All asteroids are currently classified as either family, originating from the disruption of known bodies, or non-family. An outstanding question is the origin of these non-family asteroids. Were they formed individually, or as members of known families but with chaotically evolving orbits, or are they members of old ghost families, that is, asteroids with a common parent body but with orbits that no longer cluster in orbital element space? Here, we show that the sizes of the non-family asteroids in the inner belt are correlated with their orbital eccentricities and anticorrelated with their inclinations, suggesting that both non-family and family asteroids originate from a small number of large primordial planetesimals. We estimate that ~85% of the asteroids in the inner main belt 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. These new results imply that we must seek explanations for the differing characteristics of the various meteorite groups in the evolutionary histories of a few, large, precursor bodies. Our findings also support the model that asteroids formed big through the gravitational collapse of material in a protoplanetary disk.
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