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The number of asteroids with accurately determined orbits increases fast, and this increase is also accelerating. The catalogs of asteroid physical observations have also increased, although the number of objects is still smaller than in the orbital catalogs. Thus it becomes more and more challenging to perform, maintain and update a classification of asteroids into families. To cope with these challenges we developed a new approach to the asteroid family classification by combining the Hierarchical Clustering Method (HCM) with a method to add new members to existing families. This procedure makes use of the much larger amount of information contained in the proper elements catalogs, with respect to classifications using also physical observations for a smaller number of asteroids.Our work is based on the large catalog of the high accuracy synthetic proper elements (available from AstDyS), containing data for > 330 000 numbered asteroids. By selecting from the catalog a much smaller number of large asteroids, we first identify a number of core families; to these we attribute the next layer of smaller objects. Then, we remove all the family members from the catalog, and reapply the HCM to the rest. This gives both halo families which extend the core families and new independent families, consisting mainly of small asteroids. These two cases are discriminated by another step of attribution of new members and by merging intersecting families. This leads to a classification with 128 families and currently 87095 members; the number of members can be increased automatically with each update of the proper elements catalog. By using information from absolute magnitudes, we take advantage of the larger size range in some families to analyze their shape in the proper semimajor axis vs. inverse diameter plane. This leads to a new method to estimate the family age, or ages in cases where we identify internal structures. The analysis of the plot above evidences some open problems but also the possibility of obtaining further information of the geometrical properties of the impact process. The results from the previous steps are then analyzed, using also auxiliary information on physical properties including WISE albedos and SDSS color indexes. This allows to solve some difficult cases of families overlapping in the proper elements space but generated by different collisional events.The families formed by one or more cratering events are found to be more numerous than previously believed because the fragments are smaller. We analyze some examples of cratering families (Massalia, Vesta, Eunomia) which show internal structures, interpreted as multiple collisions. We also discuss why Ceres has no family. 6 According to [Ivezić et al. 2001] the first principal component in the r − i vs g − r plane is defined as a * = 0.89(g − r) + 0.45(r − i) − 0.57. 7 Every asteroid is affected by chaotic effects over timescales comparable to the age of the solar system, but this does not matter for family classification.

A new family classification, based on a catalog of proper elements with similar to 384,000 numbered asteroids and on new methods is available. For the 45 dynamical families with >250 members identified in this classification, we present an attempt to obtain statistically significant ages: we succeeded in computing ages for 37 collisional families.\ud \ud We used a rigorous method, including a least squares fit of the two sides of a V-shape plot in the proper semimajor axis, inverse diameter plane to determine the corresponding slopes, an advanced error model for the uncertainties of asteroid diameters, an iterative outlier rejection scheme and quality control. The best available Yarkovsky measurement was used to estimate a calibration of the Yarkovsky effect for each family. The results are presented separately for the families originated in fragmentation or cratering events, for the young, compact families and for the truncated, one-sided families. For all the computed ages the corresponding uncertainties are provided, and the results are discussed and compared with the literature. The ages of several families have been estimated for the first time, in other cases the accuracy has been improved. We have been quite successful in computing ages for old families, we have significant results for both young and ancient, while we have little, if any, evidence for primordial families. We found 2 cases where two separate dynamical families form together a single V-shape with compatible slopes, thus indicating a single collisional event. We have also found 3 examples of dynamical families containing multiple collisional families, plus a dubious case: for these we have obtained discordant slopes for the two sides of the V-shape, resulting in distinct ages. We have found 2 cases of families containing a conspicuous subfamily, such that it is possible to measure the slope of a distinct V-shape, thus the age of the secondary collision. We also provide data on the central gaps appearing in some families. The ages computed in this paper are obtained with a single and uniform methodology, thus the ages of different families can be compared, providing a first example of collisional chronology of the asteroid main belt. (C) 2015 Elsevier Inc. All rights reserved

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Abstract.Using the synthetic theory, we computed proper elements for asteroids in the inner part of the main belt and in the trans-Neptunian region. We present the new results and we discuss some important implications of both their rapidly increasing number and the improved accuracy. We give complete information on the availability of asteroid proper elements through the AstDys web service, with particular emphasis on the content and update strategy of proper element catalogs. Next, we discuss the most interesting features of some important asteroid families and regions (Vesta, Phocaea, TNO). For the Vesta family we provide further evidence that the observed spread of the family members is probably due to diffusion in the proper elements caused by non-gravitational effects. We shed additional light on the long-standing question of whether Phocaea is a genuine family or an island isolated by resonances, and we show the impact of nearby secular resonances on the local dynamics. Finally, we analyzed trans-Neptunian objects by using a "dual" of the main asteroid belt, to show that the currently known population of TNOs corresponds to the unstable outer asteroid belt beyond the 2/1 mean motion resonance with Jupiter. To discuss some of the main features of the dynamics of trans-Neptunians we use two examples, one stable over at least 100 Myr, but with proper elements slightly affected by a nonlinear secular resonance g + s − g 8 − s 8 , and the other chaotic, with a Lyapounov time of the order of 4000 yr, already exhibiting macroscopic instability after 6 Myr.