Abstract

The problem of the secular evolution of a thin ring around a rapidly rotating triaxial celestial body is formulated and solved. The technology for calculating secular perturbations is based on two formulas: the azimuthally averaged force field of the central body and the mutual energy \({{W}_{{{\text{mut}}}}}\) of this body and a Gaussian ring. With \({{W}_{{{\text{mut}}}}}\) instead of the usual perturbing function, a system of differential equations for the osculating elements of the ring is obtained. An equation is obtained that allows one to find the coefficients of the zonal harmonics of the azimuthally averaged potential of an inhomogeneous ellipsoid using a unified scheme. The method is applied to dwarf planet Haumea with refined masses of the rocky core and the ice shell and the coefficients \({{C}_{{20}}}\) and \({{C}_{{40}}}\) of the po-tential’s zonal harmonics. According to new data, the ring around Haumea has a slight obliquity and must precess. It was established that the period of the retrograde nodal precession of the Haumea’s ring (without regard to self-gravity) is \({{T}_{\Omega }} = 12.9 \pm 0.7\) days and the period of the forward of the apside line precession is \({{T}_{\omega }} \approx 8.{\text{08}}\;{\text{days}}\). It is proven that the 3:1 orbital resonance for the particles of the Haumea’s ring is fulfilled only approximately and the averaging time of additional perturbations at a nonsharp resonance turned out to be an order of magnitude smaller than \({{T}_{\Omega }}\). This confirms the adequacy of the method.

中文翻译：

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旋转三轴引力体周围环的长期演化

摘要

提出并解决了围绕快速旋转的三轴天体的薄环的长期演化问题。计算世俗干扰的技术是基于两个公式：中央体的方位平均力场和互能量\（{{白} _ {{{\文本{MUT}}}}} \）这个机构和高斯环。使用\（{{W} _ {{{\ text {mut}}}}} \\）代替通常的扰动函数，获得了用于环的密合元件的微分方程组。获得了一种方程，该方程允许使用统一方案找到不均匀椭圆体的方位角平均电势的区域谐波的系数。该方法应用于具有精细质量的岩心和冰壳以及系数\（{{C} _ {{20}}} \）和\（{{C} _ {{40}} } \）电位的区域谐波。根据新数据，Haumea周围的环略有倾斜，必须进动。可以确定的是，Haumea环的节点逆行进的周期（不考虑自重）为\（{{T} _ {\ Omega}} = 12.9 \ pm 0.7 \）天，并且视线进动的前期为\（{{T} _ {\ omega}} \ approx 8。{\ text {08}} \; {\ text {days}} \\）。证明了仅能近似满足Haumea环粒子的3：1轨道共振，并且在非尖锐共振下附加扰动的平均时间比\（{{T} _ { \ Omega}} \）。这证实了该方法的适当性。