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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 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 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 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 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.

It is shown that sudden outbursts of comets, or even complete splitting of their nuclei into several parts, are rather frequent phenomena that need to be accounted for in the evolution of cometary orbits. The distribution of the points in which such events occur indicates that the tidal action of the Sun and Jupiter, and also solar radiation, are much more probable causes of these effects than are collisions with the asteroids. Splitting is found to be relatively more frequent for comets moving in hyperbolic orbits. The observed velocities of separation indicate that the disruption of the nucleus provides an effective mechanism for the ejection of the fragments from long-period into hyperbolic orbits, augmenting the loss by planetary perturbations. The outbursts can be responsible for smaller changes in the orbits, which after repetition might produce a quasi-secular variation.