High-precision gravitational measurements by orbiting spacecraft provide a means of probing the structures, fluid motions, and convective dynamos in the interiors of the rapidly rotating outer planets. Here, the classical theory of rotating homogeneous planets is briefly reviewed. Emphasis is placed on recent developments in theories and methods that relate internal structure and processes to their gravitational signatures. Whereas early theories usually treated the effects of interior density stratification and rotational distortion as perturbations to a spherical state, recent research is marked by a self-consistent perturbation approach in which the leading-order problem accounts exactly for rotational distortion, thereby determining the basic shape, internal structure, and gravitational field of the planet. The next-order problem, which is mathematically and physically coupled with the leading-order problem, describes the modifications caused by internal fluid motions. Although the theories and method...

中文翻译：

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快速旋转的类木行星的形状、内部结构、纬向风和引力场

轨道航天器的高精度重力测量提供了一种探测快速旋转外行星内部结构、流体运动和对流发电机的方法。在这里，简要回顾了旋转同质行星的经典理论。重点放在将内部结构和过程与其引力特征联系起来的理论和方法的最新发展。早期的理论通常将内部密度分层和旋转畸变的影响视为对球形状态的扰动，而最近的研究以自洽扰动方法为标志，在该方法中，前导问题准确地解释了旋转畸变，从而确定了基本形状，内部结构和行星的引力场。下一个顺序问题，它在数学上和物理上与超前阶问题相结合，描述了由内部流体运动引起的修改。虽然理论和方法...