Gravitational effects after the impact disruption of a minor planet: geometrical properties and criteria for the reaccumulation

After the catastrophic disruption of a planetary body the fragments move according to their mutual gravitational attraction, finally resulting into a more or less massive reaccumulation, as well as into the formation of binary or multiple systems. In this paper we analyze this process by means of the outcomes of the semi-empirical model of catastrophic impacts described by [Paolicchi et al., 1996] and applied to impacts at planetary sizes by [Paolicchi et al., 1993] and [Doressoundiram et al., 1997]. It is possible to identify the location in the parent body of fragments which are going to be reaccumulated or ejected, or to form binaries. Moreover, we compare the results of numerical integrations with three analytical predicting criteria existing in the literature, as well as with a new one, based on the definition of iso-velocity surfaces. We show that: (a) two of the criteria presented and used in the literature may lead to severe over- or underestimates of the amount of reaccumulated mass; (b) the new criterion introduced here and the previous one described by [Petit and Farinella, 1993] are capable of giving an accurate estimate in many cases, but are less effective when the reaccumulation is limited and not strongly concentrated onto a single big attractor; (c) the region in the target where the analytic criteria fail is generally the transition region between escaping and reaccumulating. This is the same region where other interesting phenomena, such as the formation of binaries, take place.