A commonly used shape model for the giant plants of Jupiter and Saturn is an oblate ellipsoid, a simplified model of the equipotential shape. The ellipsoidal shape models were originally derived from radio occultation data and gravity data after the Voyager flybys in 1979. Through precise Doppler tracking of NASA's Juno and Cassini spacecraft telecommunications links, zonal coefficients in a spherical harmonic expansion of the gravity field of Jupiter and Saturn have been resolved to degree 10, including the detection of nonzero odd zonal harmonics, which have been interpreted as differential rotation in the atmosphere for both planets. In this work, we construct the equipotential surfaces of Jupiter and Saturn using the recently measured gravity fields determined by Juno through perijove 8 and Cassini through end of mission. For both planets, even zonal harmonics dominate the equipotential shape, differing from the reference ellipsoid up to ~32 km at Jupiter and ~125 km at Saturn in the midlatitude regions. Saturn's internal rotation period estimated with ring seismology produces a shape that is fully consistent with the Pioneer and Voyager radio occultation measurements, and Jupiter's shape is fully consistent with the Pioneer and Voyager radio occultation measurements. With current equipotential theory, the recent analysis of the depth of the deep zonal flow on Jupiter and Saturn cannot fully be explained by the shape from current radio occultation measurements; additional occultation measurements and reanalysis of the Pioneer and Voyager radio occultations and will be useful for further constraining the shape of the planets.

中文翻译：

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使用朱诺和卡西尼大结局重力科学测量值更新的木星和土星等势形状

木星和土星的巨型植物常用的形状模型是扁椭圆形，是等势形状的简化模型。椭球形状模型最初是从1979年Voyager飞越之后的无线电掩星数据和重力数据得出的。通过对NASA朱诺和卡西尼号航天器电信链路的精确多普勒跟踪，木星和土星重力场的球谐扩展中的纬向系数具有解析为10级，包括检测非零奇数个纬向谐波，这被解释为两个行星在大气中的旋转差。在这项工作中，我们使用朱诺（Juno）通过《 periveve 8》和卡西尼（Cassini）在任务结束时确定的最近测得的重力场来构造木星和土星的等势面。对于两个行星，在中纬度地区，甚至区域性谐波也主导了等势形状，与参考椭球在木星上约32 km，在土星上约125 km上有所不同。用环形地震学估算的土星内部旋转周期产生的形状与Pioneer和Voyager无线电掩星测量完全一致，而Jupiter的形状与Pioneer和Voyager无线电掩星测量完全一致。根据目前的等电位理论，最近对木星和土星深层纬向流深度的分析不能完全由目前的无线电掩星测量的形状来解释。进一步的掩星测量和对先锋和航海家的无线电掩星的重新分析，将对进一步限制行星的形状有用。