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We investigated the motion of the perijove and ascending node of the 8th satellite of Jupiter, Pasiphae. The main perturbations by the Sun on the satellite permitted to use an intermediate orbit obtained by approximated solutions of differential equations previously transformed by the Von Zeipel method. The orbit is a non-Keplerian ellipse. The secular motion of the ascending node, argument of perijove, and essential periodic perturbations were taken into account. Using our theory we showed that the inclination and eccentricity of Pasiphae can acquire values by which the orbit becomes a librating one; but, within Pasiphae’s observation period, the motion of its perijove is circulating. Taking into account the results of our previous works on Pasiphae motion, we can conclude that the mean motion of the ascending node is similar for different values of the satellite inclination and eccentricity. But the mean motion of the perijove strongly depends on the orbit inclination and eccentricity, according to the Lidov–Kozai mechanism.

We investigate numerically the transfer routes from Jupiter-family towards Encke-like cometary orbits, including in the model all the planets as well as non-gravitational forces. The numerical integrations are started from orbital elements similar to those of 2P/Encke, changing the perihelion distance q, to obtain starting orbits in the Jupiter family, and the non-gravitational parameter A2. The results show that some of the model orbits reach the Encke-like stage within a reasonable time, comparable to a typical active cometary lifetime; along the way, at the crossing of mean motion resonances with Jupiter, temporary captures in resonance may occur. Thus, resonances and non-gravitational forces appear to be key factors in the transfer of orbits from the Jupiter family to the Encke region.

The orbital evolution of the parent body of comet 73P/Schwassmann-Wachmann 3 and its secondary nuclei B and C after its split at the end of 1995 is investigated. 1500 years backward numerical integration of the parent body and 500 years forward numerical integration of all three bodies were done. Possible consequences of the comet splitting on the population of meteoroids in the vicinity of the Earth's orbit, mainly its manifestation as a meteor shower in 2006, are presented.

The possibility to capture a small body moving on a heliocentric stable orbit by Jupiter has been investigated. Initial conditions were taken from the 8th retrograde satellite of Jupiter where we changed the orbital velocity so that the fictitious body was now in a heliocentric stable orbit. Using the numerical integrate techniques, we found conditions at which the small body can be captured by Jupiter on a retrograde orbit. To change the stable heliocentric orbit of the body to a transfer orbit to Jupiter, we used the techniques of small orbital velocity variations.

The origin of the Taurid meteor stream is investigated on the basis of the assumption that the complete set of observable quantities may be explained as a simultaneous action of nongravitational forces acting on meteoroids ejected from the parent body represented only by comet P\Encke. Discussion is concentrated on the problem of whether or not the assumption of the importance of nongravitational forces is acceptable. Numerical values for nongravitational acceleration are presented. A time evolution from 10,000 to 15,000 years is considered and graphically presented. The test is made for dust particles ejected at perihelia of the orbit of the comet Encke. The particles are released at velocities of 20–600 m s −1 . Gravitational perturbations of all planets and nongravitational effects are considered.

The activity of the Lyrid meteor shower in the years 1945–1947 and 1952 is studied. For this purpose more than 470 visual records of Lyrid meteors, observed at the Skalnate Pleso Observatory over a period of four years, are analysed and converted to zenithal hourly rates. The correction factor cosyZR with the exponent γ = 1.47 is used.

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.

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.

The Institute of Theoretical Astronomy in St. Petersburg and the Astronomical Institute in Bratislava are preparing a new edition of the Catalogue of short-period comets. This edition will be supplemented by short-period comets discovered after the year 1983 and comprises some new features, e. g. the evolution of orbital elements between the years 1750 and 2050, and the perihelion passages of comets within the 1994–2050 years. A new method has been employed for the determination of nongravitational parameters from the osculating elements of a comet based on all its observed returns.

The orbital evolution of model meteoroids ejected from the comet Encke has been investigated. The particles abandon the mother body with velocities 20 and 40 ms-1 perihelion within the interval of the past 10,000 years. Their 10,000 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 are considered, too. Orbital dispersions of the model meteoroids are presented. The importance of nongravitational forces for a long-term orbital evolution of meteoroid streams is shown.

The orbital evolutions of the asteroid 3040 Kozai and model asteroids with similar orbits have been investigated. Their osculating orbits for an epoch 1991 December 10 were numerically integrated forward within the interval of 20,000 years, using a dynamical model of the solar system consisting of all inner planets, Jupiter, and Saturn. The orbit of the asteroid Kozai is stable. Its motion is affected only by long-period perturbations of planets. With change of the argument of perihelion of the asteroid Kozai, the evolution of the model asteroid orbits changes essentially, too. The model orbits with the argument of perihelion changed by the order of 10% show that asteroids with such orbital parameters may approach the Earth orbit, while asteroids with larger changes may even cross it, at least after 10,000 years. Long-term orbital evolution of asteroids with these orbital parameters is very sensitive on their angular elements.

The orbitai evolution of Pasiphae,the 8th satellite of Jupiter, has been investigated. Its osculating orbit for the epoch 29 October 1983 was numerically integrated over the interval of 20,000 years. Within the investigated time interval also the question of the Hill's stability has been studied. The Jacobian constant, generalized to the avegaged elliptic problem. calculated from position and velocities obtained by numerical integration, changes less then the order of 10−8 The dominant pertubations by the Sun to the satellite allow us to use the intermediate orbit of the averaged elliptic three-body problem for investigation of the evolutionary change in the motion of the satellite. The mean motion of the agreement of perijove and the ascending node of the satellite are defined by analytical formulae, using the osculating non-Keplerian ellipse with moving node and perijove, and changing eccentricity. The results obtained according to this theory are comparable with those calculated from the numerical integration.

The modelling of the insufficient orbital elements of extra-solar planets (EPs) revolving around one component in a binary star system is investigated in the present paper. This problem is considered in the frame of the three-body problem using the analytical theory of Orlov & Solovaya (1998). In the general case, the motion is defined by the masses of the components and by the six pairs of the initial values of the Keplerian elements. For EPs, it is not possible to obtain the complete set of elements for the orbit, in particular, the ascending node and the angle of the inclination. So, it is possible the two different variants of orbital evolution of EPs depend on the initial conditions. In one case, the orbit is unstable. Using the stability conditions of Solovaya & Pittich (2004), which are presented by the angle of the mutual inclination of the orbits between the EP and distant star, we varied unknown angular elements and defined the regions with possible values of the elements for which the motion of EP stays stable. We applied these calculations to the particular specific EPs: HD19994b, HD196885Ab and HD222404b.

Context. The orbits of one-apparition comets discovered in the early part of the last century have formerly been determined with very different numerical methods and assumptions on the model of the solar system, including the number of planets taken into account. Moreover, observations of the comet-minus-star-type sometimes led to determination of the comet position that are less precise than what we can derive today by using a more modern star catalogue. Aims. We aim to provide a new catalogue of cometary orbits that are derived using a completely homogeneous data treatment, accurate numerical integration, and a modern model of the solar system. Methods. We collected the complete sets of observations for investigated comets from the original publications. Then we recalculated the cometary positions for the comet-minus-star-type of observations using the Positions and Proper Motions Star Catalogue, and applied a uniform method for the data selection and weighting. As a final result, new osculating orbits were determined. Secondly, dynamical calculations were performed to the distance of 250 AU from the Sun to derive original and future barycentric orbits for evolution backward and forward in time. These numerical calculations for a given object start from a swarm of virtual comets constructed using our osculating (nominal) orbit. In this way, we obtained the orbital element uncertainties of original and future barycentric orbits. Results. We present homogeneous sets of orbital elements for osculating, original, and future orbits for 38 one-apparition comets. Non-gravitational orbits are derived for thirteen of them.

The present study concerns the application of an analytical theory of the stellar three- - bodies problem to the triple stellar system ξ UMa, whose components move along short-period orbits with periods of 2 years and 60 years. For this purpose the solution of the simplified canonical system of differential equations obtained in terms of hyperelliptic integrals by Hamilton-Jacobi method was used. The precision of the solution was increased by addition of short-periodic terms computed from the formulae of the transformation by von Zeipel’s method.

Several digital techniques have been used to remove large-scale background variations caused by manufacturing and technology of the photographic processing on old photographic plates ORWO ZU-21. Suppression of these large-scale background variations improved the study of large-scale phenomena in cometary plasma tails and the determination of the solar wind characteristics.

The 20,000 years orbital evolution of massless fictitious asteroids located at a border of the Hill’s gravitational sphere has been investigated. The eleven orbits with the eccentricities from 0.0 to 0.4 in five groups of inclinations from 40° to 80° were numerically integrated with planetary perturbations of six major planets, using the numerical integration n-body program with the Everhart’s integrator RA15. For each group time evolution of orbital elements of the asteroids is presented.

Many orbits of periodic comets are subject to drastic changes due to close encounters with planets. In such cases the Inaccuracy of osculating elements determined from observations is a much more significant source of instability than the one coming from the integration procedure. The analysis of the motion of P/Shajn-Schaldach showed that its precise determination over a long time Interval is practically impossible due to repeated close encounters with Jupiter, and that it would remain so even if the orbit of the comet were known with a much greater accuracy. In this paper we try to understand how much the possibility to precisely reconstruct the past motion of a comet depends on the orbit of the individual comet under study. We have added new computations to those already made; part of these concern two more comets, while others enlarge the investigated range of initial conditions for P/Shajn-Schaldach.