New series of equilibrium figures based on the Roche model

A sequence of equilibrium figures with the strongest possible mass concentration toward the centre is constructed. The bicubic equation is solved and the explicit equation is derived for the shape of the surface of any equilibrium figure consid-ered. The new sequence of equilibrium figures is constructed proceeding from the assumption that angular rotation velocity of these figures varies as a function of normalized average density. A relation is derived between the normalized angular velocity and the oblateness ε of the equilibrium figure. Oblateness values of figures lie in the range 0 < ε < 1/3. In the extreme case of the weakest possible potential (the largest ε) the figure has the shape of the limiting Roche lens. (© 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)