Rotational distortion of the stars of arbitrary structure: Fourth approximation

Abstract

Clairaut's theory of the rotational distortion of self-gravitating configurations of arbitrary structure, arising from axial rotation with constant angular velocity, previously developed (cf. Kopal, 1973) to quantities of third order in superficial distortion, has now been extended to terms of fourth order. The differential equations governing the form and exterior potential of stars so rotating have been set up by the method followed in our previous paper (Kopal, 1973) together with their boundary conditions; but their applications to practical cases are being postponed for a subsequent investigation.