On the distribution of sernimajor axes among comet orbits

The Oort stochastic theory of cometary period changes is bution of cometary radii would be of the form R-1 7 dR, with a generalized to include any assumed law of comet disintegration. maximum diameter less than 100 km. Numerical solutions for the distribution of 1/a among long-period The observational data cannot be satisfied by a stochastic comet orbits are derived for two assumed distribution laws of theory based solely on an absorbing barrier at 1/a=0 and a potential lifetimes among `new" comets. The laws are of the reflecting barrier at some larger value of 1/a (e.g., 1/ .5). forms 1/Li and 1/L2, where L is the number of orbital revolutions It is possible, however, that the Oort theory, so generalized, before final disintegration in an unchanged orbit. For long-period can be made to account for the periodic comets by increasing the comets the observed distribution of 1/a lies between the distribu- upper limit of maximum potential lifetime and assuming that tions calculated from the two assumed laws of potential lifetime, short-period comets are accumulated by what might be called a "Jupiter perturbation trap." The problem of the short-period near 1/L1.7, with a maximum comet lifetime of the order of 1 comets requires still more attention from the viewpoint of Oort's revolutions. The distribution of inclinations is qualitatively satis- basic assumptions, including the possibility of systematic physical fled for the long-period comets. changes in period of revolution, and particularly the effects of On the basis of the icy comet model, the corresponding distri- large perturbations.