Proper Elements, Families, and Belt Boundaries

Abstract

Families of asteroids were first found by Hirayama (1918, 1923, 1928). More recently Brouwer (1951) and Arnold (1969) have extended greatly the number of families known from the cataloged asteroids. The Palomar-Leiden survey (PLS) (van Houten et al., 1970), which mainly covered very faint, uncataloged objects, found several more families.Except for the work of Hirayama (1918), which used osculating elements, all of the above studies looked for clusterings of the semimajor axis a, the proper eccentricities é, and proper inclinations í. The calculation of proper elements involves using a theory of secular perturbations to remove the long-period, large-amplitude disturbances of the major planets. The theory used Up to now (Brouwer and van Woerkom, 1950; Brouwer and Clemence, 1961) involved a low-order expansion in the eccentricities and inclinations. There is now a theory available (Williams, 1969) that will accurately handle much higher eccentricities and inclinations than before.