between asteroids which grind them down to small bodies. Such small asteroids then become subject to perturbations such as the Yarkovsky effect that can push them towards orbital resonances with Jupiter over time. Once there, they are relatively rapidly ejected from the asteroid belt. Tentative age estimates have been obtained for some families, ranging from hundreds of millions of years to less than several million years as for the compact Karin family. Old families are thought to contain few small members, and this is the basis of the age determinations. It is supposed that many very old families have lost all the smaller and medium-sized members, leaving only a few of the largest intact. A suggested example of such old family remains are the 9 Metis and 113 Amalthea asteroid pair. Further evidence for a large number of past families (now dispersed) comes from analysis of chemical ratios in iron meteorites. These show that there must have once been at least 50 to 100 parent bodies large enough to be differentiated, that have since been shattered to expose their cores and produce the actual meteorites (Kelley & Gaffey 2000). Identification of members, interlopers and background asteroids When the orbital elements of main belt asteroids are plotted (typically inclination vs. eccentricity, or vs. semi-major axis), a number of distinct concentrations are seen against the rather uniform distribution of non-family background asteroids. These concentrations are the asteroid families (see above). Interlopers are asteroids classified as family members based on their so-called proper orbital elements but having spectroscopic properties distinct from the bulk of the family, suggesting that they, contrary to the true family members, did not originate from the same parent body that once fragmented upon a collisional impact. Description Strictly speaking, families and their membership are identified by analysing the proper orbital elements rather than the current osculating orbital elements, which regularly fluctuate on timescales of tens of thousands of years. The proper elements are related constants of motion that remain almost constant for at least tens of millions of years, and perhaps longer. The Japanese astronomer Kiyotsugu Hirayama (1874–1943) pioneered the estimation of proper elements for asteroids, and first identified several of the most prominent families in 1918. In his honor, asteroid families are sometimes called Hirayama families. This particularly applies to the five prominent groupings discovered by him. Hierarchical clustering method Present day computer-assisted searches have identified more than