Application of a New Formula for Angular Velocity of Rotation to the Planetoid Haumea

The aim of the work is to test a new formula for the angular velocity of rotation Ω of inhomogeneous equilibrium figures on the model of a unique rapidly rotating trans-Neptunian dwarf planet Haumea. The three-axis two-component model of Haumea consists of an ellipsoidal rocky core and a thick confocal ice shell. The parameters of this model are determined from a system of eight algebraic equations that take into account the complete kinematic-photometric information about the planetoid. Using the methods of potential theory, the components of the internal and external gravitational energy of the model on which this Ω depends are found. For this purpose, a refined expression for the gravitational energy of a homogeneous confocal shell and a formula for the mutual energy of the core and the shell are used. It was found that in order to be consistent with the observed rotation period of Haumea τ = 3.915, this model should be considered as a polytrope with the index