ASYMPTOTIC LIMIT OF THE FORM-FACTOR-ALPHA AND FORM-FACTOR-BETA PRODUCT FOR CELESTIAL BODIES

The applicability of the properties of central configurations proceeding from the many-body problem to study of gaseous sphere cloud evolution during its gravitational contraction is justified. It is shown that the product αβ runs to a constant value in the asymptotic time limit of simultaneous collision of all the particles of the cloud where α is a form-factor of the potential energy and β is a form-factor of the moment of inertia. The spherical bodies as well as ellipsoids of rotation and general ellipsoids with a one-dimensional mass distribution ρ{variant}(k), k∈[0, 1] are found to possess the property αβ=const. © 1979 D. Reidel Publishing Co.