We have recently built a coherent theory of the motion of the satellites Mimas, Enceladus, Tethys, Dione, Rhea, Titan and Iapetus. The final form of the “Théorie Analytique des Satellites de Saturne” (TASS1.6) is presented in Vienne & Duriez (1995). The internal precision of TASS is a few kilometers over three years and some tens kilometers over one century. The root-mean-square residuals of the adjustment of TASS over one century of Earth based observations reach 0″.12 for the best data sets, until 0″.015 for the few mutual phenomenas of 1981.

New constants for Sampson-Lieske theory of the Galilean Satellites have been derived using 6360 individual photographic positions (1891–1990) and 438 pseudo astrometric positions from mutual occultations during 1973, 1979, 1985 and 1991. Using these new sets of constants, significant improvement is noticed in the O-C values of the sky plane coordinates of the mutual event data set and residuals in longitude for Io and Europa are found to improve. Problems concerning the inclusion of mutual event data in attempting evaluation of secular variations of the mean motions of the satellites are discussed.

This work is a continuation of our study of the efficiency of two well-known methods for the numerical integration of the equations of motion of planetary satellites together with the variational equations of the system. The methods are the 10th-order Gauss-Jackson backward-difference method described in [4, 6] and the Runge-Kutta-Nyström RKN12(10)17M [1].

Somewhat more than a century after its introduction for the purpose of discovering minor planets, photography is now rapidly giving way to the CCD as the technology of choice for observing these bodies. A CCD has been used in scanning mode in the University of Arizona's ‘Spacewatch’ program for the discovery of minor planets since as long ago as 1984 (Gehrels 1984, Gehrels et al. 1986), while a CCD in stare mode was first applied as a matter of routine to an established observing program for astrometric follow-up in 1989—that at the Oak Ridge Observatory in Massachusetts (McCrosky 1990). After its initial 1984–1986 success, Spacewatch was modified with the help of a larger CCD and improved computer software and with the adoption of the particular mission of searching for NEOs, or minor planets (and comets) that pass close to the earth (Rabinowitz 1991, Scotti 1994). The Oak Ridge program utilizes a 1.5-m reflector, and the first CCD observations were reduced using the Astrographic Catalogue, the mainstay of the Oak Ridge photographic program back to its inauguration in 1972, as well as of other older photographic programs in which the fields observed were significantly less than 1° across. Within months, the availability, on CD-ROMs, of the STScI Guide Star Catalogue (Villard 1989) effectively consigned the venerable AC to the scrap-heap, and the rapid development of ready-made and relatively inexpensive CCD systems (e.g., di Cicco 1992) has recently increased the volume of CCD astrometry considerably, allowing it to be conveniently and reliably carried out, even by amateur astronomers. At the present time, very nearly 50 percent of the astrometric observations, typically 6000, published each month in the Minor Planet Center's Minor Planet Circulars are obtained by means of a CCD.

In the context of the search of asteroid families (i.e. identification of minor planets as potential fragments of an old bigger body), the calculation of proper elements plays an important role. They are quasi-invariants of the motion, obtained by a double averaging process of the restricted N-body problem; firstly the osculating elements are averaged over the short periodic terms (namely the longitudes of the asteroid and of the perturbing planets) so to get the mean elements, and secondly, the mean elements are averaged over the long periodic terms (longitudes of the pericenters and of the nodes of the asteroid and of the perturbing planets) to obtain the proper elements.

The author's theory of Trojan asteroids (Érdi, 1988) is developed further. The motion of the Trojans is considered in the framework of the three-dimensional elliptic restricted three-body problem of the Sun-Jupiter-asteroid system including also the secular changes of Jupiter's orbital eccentricity and the apsidal motion of Jupiter's elliptic orbit. An asymptotic solution is derived, by applying the multiple-timescale method, for the cylindrical coordinates of the asteriods and for the perturbations of the orbital elements. This solution is used for the analysis of the long-time dynamical behaviour of the perihelion and the eccentricity of the Trojans.

An asteroid captured in the Hecuba gap (2/1 resonance with Jupiter) may remain there for a long time before escaping. However, the study of the diffusion of orbits in the gap indicates an escape timescale in the range 107–109 years. The short-period perturbations of Jupiter's orbit play a determinant role in the creation of the stochasticity responsible for the escape.

For chaotic asteroidal trajectories exhibiting multiple bursts of eccentricity in the 3/1 Jovian resonance, we derive the distribution function of time intervals between such bursts. At the onset, the resulting distribution decays exponentially. In the tail, an algebraic decay is observed, with the power-law index for the integral distribution in the range −2 to −1.

The orbital evolutions of fictitious asteroids with high inclinations have been investigated. The selected initial orbits represent asteroids with movement, which corresponds to the conditions of the Tisserand invariant for C = C (L1) in the restricted three body problem. Initial eccentricities of the orbits cover the interval 0.0–0.4, inclinations the interval 40–80°, and arguments of perihelion the interval 0–360°. The equations of motion of the asteroids were numerically integrated from the epoch March 25, 1991 forward within the interval of 20,000 years, using a dynamical model of the solar system consisting of all planets. The orbits of the model asteroids are stable at least during the investigated period.

Differential correction procedure allows us to improve orbits for which new observations are available; however, it only works provided the original orbit is within the convergence domain of the pseudo-Newton method. Given the strong nonlinearity of the problem, this only occurs when the residuals of the new observations with respect to the old orbit are quite small.

One of the most popular methods for orbital elements correction, by means of O-C calculus, is based on Brouwer's method [2], which is very well adapted for integrating short periods of time. We propose a general method to integrate over long intervals of time, when we have good observations, based upon a time-dependent functional relation between the derivatives of all elements with respect to all variations in the initial elements. First, we verify the truth of the unrestricted hypothesis by means of the proposed analytical method and a numerical derivation. In [6], we have incorporated a correction frame model jointly with this general method and, then, we have constructed the residual function which is minimized by the least squares method. But, as we are going to see later, there are correlations between the parameters frame correction model and the initial elements involved in the adjustment. They are obtained here, as well as an expression for the equinox correction from these frame parameters. Finally, by means of a simply weighted method, with the observations from MPC's magnetic tape, in FK4 system, we obtain an estimation for these frame parameters and an equinox correction which is in great accord with the adopted value (see [3]).

Recent improvements of observational accuracy, stellar catalogues and efficiency of the procedures for searching for asteroid close encounters (Kuzmanoski and Knežević, 1993) gave rise to an increased interest in the problem of determination of asteroid masses (Bowell et al., 1995).

It is well known that the perturbing effects of any asteroid are negligible at all times, except during a close encounter. The influence of a perturbing asteroid on the motion of a perturbed one can be investigated by means of the differences of the right ascensions and declinations of the perturbed asteroid, as inferred from two numerical integrations, the one with and the other without taking into account the effects of the perturbing asteroid (Kuzmanoski and Knežević, 1994). These effects before reaching the epoch of the close encounter are very small, as expected. Beyond this epoch, the differences increase with time, due to the fact that the orbit is changed on account of the influence of the perturbing body during the close approach, so that perturbations by major planets act on it in a different way.

Investigators generally conjecture a steady flux of new comets from the Oort cloud through the inner Solar system. Due to gravitational perturbations by major planets these objects may escape, become long period comets (LPCs) if their orbital periods P are larger than 200yr or become short period comets (SPCs) when their period is less than 200yr. SPCs are further divided in two types: the Halley type comets (HT, for P > 20yr) and the Jupiter family comets (JF, for P < 20yr).

The hypothetical model of capture I consider is as follows: a comet with an initial conic orbit, meets close to one of its vertices an outer planet and generates one or several little comets (crossing of the Roche limit) with an elliptic orbit. This initial vertex always remains one of the vertices of the captured orbit by the Solar System. Even if there is a discontinuity of all the orbital elements during a very short time of the capture, I assume that the orbital plane is unchanged during the capture, as indeed was the case for Brooks 2 in 1886 (see Belyaev et al., 1986) or will be for Gehrels 3 in 2300 (see Carusi et al., 1985). After this first decisive step, the “new” comets may be subject to some other captures by jovian planets during their evolution with the same scenario. All these hypotheses allow to find particular numerical results for 142 comets whose current orbital elements were found in the Marsden catalog or given by P. Rocher, but I shall only give several examples in the following section.

The orbital evolution of model meteoroids ejected from the comet Encke and from the asteroid Hephaistos was investigated. The particles abandoned the mother body with velocities 40, 150 and 600 ms−1 at their perihelia within the interval of 10,000 to 20,000 years, respectively. Their 10,000 to 20,000 years old osculating orbits were numerically integrated forward, using a dynamical model of the solar system consisting of all planets. Forces from solar electromagnetic and corpuscular radiation effecting the particles were considered, too. Orbital dispersions of the model meteoroids, ejected in different epochs, compared with those obtained from observations. It seems probable that the comet Encke and the asteroid Hephaistos are sufficient to produce the observed Taurid meteor complex.

Outbursts of the comet's brightness play a significant role in the study of the physical nature and evolution of comets. The causes of cometary outbursts are still not properly understood. It is known, however, that there is correlation between the outbursts and the high-velocity flux of solar wind. The evidences of such causal relationship are the following: the existence of the correlation between the geomagnetic perturbations and the outburst activity of the comets [1]; two-peaks distribution of the comet's outbursts, which depends on the 11-year solar cycle phase with maxima at phases 0.2–0.3 and 0.7–0.8, in coincidence with the distribution of physical characteristics of high-velocity fluxes [2]; the repeated character of the outbursts with main intervals of 7–8, 14–15, 22–24 and 30 days, this corresponds to the four-sector structure of the interplanetary magnetic field [3].

The process of capture into a mean motion resonance induced by a non conservative force has been studied by many authors (Henrard, 1982); Peale, 1986). Capture probabilities have been established through the use of an analytical model based on averaged Hamiltonian systems, with an adiabatic varying parameter (Henrard, 1982; Lemaitre, 1984). For each resonance, these probabilities are basically function of the orbital element involved (eccentricity and/or orbital inclination) far from the resonance and the perturber's mass, there being no dependence on the dissipation rate. However when the process is not adiabatic, the dissipation rate has a fundamental importance for capture probabilities (Gomes, 1995). For these processes, an analytical association of orbital elements far from the resonance with capture probabilities is still an open question. Association of orbital elements just before resonance with the process of capture is presented in (Marzari and Vanzani, 1994) and (Lazzaro et al, 1994). In these works the eccentricity and longitude of the perihelion are checked for in respect with capture into resonance. Here we aim at verifying how the trapping process changes with orbital elements just before resonance, but not restricting ourselves to the pair eccentricity-perihelion.

As meteorites from the Moon and Mars continue to be discovered, it is increasingly clear that impact fragments can escape from large bodies more easily than previously believed. These escaping fragments are then subject to the gravitational perturbations of the planets, allowing them to be transferred to a body other than their parent. The lunar meteorites and SNC meteorites prove the plausibility of this process. Warren (1994) summarizes cosmic ray exposure ages and other properties of the lunar and martian meteorites. Their existence confirms that lightly shocked material can be launched at greater than the escape speed of the Moon and Mars.

Dissipative effects arising from the core–mantle interaction are treated in a Hamiltonian framework, using a simple model. Analytical solutions are obtained for free and forced motions. The first show the persistence or damping of the different components. The latter, frequency dependent changes of amplitude and phase. Preliminary numerical values are in acceptable agreement with observational data.