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>Third-order development of shape, gravity, and moment of inertia for highly flattened celestial bodies. Application to Ceres
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Third-order development of shape, gravity, and moment of inertia for highly flattened celestial bodies. Application to Ceres
Context. We investigate the hydrostatic shape and gravitational potential coefficients of self-gravitating and rotating bodies large enough to have undergone internal differentiation and chemical stratification. Quantifying these properties under the assumption of hydrostatic equilibrium forms the basis for interpreting shape and gravity data in terms of interior structure and infer deviations from hydrostaticity that can bring information on the thermal and chemical history of the objects. Aims. The main purpose is to show the importance of developing the reference hydrostatic shape for relatively fast rotating bodies up to third order to reach an accuracy of a few tens of meters. This paper especially focuses on Ceres, for which high-resolution shape data are being obtained by the Dawn spacecraft, with a projected accuracy better than 200 m/pixel. Methods. To improve the accuracy on the determination of geodetic parameters, we numerically integrated Clairaut’s equations of rotational equilibrium expanded up to third order in a small parameter m, the geodetic parameter. Results. Previous studies of Ceres have been based on shape models developed to first order. However, we show that the first-order theory underestimates (a?c) (where a and c are the equatorial and polar radii) by 1.8 km, which leads to underestimating the extent of mass concentration and is insufficient to interpret the upcoming observations by Dawn space mission. Instead, by using the third-order theory, we obtain an accuracy of 25 meters that is better than the accuracy expected from Dawn. Then, we derive the following geodetical quantities: flattening and other shape parameters, gravitational potential coefficients, and moments of inertia, by using the Ceres models constrained by observations obtained with the Hubble Space Telescope and ground-based adaptive optics telescopes. The difference in equatorial and polar radii for a large parametric space of interior models is investigated, and the large (a?c) corresponds to a model with a low density contrast. Conclusions. This type of modeling will also prove instrumental to infer non-hydrostatic contributions to Ceres’ shape that are to be measured by Dawn.
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机译：上下文。我们研究了足够大以经历内部分化和化学分层的自重和旋转体的静水形状和重力势能系数。在静水平衡的假设下对这些特性进行量化，构成了根据内部结构解释形状和重力数据的基础，并推断出与静水有关的偏差，这些偏差可以带来有关物体热和化学历史的信息。目的主要目的是显示出为相对快速的旋转体开发参考静液压形状的重要性，直到第三阶，以达到几十米的精度。本文特别关注谷神星，其黎明形状飞船正在获取高分辨率形状数据，其投影精度优于200 m /像素。方法。为了提高大地测量参数确定的准确性，我们在一个大参数m（大地测量参数）中将Clairaut的旋转平衡方程数值扩展到三阶。结果。谷神星的先前研究已经基于发展到一阶的形状模型。但是，我们表明，一阶理论低估了（a？c）（其中a和c是赤道半径和极地半径）1.8 km，这导致低估了质量集中程度，不足以解释即将发生的观测值。黎明太空任务。相反，通过使用三阶理论，我们获得了25米的精度，该精度比Dawn预期的精度高。然后，通过使用由哈勃太空望远镜和地面自适应光学望远镜获得的观测值约束的Ceres模型，得出以下测地量：展平和其他形状参数，重力势系数和惯性矩。对于内部模型的大参数空间，研究了赤道半径和极半径的差异，并且大（a？c）对应于密度对比较低的模型。结论。这种类型的建模还将证明有助于推断将由Dawn测量的对谷神星形状的非静水作用。
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