In this paper the early history of search for asteroid groupings is briefly reviewed. Starting from the first attempts by Kirkwood, who managed to identify a number of asteroid pairs and triples with adjacent orbits, via the similar contributions of Tisserand and Mascart, we arrive to Hirayama and his discovery of asteroid families, marking the beginning of modern asteroid science.

The materials of large asteroids and asteroid families are sampled by meteorites that fall to Earth. The cosmic ray exposure age of the meteorite identifies the collision event from which that meteorite originated. The inclination of the orbit on which the meteoroid impacted Earth measures the inclination of the source region, while the semi-major axis of the orbit points to the delivery resonance, but only in a statistical sense. To isolate the sources of our meteorites requires multiple documented falls for each cosmic ray exposure peak. So far, only 36 meteorites have been recovered from observed falls. Despite these low numbers, some patterns are emerging that suggest CM chondrites originated from near the 3:1 resonance from a low-inclined source (perhaps the Sulamitis family), LL chondrites came to us from the ν6 resonance (perhaps the Flora family), there is an H chondrite source at high inclination (Phocaea?), and one group of low shock-stage L chondrites originates from the inner main belt. Other possible links are discussed.

Here, we discuss the YORP equilibria, to which asteroids can come as the result of their evolution due to the YORP effect.

In this work we map one of the most populated regions in the main belt - the asteroid family Themis. Computed with a good choice of parameters, the map enables us to get a refined picture of the dynamics in the family, to reexamine the role of resonances therein, to understand better the distribution of asteroids inside the region and to identify dynamical pathways along which particles can drift away.

To select asteroid families, the D(a) distribution of asteroid sizes by their semimajor axes and the N(p) distribution of the number of asteroids by their albedo values for individual families were used. A statistically significant reduction in the mean albedo with increasing semimajor axis is observed for almost all correctly identified families that are not truncated by resonances. This points on an action of a specific nongravitational effect (NGE) in the asteroid belt, and results in the spatial separation of asteroids with different albedos.

Using color indexes from SDSS and albedos from WISE we tested the homogeneity of 56 large Main belt families from Nesvorny list using the “color - albedo” plots. 25% of the analyzed families are non-homogeneous in terms of albedos and colors. Only two families (Flora and Vesta) contain low, moderate and high albedo asteroids, that are separated in a “color-albedo” plot. The fraction of the low albedo asteroids in bimodal families is not negligible (10-30%). Seven bimodal families may contain members from two overlapping families.

Because the number of asteroids in the IMB with absolute magnitude H<16.5 is effectively complete, the distributions of the sizes and the orbital elements of these asteroids must be devoid of observational selection effects. This allows us to state that the observed size-frequency distributions (SFDs) of the five major asteroid families in the IMB, defined by Nesvorný (2015) using the Hierarchical Clustering Method (Zappala et al. 1990), are distinctly different and deviate significantly from the linear log-log relation described by Dohnanyi (1969). The existence of these differences in the SFDs, and the fact that the precursor bodies of the major families have distinctly different eccentricities and inclinations, provides a simple explanation for the observations that the mean sizes of the family asteroids, taken as a whole, are correlated with their mean proper eccentricities and anti-correlated with their mean proper inclinations. While the latter observations do have a simple explanation, we observe that the mean sizes of the non-family asteroids in the IMB are also correlated with their mean proper eccentricities and anti-correlated with their mean proper inclinations. We deduce from this, and from the fact that the SFDs of the non-family and the family asteroids (again taken as a whole) are almost identical, that the family and most of the non-family and asteroids have a common origin. We estimate that ~85% of all the asteroids in the IMB with H<16.5 originate from the Flora, Vesta, Nysa, Polana and Eulalia families with the remaining ~15% originating from either the same families or, more likely, a few ghost families (Dermott et al. 2018).

A search for asteroid families among the Hildas and Jupiter Trojans was performed with the use of a new set of proper elements. The proper elements were calculated by the empirical method. Besides well known families, several new probable families were found in addition.

We searched for associations (not for families) amongst the near Earth asteroids (NEAs) and, similarly as in our previous studies (Jopek 2011; Jopek 2015),AQ: Please provide reference detail for Jopek 2012. a dozen groups of 10 or more members was found with high statistical reliability. We present some details of our most numerous finding: association (2061) Anza which, at the moment, incorporates 191 members.

Orbits of potential Trojans of different planets in the solar system were selected from the MPC catalog on February, 2017. The evolution of those orbits was calculated. The bodies on librating orbits around the points L4 and L5 were determined. The quantities of real Trojans in the MPC catalog are as follows: Mars - 5, Jupiter - over 4500, Saturn - none, Uranus - 2, Neptune - 15. A reasoned explanation of such distribution of Trojans in the solar system is proposed.

We present photometric observations of (4055) Magellan, (143404) 2003 BD44, 2014 JO25 and (3122) Florence, four potentially hazardous Near Earth Asteroids (NEAs). The data were taken near their approaches to Earth by 3 observatories participating in the Mexican Asteroid Photometry Campaign (CMFA). The results obtained: light curves, spin rates, amplitudes and errors, are in general agreement with those obtained by others. During the day of a NEAs maximum approach to our planet, its light curve may present significant changes. In the spin rate, however, only minute changes are observed. 2014 JO25 is briefly discussed in this regard.

Thousands of new asteroids are discovered every year and the rate of discovery is by far larger than the determination rate of their physical properties. In 2015 a group of researchers and students of several Mexican institutions have established an observational program to study asteroids photometrically. The program, named Mexican Asteroid Photometry Campaign, is aiming to derive rotation periods of asteroids based on optical photometric observations. Since then four campaigns have been carried out. The results obtained throughout these campaigns, as well as future work, are presented.