Although there are currently no professional search programs specifically designed for comets, comet discoveries are a significant by-product of the current search programs for near-earth asteroids. With their emphasis on the opposition point and the ecliptic, asteroid patrols are clearly biased toward discovering short-period comets. A. comparison of the comet discoveries made at elongations of less than 120° from the sun during the ten-year intervals ending in 1892 and 1992 indicates that the current opposition searches are not able to displace visual searches in the vicinity of the sun. Modification of the near-opposition search region to that proposed for the Spaceguard Project would be helpful, but—as also proposed for Spaceguard—supplementation is still necessary for high-inclination objects. CCD experimentation in the regions traditionally searched visually by amateurs would be useful. Searches for particular types of object like Kreutz sungrazers and comets near Jupiter in space are briefly discussed.

The Spacewatch program at the University of Arizona has pioneered automatic methods of detecting Near Earth Objects. Our software presently includes three modes of object detection: automatic motion identification; automatic streak identification; and visual streak identification. For automatic motion detection at sidereal drift rates, the 4σ detection threshold is near magnitude V = 20.9 for nearly stellar asteroid images. The automatic streak detection is able to locate streaks whose peak signal is above ~4σ and whose length is longer than about 10 pixels. Some visually detected streaks have had peak signals near ~1σ.

Between 1990 September 25 and 1993 June 30, 45 new Near Earth asteroids, two comets and two Centaur's have been discovered with the system. An additional six comets, five Near Earth asteroids, and one Centaur were also “re-discovered”. The system has directly detected for the first time Near Earth Objects in the complete size range from about 5 kilometers to about 5 meters. Each month ~2,000 main belt asteroids are also detected.

Future upgrades in both hardware, software, and telescope aperture may allow an order of magnitude increase in the rate of discovery of Near Earth Objects in the next several years. Several of the techniques proposed for the Spaceguard Survey have already been tested by Spacewatch, and others will need to be tested in the near future before such a survey can be implemented.

The existence of a belt of comets in the outer solar system (the “Kuiper belt”) has been postulated for a variety of reasons, including the need for a source for the short-period comets. The existence of the belt seems supported by the discoveries of the trans-Neptunian objects 1992 QB1, 1993 FW, 1993 RO, 1993 RP, 1993 SB, and 1993 SC. If these objects are members of the Kuiper belt, crude lower limits on the belt population can be established from the discoveries. The Kuiper belt comets are likely to be primordial remnants of the disk from which the solar system accreted. According to the current theories of cometary nucleus evolution, these objects are expected to possess mantles (“irradiation mantles”) which are different from mantles of comets which have been heated to the point of sublimation (“rubble mantles”). Kuiper belt comets on their way to short-period comet orbits may exist among the Centaur objects.

According to the investigation technique it is customary to divide meteoroids into three groups: 1) micrometeorites, with masses between 10–13 g and 10–6 g, and densities between 0.4 and 4 g/cm3; 2) meteorites, for which the chemical composition is studied in detail, and having densities from 2 to 8 g/cm3; 3) meteoroids proper, with masses larger than 10–6 g, which produce meteoric phenomena in the Earth's atmosphere detected by optical and radar means.

On the basis of available photographic and radar observations in Dushanbe the influx M(m) of meteoroids with mass equal or greater than m is determined as log in kg to the Earth per day. This formula is applicable to a mass range from 10–6 g to 102 g.

The phenomenon of meteoroid fragmentation in the atmosphere was observed repeatedly by means of different methods and especially using the photographic technique of instantaneous exposure. Among four principal forms of fragmentation, the quasi-continuous fragmentation, i.e. a gradual release of smallest fragments from the surface of a parent meteoroid and their subsequent evaporation, is most common. The analysis of photographic observations shows that about 30% of meteoroids display this type of fragmentation. According to the theory of quasi-continuous fragmentation and on the basis of lightcurves of meteors, the densities of 85 meteoroids have been determined, which vary in the range from 0.1 to 8 g/cm3. Not only porous and crumbly meteoroids but more dense stony and stony-iron meteoroids are also the subjects of fragmentation as well.

This paper discusses the status of our knowledge regarding asteroid sizes and albedos. It presents a brief discussion of the methods used to determine sizes and albedos beginning with attempts using filar micrometers as early as 1802 and culminating with the 1993 publication of the IRAS Minor Planet Survey. It addresses the completeness and reliability of the IRAS Minor Planet Survey, summarizes the statistical adjustments made to the derived results, and considers the implications of those results.

The definition, population, extent, origin and evolution of the individual subsystems of comets and transitions between them are discussed, together with presentation of the relevant statistical data and their changes with time. The largest outer subsystems are unobservable, but their existence is documented by the necessity of progressive replenishment of the observable populations, with limited survival times. There is persuasive evidence for two different evolutionary paths, one from the Oort cloud and another from the Kuiper belt. While the extent and accuracy of the data available is increasing rapidly, the Jupiter family of comets is the only one for which the evolutionary time scales do not exceed by many orders of magnitude the history of astronomical observations. The individual comet populations differ from one another not only by the distribution of orbits, but also by the size distribution and aging rate of their members. Their dynamical evolution is coupled with disintegration processes, which make it questionable whether the present state can be interpreted as a long-term average.

The phenomenon of a comet-asteroid transition presents the opportunity to study the comet reservoir in comparison to that from which asteroids are derived and to understand the evolution of comets. I discuss six significant areas which have impacted understanding of the comet-asteroid transition from recent years: new discoveries, discovery of dust and volatile comae at 2060 Chiron, observations of comet nuclei, observations of extinct-comet candidates, observations of dust trails associated with short period comets, and discovery of a dust tail on a prediscovery image of 4015 Wilson-Harrington. It is currently possible to recognize an object only as either a comet or an asteroid. There is currently insufficient information to recognize dormant or extinct cometary nuclei, though this is certainly the major goal being sought.

Meteoroid streams, producing meteor showers if some part of the stream has a node near 1 AU, have complex structures which are only just beginning to be understood. The old simplistic idea of a narrow loop being formed about the orbit of a parent comet with one, or possibly two, terrestrial intersection(s) is now being replaced by the recognition that their dynamical evolution may render convoluted and distorted ribbon shapes with eight or more distinct showers being generated. As such the streams are excellent tracers of the sorts of orbital evolution which may be undergone by larger objects (asteroids and comets) in the inner solar system; indeed it is now known that objects presently observed as Apollo-type asteroids may also be the progenitors of streams.

Searches for showers associated with newly-discovered possible parent objects may be carried out either via the calculation of theoretical meteor radiants (which have hitherto been derived using an untenable method), or through searches of catalogues of individual meteor orbits. In order to accomplish the latter, about 68,000 radar, photographic and TV meteor orbits from various programmes in the U.S.A., the former Soviet Union, Canada and Australia are available from the IAU Meteor Data Center, and more than 350,000 orbits of very faint meteors have been determined over the past three years using a new facility in New Zealand.

The discovery amongst IRAS data of dust trails lagging behind comets has opened up a new way in which meteoroid streams may be investigated, although the relationship between these trails and the streams observed as meteor showers at the Earth is by no means clear at this stage. Similarly radar, radio and spacecraft impact observations of meteoroids near cometary nuclei have added to our knowledge.

In spite of the improvement in our understanding of meteoroid streams over the past few years it is clear that there is much still to be done. The words of W.F. Denning in 1923 are still pertinent: “Few astronomers occupy themselves with the observation and investigation of meteors, and yet it is an attractive field of work offering inviting prospects of new discoveries”.

One of the outstanding problems in solar system science is the source of the particles that constitute the zodiacal cloud. The zodiacal dust bands discovered by IRAS have a pivotal role in this debate because, without doubt, they are the small, tail end products of asteroidal collisions. Geometrical arguments are probably the strongest and the plane of symmetry of the dust bands places their source firmly in the asteroid belt. A cometary source, Comet Encke for example, could exist at the distance of the mainbelt, but the dynamics of cometary orbits makes the formation of cometary dust bands impossible, unless, of course, there is a significant (comparable in volume to the asteroidal families) source of comets interior to the orbit of Jupiter with low (asteroidal) orbital eccentricities. We have suggested that the dust bands are associated with the prominent asteroidal families. The link with the Themis and Koronis families is good but the link with Eos remains to be proved. We show here by detailed modeling that even though the filtered infrared flux in the 25μm waveband associated with the dust bands is only ~1% of the total signal, this is only the “tip of the iceberg” and that asteroidal dust associated with the bands constitutes ~10% of the zodiacal cloud. This result, plus the observed size-frequency distribution of mainbelt asteroids and the observed ratio of the number of family to non-family asteroids allows us to estimate that asteroidal dust accounts for about one third of the zodiacal cloud. The discovery of the “leading-trailing” asymmetry of the zodiacal cloud in the IRAS data and our interpretation of this asymmetry in terms of a ring of asteroidal particles in resonant lock with the Earth is important for two reasons. (1) The existence of the ring strongly suggests that large (diameter ≥ 12μm) asteroidal particles (or particles with low orbital eccentricities) are transported to the inner solar system by drag forces. (2) The observed ratio of the trailing-leading asymmetry allows an independent estimate of the contribution of asteroidal particles to the zodiacal cloud. These new results have important implications for the source of the interplanetary dust particles (IDPs) collected at the Earth. Because asteroidal particles constitute about one third of the zodiacal cloud and are transported to the inner solar system by drag forces, gravitational focussing by the Earth that results in the preferential capture of particles from orbits with low inclinations and low eccentricities and the possible “funneling” effect of the ring itself, imply that nearly all of the unmelted IDPs collected at the Earth are asteroidal.

Four perturbation theories presently used to compute asteroid proper elements are reviewed, and their results are briefly discussed (Milani and Knežević, 1990, 1992, 1994, for low to moderate eccentricity/inclination main belt objects; Lemaitre and Morbidelli, 1994, for high e, I objects; Milani, 1993, for Trojans; Schubart, 1982, 1991 for Hildas). The most important recent improvements are described, in particular those pertaining to the upgrades of the previous analytic and semianalytic solutions. The dynamical structure of the asteroid main belt, as defined by the low order mean motion resonances and by linear and nonlinear secular resonances, is considered from the point of view of the effects of these resonances on the accuracy and/or reliability of the computation of proper elements and on the reliability of the identification of asteroid families.

The state of the art in the dynamics of the Trojan asteroids has progressed rapidly, since it has been possible to perform numerical integrations of many orbits for millions of years. Accurate proper elements are now computed by the synthetic method, that is from the output of a numerical integration; their stability, at least for time spans of a few million years, is good. This has allowed identification of Trojan families with an automated procedure closely mimicking the one used in the main belt. Although the families identified in a reliable way are only four, the occurrence of significant collisional evolution, not unlike that of the main belt, can be confirmed. The dynamical structure of the Trojan cloud, including the location of the main secular resonances, can be deduced from the proper elements and frequencies by a simple fit. However, many problems are not solved: the origin of a significant percentage of chaotic orbits showing no indications of instability; the location of the stability boundary of the Trojan cloud; the origin of the high inclination of most Trojans. We also do not know if there are “Trojans” for some other planets beside Jupiter: only one Mars Trojan has been found.

This paper is a short review of the dynamics of the asteroidal resonances as currently determined from maps and simulations over 106 – 107 years. The main recent results concern the extensive exploration of the phase space to determine domains of initial conditions leading to close approaches to the inner planets, the topological dynamics of the planar Sun-Jupiter-asteroid problem at very high eccentricities and the differences amongst 2/1 and 3/2 resonances able to explain the existence of a gap in the asteroidal belt at the 2/1 resonance and of a group of asteroids in the 3/2 resonance. Current results point to a confirmation of Wisdom's theory for the formation of the gaps by gravitational evolution and scattering by the inner planets.

In the last three years new studies on secular resonances have been done. The second–order and fourth–degree secular perturbation theory of Milani and Knežević allowed to point out the effect of mean motion resonances on the location of the linear and non linear secular resonances. Moreover this theory improved the knowledge of the exact location of the g = g6 (i.e. ν6) resonance at low inclination. Morbidelli and Henrard revisited the semi–numerical method of Williams, taking into account the quadratic terms in the perturbing masses. They computed not only the location of secular resonances, but also provided a global description of the resonant dynamics in the main secular resonances namely g = g5 (i.e. ν5), g = g6 (i.e. ν6) and s = s6 (i.e. ν16). The resonant proper element algorithm developed by Morbidelli allows to identify the dynamical nature of resonant objects, and is a powerful tool to study the mechanisms of meteorite transport to the inner Solar System. Purely numerical experiments have been done, which show: (i) the complexity of the dynamics when two resonances overlap; (ii) the efficiency of successive crossings of non linear resonances in pumping up the inclination of small bodies; (iii) the efficiency of the secular resonance ν6 as a source of meteorites up to 2.4 AU.

Understanding how meteorites and near–Earth asteroids reach their Earth–crossing orbits starting as fragments from main–belt asteroids is a basic prerequisite to identifying the original parent bodies of these objects and building a self–consistent cosmogonical interpretation of the observed properties of meteorites. We review the recent progress made in this area and the most important remaining open problems. These concern the physics of asteroidal collisions, the size distribution of small main–belt asteroids, the efficiency of different dynamical routes, and the relationships between asteroid taxonomic types based on spectrophotometry data and meteorite classes having different thermal histories and compositions.