An analytical method is developed for finding the coefficients of zonal spherical harmonics of the azimuthally averaged potential of a rotating stratified inhomogeneous triaxial ellipsoid. Two models are considered: i) an ellipsoid of discrete layers of finite thickness, including the two-component Core – Shell model; ii) an inhomogeneous ellipsoid consisting of infinitely thin equidensity layers with arbitrary elliptic profiles from the center to the periphery. For both types of models, equations were obtained that allow calculating the coefficients of zonal spherical harmonics of any degree according to a single scheme. Along with the general stratification, special cases of ellipsoids consisting of homeoids and focaloids were also considered. It is proved that for confocal stratification the coefficients of zonal spherical harmonics of homogeneous and congruent inhomogeneous ellipsoids coincide. The method is applied to the construction of a near-equilibrium model of the dwarf planet Haumea. It has been established that the nodal precession period of the Haumea’s ring is \(T_{\mathit{prec}} = 12.9 \pm 0.7~\text{days}\).

开发了一种分析方法，用于寻找旋转分层非均匀三轴椭球的方位平均势的纬向球谐函数系数。考虑了两种模型： i) 有限厚度离散层的椭球体，包括双组分核壳模型；ii) 由无限薄的等密度层组成的非均匀椭球，从中心到外围具有任意椭圆轮廓。对于这两种类型的模型，获得的方程允许根据单一方案计算任何程度的纬向球谐函数的系数。除了一般分层外，还考虑了由homeoids和focaloids组成的椭球的特殊情况。证明了对于共焦分层，均匀和全等非均匀椭球的纬向球谐系数是一致的。将该方法应用于矮行星Haumea近平衡模型的构建。已经确定 Haumea 环的节点岁差周期是\(T_{\mathit{prec}} = 12.9 \pm 0.7~\text{days}\)。