The exploration of our Solar System is rapidly growing in importance as a scientific discipline. During the last decades, great progress has been achieved as the result of space missions to planets and small bodies and improved remote-sensing methods, as well as due to refined techniques of laboratory measurements and a rapid progress in theoretical studies, involving the development of various astrophysical and geophysical evolutionary models, based in particular on the approach of comparative planetology. In the crossroads of astronomy and geophysics, recent years have seen a growing understanding of the importance of impact phenomena throughout the history of the Solar System and, therefore, the necessity to get more insight into the problem of interactions of planets and small bodies. This importance is clearly manifested by the observed cratering records of planetary surfaces and such dramatic events as the explosions of the comet P/Shoemaker-Levy 9 fragments in Jupiter’s atmosphere in 1994, that of the Tunguska object over Siberia in 1908, and the Chicxulub event dating back to the end of the Cretaceous.

Ideas about the contents of the Solar System beyond Neptune and Pluto can be traced back to at least Edgeworth (1943, 1949) and Kuiper (1951), who speculated on the existence of pre-planetary small bodies in the outer Solar System beyond the orbit of Neptune - remnants of the accretion process in the primordial Solar Nebula. The basis for the speculation was primarily the argument that the Solar Nebula was unlikely to have been abruptly truncated at the orbit of Neptune, and that in the trans-Neptunian accretion timescales were too long for bodies larger than about ˜ 1000 km in radius to have formed in the 4.5 billion year age of the Solar System. Another important theoretical argument relevant to this region of the Solar System is related to the origin of short period comets. Fernández (1980) suggested that the short period comets may have an origin in a disk of small bodies beyond Neptune, rather than being “captured” from the population of long period comets originating in the Oort Cloud, the latter scenario having considerable difficulty reconciling the observed flux of short period comets with the exceedingly low efficiency of transfer of long period comet orbits to short period ones by means of the gravitational perturbations of the giant planets. The new scenario received further strength in the numerical work of Duncan et al. (1988) and Quinn et al. (1990) which showed that the relatively small orbital inclinations of the Jupiter-family short period comets were not consistent with a source in the isotropic Oort Cloud of comets but could be reproduced with a source in a low-inclination reservoir beyond Neptune’s orbit. Duncan et al. named this hypothetical source the Kuiper Belt, and the name has come into common use in the last decade (although other names are also in use, e.g. Edgeworth-Kuiper Belt, and trans-Neptunian objects). A recent theoretical milestone was the work by Holman and Wisdom (1993) and Levison and Duncan (1993) on the long term stability of test particle orbits in the trans-Neptunian Solar System. This work showed that low-eccentricity, low-inclination orbits with semimajor axes in excess of about 43 AU are stable on billion year timescales, but that in the region between 35 AU and 43 AU orbital stability times range from 107 yr to more than 109 yr [see, for example, figure 1 in Holman (1995)]. Orbital instability in this intermediate region typically leads to a close encounter with Neptune which causes dramatic orbital changes, with the potential for subsequent transfer to the inner Solar System. Thus, this region could in principle serve as the reservoir of short period comets at the present epoch. However, the idea of a kinematically cold — i.e. low-eccentricity, low-inclination — population in this region is at odds with recent observations, and the question of the origin of short period comets remains unsettled at the present time.

In this paper it is explained how asteroids with large aphelion distances avoid very close approach to Jupiter. Namely, since for asteroids with resonant mean motions the critical arguments librate as it has been known for many years, and for those with non-resonant mean motions the eccentricities change with the argument of perihelion so the distance to Jupiter cannot be very small.

Also some behaviours of Kuiper-belt asteroids are studied by a similar way and it is found that the libration region for the argument of perihelion appears only when the eccentricity is very large. Therefore, even though the eccentricity is very large it is possible for any Kuiper-belt asteroid to avoid very close approach to any of the planets.

P/1996 N2 Elst-Pizarro was discovered with a tail of dust in July 1996 and was thus classified as periodic comet. From the orbit point of view it belongs to the outer asteroid belt and is very likely a member of the Themis family, a group of bodies originating from an asteroid collision.

The absence of a coma and the presence of the needle-like anti-tail in August 1996 did not exclude the possibility of a sudden emission event which could have been caused by the impact of another minor body on the object. However, with the development of a normal tail between September and November 1996 it became obvious that the dust emission episode continued at least for 2 months after perihelion, a scenario that is typical for gas-driven cometary activity. However, it is still possible that a collision triggered the event.

The paper summarizes the observational pro and cons for impact-induced activity in this object, possibly the first ever detected comet-asteroid of the solar system.

The evidence for a major population of small comets (SCs) is summarized in two steps. First, we briefly summarize our previous work. Second, we describe recent work that continues to find SCs. When new capabilities become available that can detect SCs, we expect to find them and this is occurring. At present, their detection is a haphazard process and we advocate a dedicated, optimized search program.

We define SCs as those icy bodies (i.e., sublimating bodies) with radius less than 1000 meters. Often the existence of SCs is inferred from effects ascribed to them. These “effects” include: lunar cratering; cratering on Ganymede; excess interplanetary hydrogen; delivery of volatile materials to the terrestrial planets; and a source of fragile bodies entering the Earth’s atmosphere. While some of these indirect methods support the existence of SCs, direct observations are clearly preferred.

This paper briefly summarises the contribution to the understanding of meteoroids and their orbits from recent radar studies of meteors. New data from VHF and UHF observations indicates that some meteoroids are ablating at heights up to 160 km and modelling work suggests that such meteoric ionization can only be deposited by meteoroids that ablate at temperatures below 1000° K. Meteoroids with entry speeds well in excess of 100 km/s are clearly interstellar and some tentative sources have been identified. The distributions of the orbital elements of earlier data have been reanalysed in the light of a new understanding of the selection effects in those radar studies, and the presence of a significant set of retrograde orbits identified. The new technique of observing meteors ‘coming down the radar beam’ has led to very accurate measures of deceleration and detailed analysis of fragmentation events.

The hypothesis relating mass extinctions of life on Earth to impacts of comets whose flux is partly modulated by the dynamics of the Milky Way Galaxy contains a number of postulates that can be tested by geologic evidence and statistical analyses. In an increasing number of cases, geologic evidence for impact (widespread impact debris and/or large impact craters) is found at times of mass extinction events, and the record of dated impact craters has been found to show a significant correlation with mass extinctions. Statistical analyses suggest that mass extinction events exhibit a periodic component of about 26 to 30 Myr, and periodicities of 30± 0.5 Myr and 35 ±2 Myr have been extracted from sets of well-dated impact craters. The evidence is consistent with periodic or quasi-periodic showers of impactors, probably Oort Cloud comets, with an approximately 30-Myr cycle. The best explanation for these proposed quasi-periodic comet showers involves the Sun’s vertical oscillation through the galactic disk, which may have a similar cycle time between crossings of the galactic plane.

We consider the subject of time dependence of the Oort cloud comet flux. Over long time scales the flux is likely to be dominated by the adiabatic galactic tide. This tide is substantially modulated as the Solar System moves in its galactic orbit. If Shoemaker was correct in his estimate that virtually all terrestrial craters of diameter > 100 km are produced by long period comets, then the phase and plane crossing period of the Solar System about the galactic disk should be consistent. with the ages of accurately dated large craters. A time series analysis of these ages in which the Solar oscillation phase is fixed to be consistent with observations indicates a maximal correlation for a period of 36 ± 2 Myr. This period is well within observational limits. If improvements in stellar velocity dispersion studies continue, it is possible that a sufficiently accurate determination of the Solar oscillation period can be found to unambiguously answer the following questions. Is the Solar oscillation cycle correlated with the time series of ages for large craters? If so, can we reject the hypothesis that the correlation is an artifact that could likely be reproduced by a random distribution of ages? We present evidence which suggests that if it is found that the data requires a plane crossing period in the range 36 ± 2 Myr, the answer to both of these questions will be affirmative.

Different options for searching for near-Earth asteroids that may pose an impact hazard to the Earth in the future are discussed. The space option has not been studied in as much detail as the ground-based survey option, so a more detailed study of the space option might be appropriate. It is not evident, however, that a space-based system can be competitive or superior to the ground-based option, because past experience argues very strongly to the contrary.