The evolution of near-parabolic orbits with perihelia in the trans-neptunian region has been studied, considering the action of planetary, Galactic and stellar perturbations for the age of the Solar System. This investigation has led to the conclusion that the observed trans-neptunian objects in high-eccentricity orbits might originate from the inner core of the Oort cloud.

Transient redshifted events monitored in the spectrum of β Pictoris have been interpreted as resulting from the evaporation of numerous comet-like bodies in the vicinity of this star. The dynamical origin for this phenomenon is attributed to mean-motion resonances (4:1 and 3:1) with a Jovian-like planet. Numerical simulations of this phenomenon are able to correctly reproduce the dynamical characteristics of the star-grazers observed. The numerical study allows to estimate the density of the planetesimal disk from which the bodies are supposed to originate, i.e. ∼ a few 108 bodies per AU. A key issue with this model is the refilling of the resonances, as without refilling they should be cleared within a few 105 yr and the observed phenomenon should stop. Collisions among planetesimals are a plausible mechanism. Collisional simulations show that collisions are able to sustain the observed phenomenon over much more than 106 yr, provided the population of the disk is high enough. The mass density of this population is estimated to a few tens of Earth masses per AU, which is only marginally realistic. However, the mass estimate is very poorly constrained.

Recent observational results from ground and space-based observatories in combination with laboratory simulations allow us to monitor the evolution, survival, transport and transformation of cosmic dust from molecular clouds and the diffuse interstellar medium, until their incorporation into Solar System material. The composition of comets encodes information on their origin and can be used as a tracer for processes which were predominant in the protosolar nebula. A comparison of the composition and abundances of interstellar molecules and cometary volatiles reveals a general correspondence, but discrepancies are also apparent. Detailed studies indicate that cometary ices are a mixture of original interstellar material with material that has been moderately to heavily processed in the pre-solar nebula. The inventory and distribution of ice and organic molecules in interstellar clouds and in comets and their common link are briefly described.

Spectra obtained with the Infrared Space Observatory ISO of the dusty disks surrounding young stars display several characteristics which suggest the presence of large amounts of cometary material during these early stages. Of special interest are crystalline silicates and hydrated silicates, which surprisingly appear to be present already in cool material surrounding young objects. Another surprise is the occurrence of cometary features in the disks surrounding some binary post-AGB stars.

As part of an observing programme with the ISAAC infrared spectrometer at the 8-m Antu telescope of the ESO-Very Large Telescope (Chile) devoted to the study of the surface composition of Kuiper Belt Objects and Centaurs, we obtained, in May 1999, spectra of the red Centaur Asbolus in the J, H and K bands. The spectra appear featureless.

We propose a wide-shallow TNO search to be done with the Wide Field Imager (WFI) instrument at the 2.2m MPG/ESO telescope in La Silla/Chile. The WFI is a half-deg camera equipped with an 8kx8k CCD (0.24 arcsec/pixel). It was used in 1999 to run a pilot project for a TNO search. Using the images of typically 24mag limiting brightness and an automatic detection software (developed at ESO Chile) it was possible to discover 6 TNOs in a small search area of 1.5 sdeg. The project is now continued on a somewhat larger scale in order to discover more TNOs in a systematic way and to reach operational status for a full on-line detection of the objects as well as astrometric and photometric reduction at the telescope. The final goal is to perform a survey of a major part of the sky (typically 2000 sdeg in and out of the ecliptic) down to 24mag. Follow-up astrometry and photometry of the expected more than 3000 discovered objects will secure their orbital and physical characterisation for synoptic dynamical and taxonomic studies of the transneptunian population.

Long term integrations of highly eccentric orbits are necessary to study the orbital evolution of comets and some minor planets. We discovered that the KS regularization is effective not only in the sense the magnitude of local error is reduced in the close approach but in the sense it dramatically reduces the positional error growth. In fact, it is in proportion to the fictitious time s while the Cowell method, the usual integration in 3-dimensional space leads to the positional error growing as a quadratic function of time. This good property is independent of the type of the integrators, of the type of the perturbations or of the magnitude of the nominal eccentricity. This phenomenon is based on the fact that the equations of motion in the KS variables are those of perturbed harmonic oscillators. As the best numerical integrator, we recommend the predictor formula of symmetric linear multistep method because (1) it runs fast since only one functional evaluation is required at each step, (2) its error constants are close to the minimum among the class of linear multistep methods, (3) its numerical error of the conserved quantities remains almost constant with time, and (4) it shows no stepsize resonance/instability in integrating the KS regularized equation of motions and the harmonic oscillator potential is the only case where the step size instability does not appear. Therefore the KS regularization is useful to investigate the long term behavior of perturbed two body problems for studying comets, minor planets, Moon, and artificial satellites.

Nowadays many attempts are made to establish a qualitative and a quantitative connection between Kuiper Belt Population and Jupiter Family Comets. Basically, this can be thought as a diffusion process throughout the outer Solar System due to multiple close encounters with the giant planets. But, following the path of a body in such a process is not an easy task to be approached analytically nor numerically, because the motion is very chaotic and spread over a long time. A statistical approach seems to be a reasonable way and is the purpose of this paper.

More than two hundred transneptunian Kuiper-Belt Objects (KBOs) have so far been identified. Because of their large distances from the Sun, and their intrinsically small sizes, only the largest members (diameters more than 100 km) can be observed by direct imaging with large telescopes. Even smaller KBOs, though expected to be more numerous on theoretical grounds, cannot be seen directly unless they happen to block out the light from background stars. The Taiwan-America Occultation Survey (TAOS) project is a collaboration among the Lawrence Livermore Laboratory (USA), Academia Sinica, National Central University (both of Taiwan), and other institutes, that aims to measure the frequency of such chance stellar occultations, and thereby conduct the census of the Kuiper-Belt population down to a few kilometer sizes. An array of robotic telescopes are being set up in central Taiwan to monitor the brightness variation of several thousand stars at a rate of a few Hz. Observations will be operated in a synchronized and coincidence mode, so the sequence and timing of any candidate occultation event can be recorded and distinguished against a false detection. The full survey is expected to start in the fall of 2000.

Due to gravitational interactions with large trans-neptunian objects (TNOs) several percent of TNOs can change their semimajor axes by more that 1 AU during last 4 Gyr. Now about 30000 1-km former TNOs can be Jupiter crossers and about 20% of Earth-crossing objects can be former TNOs which now move in Jupiter-crossing orbits.

The Trans-Neptunian Objects (TNOs) are very difficult to observe due to their faintness. Spectra can be obtained for only few objects. For this reason, broad band photometry is the only available technique to study their physical properties from a statistical point of view. To improve the knowledge about the physical nature of the Kuiper Belt, we have obtained several observing runs at different four-meter class telescopes (NTT - Chile; CFHT - Hawaii).

The data presented here were obtained at NTT (ESO - Chile) during three observing runs from 1997 to 2000. We used the SUSI and SUSI 2 CCD cameras with the Bessel B, V, R, and I filters.

Our numerical simulations of the Edgeworth-Kuiper Belt objects gravitationally scattered by the four giant planets accounting for mean motion resonances reveal numerous resonant gaps in the distribution of the scattered population.

Astrometry for an accurate orbit determination of distant objects is usually made with large telescopes ranging from 2 to 10 meters. In selected cases the bright(er) part of their population has been effectively observed with small 0.6 to 1 meter class telescopes. We point out here methods and techniques used at the Kle Observatory including our results. The extension of this programme using a new larger telescope is in preparation. We also mention a possibility of using some web tools for call for follow-up.

We consider initial determination of orbits for trans-neptunian objects (TNOs), a topical theme because of the rapidly growing TNO population and the challenges in recovering lost TNOs. We apply the method of initial phase-space ranging of orbits to the poorly observed TNOs. The rigorous a posteriori probability density of the TNO orbital elements is examined using a Monte Carlo technique by varying the TNO topocentric ranges corresponding to the observation dates. We can optionally adopt a Bayesian approach to select the region of phase space containing the most plausible orbits. This is accomplished by incorporating semimajor axes, eccentricities, inclinations, and absolute magnitudes of multi-apparition TNOs as a priori information. The resulting a posteriori distributions permit ephemeris and ephemeris uncertainty prediction for TNO recovery observations.

Our understanding of transport processes in stars is still in its infancy. First consider overshooting. There is now ample evidence from, e.g., the best-observed binary stars and fits of models to observed colour-magnitude (C-M) diagrams that some amount of mixing must occur beyond the classical boundary of the convective core set by the Schwarzschild criterion. Such mixing can be achieved by convective penetration; however, despite impressive progress on the theoretical front, a rigorous prediction of the extent of overshooting has not yet been achieved. As a result, most stellar evolutionary calculations have simply opted to extend convective core sizes by an amount (usually measured as a fraction of a pressure scale height) that produces reasonable consistency with observations. But how realistic are such models? To what extent does the overshooting depend on mass and/or evolutionary state? What is the role of rotation in determining the size of convective cores? How much does rotation-induced meridional circulation contribute to such mixing?

This talk reviews recent results relevant to identifying and constraining the processes that mix and transport specific elements in the envelopes of main sequence stars.

The chemical composition of globular cluster stars is briefly reviewed, attention being given principally to the following problems: (1) primordial and evolutionary abundance variations among globular cluster stars, and (2) abundance differences between cluster and halo field giants.

ω Cen is unique among the Galactic globular clusters. It exhibits not only classical mixing signatures, but also those of primordial chemical enrichment by both massive and intermediate-mass stars: the abundances of all elements vary, not just those of the C, N, O, Na, Mg, and Al. The challenge is to disentangle the roles of mixing and primordial phenomena. We discuss here what sets ω Cen apart from the other clusters.

Based on Strömgren uvby CCD photometry, and UVES spectroscopy we present evidence that possibly all globular clusters show large variations in their abundances of nitrogen, aluminium and sodium, which are not only due to internal mixing processes. Furthermore the evidence for radiative levitation among hot horizontal branch stars is briefly discussed.

Three critical tests are applied to the models that hypothesize the transport of angular momentum and material via turbulence. The models fail on all three counts.