A finite element method (FEM) for computing the gravitational interactions between two arbitrarily shaped celestial bodies is proposed. Expressions for the gravitational potential, attraction and torques are derived in terms of the finite element mesh division and mass density distribution. This method is implemented to a parallel-simulation package on a local cluster. Benchmarking tests are performed to confirm the convergence properties and to measure the computational costs. For a representative application, we construct the FEM model of the binary Near-Earth asteroid 65803 Didymos and simulate the coupled spin–orbit motion of its two components. The results show our method propagates the binary motion precisely, which is significantly dependent on the primary’s internal structure. In this numeric example, we show the finite element method is capable of modeling complex geometry and dissimilar material properties, which is useful to address questions in predicting the evolution of actual binary asteroids.

中文翻译：

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计算全二体问题的一种有限元方法：I. 双线性四面体元的互势和导数

提出了一种用于计算两个任意形状天体之间引力相互作用的有限元方法 (FEM)。根据有限元网格划分和质量密度分布推导出重力势、吸引力和扭矩的表达式。该方法是在本地集群上的并行仿真包中实现的。执行基准测试以确认收敛特性并测量计算成本。对于具有代表性的应用，我们构建了双星近地小行星 65803 Didymos 的 FEM 模型，并模拟了其两个分量的耦合自旋轨道运动。结果表明我们的方法精确地传播了二元运动，这在很大程度上取决于初级的内部结构。在这个数字示例中，