Rotational Distortion of Stars Having Arbitrary Structure Described by Fourth-Order Sectorial Harmonics. I. Equipotential Surfaces in Sectorial Harmonics

In a series of papers, the equilibrium configurations of highly rotating fluid bodies have been derived. The deformation of these inhomogeneous self-gravitating fluid, of arbitrary internal structure are due to centrifugation potential. These level surfaces are expressed in terms of fourth-order sectorial harmonics. In this paper, the main equations of the problem — such as the surface of the distorted body, the gravitational potential at an arbitrary point and the disturbing potential — have been expanded to the fourth-order in terms of the even-order sectorial harmonics.