prometheus–Pandora system

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.     

Equipotential surface and normal gravity of the Galilean satellites

In this article, expanded equations of normal gravity on the equipotential surface are proposed for a natural satellite whose orbital plane is close to its equatorial plane. Tidal effects on the normal gravity are also discussed. The authors apply these to the Galilean satellites. Calculations suggest that the tides raised by Jupiter weakly affect the Galilean satellites. The radial displacements of the gravity due to the tides are in the range between 10⁻³ and 10⁻⁵ m s⁻², which are similar to the latitudinal and longitudinal displacements. The variations along the latitude circle are larger than those along the longitude circle. We conclude that the tidal effects on most of the Galilean satellites are larger than those on the Moon.     

On the periodically evolving orbits in the singly averaged Hill problem

We continue to analyze the periodic solutions of the singly averaged Hill problem. We have numerically constructed the families of solutions that correspond to periodically evolving satellite orbits for arbitrary initial values of their eccentricities and inclinations to the plane of motion of the perturbing body. The solutions obtained are compared with the numerical solutions of the rigorous (nonaveraged) equations of the restricted circular three-body problem. In particular, we have constructed a periodically evolving orbit for which the well-known Lidov-Kozai mechanism manifests itself, just as in the doubly averaged problem.     

Particular solutions of the singly averaged Hill problem

We consider the case of averaging the perturbing function of the Hill problem over the fastest variable, the mean anomaly of the satellite. In integrable special cases, we found solutions to the evolutionary system of equations in elements.     

The orbital evolution of NEAs and the resonances with Jupiter

two near-earth-asteroids associated with resonances with Jupiter are studied over a time span of 10⁵ yrs. We found that asteroid (887) is temporary trapped in the 3:1 resonance; thus indicating that this resonance could be a source of short-lived NEAs. We also found that asteroid (3552) with a large eccentricity and a high inclination is wandering about the 1:1 resonant region.     

Celestial-mechanical peculiarities of Uranus’s satellite system

We consider the structural peculiarities of Uranus’s satellite system associated with its separation into two groups: inner equatorial satellites moving in nearly circular orbits and distant irregular satellites with retrograde motion in highly elliptical orbits. The intermediate region is free from satellites in a wide range of semimajor axes. By analyzing the evolution of satellite orbits under the combined effect of solar attraction and Uranus’s oblateness, we offer a celestial-mechanical explanation for the absence of equatorial satellites in this region. M.L. Lidov’s studies during 1961–1963 have served as a basis for our analysis.     

The in-plane motion of a Geosynchronous satellite under the gravitational attraction of the sun,the moon and the oblate earth

The in-plane motion of a Geosynchronous satellite under the gravitational effects of the sun, the moon and the oblate earth has been studied. The radial deviation (Δr) and the tangential deviation (r _cΔθ) have been determined. Herer _c represents the synchronous altitude. It has been seen that the sum of the oscillatory terms in Δr for different inclinations is a small finite quantity whereas the sum of the oscillatory terms inr _cΔθ for different inclinations is quite large due to the presence of the low-frequency terms in the denominator     

The assessment of the semi-analytical method in the long-term orbit prediction of Earth satellites

To understand the long-term evolution and distribution of the space objects, it is necessary to predict their orbits. Compared with the short-term prediction of a few days, the priority concerns of the long-term orbit prediction are the calculation speed, and the accuracies of major orbital elements, including the semi-major axis and eccentricity which define the shape of the orbit, as well as the orbital inclination and the right ascension of ascending node which define the orientation of the orbit. Given these requirements, it is preferable to adopt the semi-analytical method, which averages the system over the orbital period, and integrates the averaged system using the numerical method. It is not new, however, in the available literature, we can hardly find a quantitative assessment regarding its accuracy and speed when it is applied to various types of orbits. In this paper, we would like to report our implementation and assessment of the semi-analytical method, expecting that it would help to estimate its feasibility in the long-term orbit prediction. The quantitative assessment covers the commonly used orbits for the Earth satellites. In some rare and special cases where the performance of our method appears abnormal, we discuss the reasons and possible solutions. We hope our results can provide some useful reference for the similar applications of the semi-analytical method since our method is a relatively common approach in terms of both accuracy and implementation.     

On critical values concerning the evolution of the long period families

In a previous paper, we proposed another special critical value concerning the evolution of the long period family around the equilateral equilibrium points, besides the two values given by Henrard. Are there any other special critical values? After studying the stability curves of the long period family carefully, we gave a negative answer. During the study, we found an interesting family of periodic orbits which we called the homo family. We studied the evolution of this family following the increase of μ. With these findings, we were able to explain the origin of the four branches of periodic families emanating from L4 and the stability results of the equilateral equilibrium points.     

The web of three-planet resonances in the outer Solar System

In this paper we numerically detect the web of three-planet resonances (i.e., resonances among mean anomalies, nodes and perihelia of three planets) with respect to the variation of the semi-major axis of Saturn and Jupiter, in a model including the planets from Jupiter to Neptune. The measure confirms the relevance of these resonances in the long-term evolution of the outer Solar System and provides a technique to identify some of the related coefficients.     

Two‐body system with a rotating central body (e.g. Earth‐Moon system) within the Projective Unified Field Theory

In this treatise the well‐known 2‐body problem with a rotating central body is systematically reinvestigated on the basis of the Projective Unified Field Theory (PUFT) under the following aspects (including the special case of the Newton mechanics): First, equation of motion with abstract additional terms being appropriate for the interpretation of the various effects under discussion: tidal friction effect as well as non‐tidal effects (e.g. rebound effect as temporal variation of the moment of inertia of the rotating body, general‐relativistic Lense‐Thirring effect, new scalaric effects of cosmological origin, being an outcome of the scalarity phenomenon of matter (PUFT). Second, numerical evaluation of the theory. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.