由潮汐势变形的旋转行星和卫星的层的变形
The flattenings of the layers of rotating planets and satellites deformed by a tidal potential
摘要：
我们认为克莱洛理论的平衡椭球形的分化非均匀的机构在非同步旋转添加到它的潮汐变形由于存在的外部引力。我们假设该机构是一个流体形成的$n$均匀层的椭圆形，我们计算的外部极面和平均半径的每一层，或等效地，他们的半轴。对于第一阶方程，一般解可以写成$ε_k={\cal H}_k*ε_h$和$μ_k={\cal H}_k*μ_h$，其中$\cal{H}_k$是每层的特征系数，它只取决于物体的内部结构，而$ε_h, μ_h$是等价齐次问题的方程。对于连续情况，我们研究了扁率剖面的克莱洛微分方程，并利用Radau变换找到了附加潮位时的边界条件。最后，该理论适用于几个例子：i）一个机构组成的两个均匀层; ii）机构与简单的多项式密度分布规律和iii）机构遵循多方压力密度法。
英文摘要：
We consider the Clairaut theory of the equilibrium ellipsoidal figures for differentiated non-homogeneous bodies in non-synchronous rotation adding to it a tidal deformation due to the presence of an external gravitational force. We assume that the body is a fluid formed by $n$ homogeneous layers of ellipsoidal shape and we calculate the external polar flattenings and the mean radius of each layer, or, equivalently, their semiaxes. To first order in the flattenings, the general solution can be written as $ε_k={\cal H}_k*ε_h$ and $μ_k={\cal H}_k*μ_h$, where $\cal{H}_k$ is a characteristic coefficient for each layer which only depends on the internal structure of the body and $ε_h, μ_h$ are the flattenings of the equivalent homogeneous problem. For the continuous case, we study the Clairaut differential equation for the flattening profile, using the Radau transformation to find the boundary conditions when the tidal potential is added. Finally, the theory is applied to several examples: i) a body composed of two homogeneous layers; ii) bodies with simple polynomial density distribution laws and iii) bodies following a polytropic pressure-density law.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
