The orbital elements of the main-belt population of asteroids tend to cluster about specific sets of values. Three of these groups (whose largest members are 24 Themis, 221 Eos and 158 Koronis) were discovered by Hirayama (1918a), who called them asteroid families. Hirayama hypothesized that the family members were in fact fragments of an originally larger parent asteroid, which had been disrupted by a collision with another smaller one.
Osculating and proper orbital elements
Asteroids move on elliptic orbits with the Sun located at one of the foci. Each of these orbits is described by five quantities, which are the semimajor axis a, the eccentricity e, the inclination i, the argument of perihelion ω and the longitude of node Ω, characterizing respectively the size, shape, inclination with respect to the ecliptic and (for the last two) the orientation in space of the ellipse. Together with the mean anomaly M(giving the instantaneous position of the body in its orbit) these quantities...
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Valsecchi, G.B. (1997). Asteroid: Families . In: Encyclopedia of Planetary Science. Encyclopedia of Earth Science. Springer, Dordrecht. https://doi.org/10.1007/1-4020-4520-4_22
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