In this work we have estimated 10 collisional ages of 9 families for which for different reasons our previous attempts failed. In general, these are difficult cases that required dedicated effort, such as a new family classifications for asteroids in mean motion resonances, in particular the 1/1 and 2/1 with Jupiter, as well as a revision of the classification inside the 3/2 resonance.Of the families locked in mean motion resonances, by employing a numerical calibration to estimate the Yarkovsky effect in proper eccentricity, we succeeded in determining ages of the families of (1911) Schubart and of the "super-Hilda" family, assuming this is actually a severely eroded original family of (153) Hilda. In the Trojan region we found families with almost no Yarkovsky evolution, for which we could compute only physically implausible ages. Hence, we interpreted their modest dispersions of proper eccentricities and inclinations as implying that the Trojan asteroid families are fossil families, frozen at their proper elements determined by the original ejection velocity field. We have found a new family, among the Griquas locked in the 2/1 resonance with Jupiter, the family of (11097) 1994 UD1.We have estimated the ages of 6 families affected by secular resonances: families of (5) Astraea, (25) Phocaea, (283) Emma, (363) Padua, (686) Ger- suind, and (945) Barcelona. By using in all these cases a numerical calibration method, we have shown that the secular resonances do not affect significanly the secular change of proper a. For the family of (145) Adeona we could estimate the age only after removal of a number of assumed interlopers.With the present paper we have concluded the series dedicated to the determination of asteroid ages with a uniform method. We computed the age(s) for a total of 57 families with > 100 members. For the future work there remain families too small at present to provide reliable estimates, as well as some complex families (221, 135, 298) which may have more ages than we could currently estimate. Future improvement of some already determined family ages is also possible by increasing family membership, revising the calibrations, and using more reliable physical data.

Here we report on the significant role of a so far overlooked dynamical aspect, namely a secular resonance between the dwarf planet Ceres and other asteroids. We demonstrate that this type of secular resonance can be the dominant dynamical factor in certain regions of the main asteroid belt.Specifically, we performed a dynamical analysis of the asteroids belonging to the (1726) Hoffmeister family. To identify which dynamical mechanisms are actually at work in this part of the main asteroid belt, i.e. to isolate the main perturber(s), we study the evolution of this family in time. The study is accomplished using numerical integrations of test particles performed within different dynamical models. The obtained results reveal that the post-impact evolution of the Hoffmeister asteroid family is a direct consequence of the nodal secular resonance with Ceres.This leads us to the conclusion that similar effects must exist in other parts of the asteroid belt. In this respect, the obtained results shed light on an important and entirely new aspect of the long-term dynamics of small bodies. Ceres' fingerprint in asteroid dynamics, expressed through the discovered secular resonance effect, completely changes our understanding of the way in which perturbations by Ceres-like objects affect the orbits of nearby bodies.

In this work we aim to constrain the slope of the size distribution of main-belt asteroids, at their primordial state. To do so we turn out attention to the part of the main asteroid belt between 2.82 and 2.96~AU, the so-called "pristine zone", which has a low number density of asteroids and few, well separated asteroid families. Exploiting these unique characteristics, and using a modified version of the hierarchical clustering method we are able to remove the majority of asteroid family members from the region. The remaining, background asteroids should be of primordial origin, as the strong 5/2 and 7/3 mean-motion resonances with Jupiter inhibit transfer of asteroids to and from the neighboring regions. The size-frequency distribution of asteroids in the size range $17

We report the discovery of a new asteroid family among the dark asteroids residing in the Phocaea region the Tamara family. We make use of available physical data to separate asteroids in the region according to their surface reflectance properties, and establish the membership of the family. We determine the slope of the cumulative magnitude distribution of the family, and find it to be significantly steeper than the corresponding slope of all the asteroids in the Phocaea region. This implies that sub-kilometer dark Phocaeas are comparable in number to bright S-type objects, shedding light on an entirely new aspect of the composition of small Phocaea asteroids. We then use the Yarkovsky V-shape based method and estimate the age of the family to be 264 ± 43 Myr. Finally, we carry out numerical simulations of the dynamical evolution of the Tamara family. The results suggest that up to 50 Tamara members with absolute magnitude H < 19.4 may currently be found in the near-Earth region. Despite their relatively small number in the near-Earth space, the rate of Earth impacts by small, dark Phocaeas is non-negligible.