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

The study has been aimed to test a new formula for the \({{\Omega }}\) angular velocity of rotation of inhomogeneous equilibrium figures using 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 have been 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 \({{\Omega }}\) depends have been 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 have been used. It has been found that in order to be consistent with the observed rotation period of Haumea of \({{\tau }_{{{\text{rot}}}}} = {{3}^{{\text{h}}}}{\text{.915}}{\text{,}}\) this model must be considered as a polytrope with the index of \(n \approx 0.{\text{984}}\). This result has confirmed the relevance of the developed method for studying inhomogeneous equilibrium figures.