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arXiv 2301.10083astro-ph.EP
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双星小行星模拟中互势近似的精度

The accuracy of mutual potential approximations in simulations of binary asteroids

Alex Ho, Margrethe Wold, Mohammad Poursina, John T. Conway

摘要:

小行星双星的模拟通常使用由级数展开近似的相互引力势,导致截断误差,并且当天体接近时也阻止了力和扭矩的正确计算。我们使最近开发的方法,其中的相互潜在的计算与使用的表面积分,是精确的椭球体形状。表面积分法产生的解决方案进行了比较的方法,扩大了相互潜力,截断在第二和第四阶。近似解是用“通用二元小行星模拟器”(gubas)生成的。我们发现,在力和扭矩的差异是最大的,当身体几乎接触。如果初级线圈的形状是高度细长的,则这些差异可以超过1000%。长期模拟显示,如果天体最初靠近,则动力学差异超过100%,而如果天体最初远离,则差异可以忽略不计。对于两个三轴椭球体的模拟,表面积分方法的计算效率与Gubas的四阶近似相当,并且优于截断到八阶或更高阶的电位。

英文摘要:

Simulations of asteroid binaries commonly use mutual gravitational potentials approximated by series expansions, leading to truncation errors, and also preventing correct computations of the forces and torques when the bodies are close. We make of a recently developed method where the mutual potential is calculated with the use of surface integrals and is exact for bodies of ellipsoidal shapes. The solutions produced by the surface integration method are compared with an approach that expands the mutual potential, truncated at second and fourth order. The approximate solutions are generated with the ``General Use Binary Asteroid Simulator'' (gubas). We find that the differences in the forces and torques are the largest when the bodies are nearly touching. These differences can exceed 1000% if the shape of the primary is highly elongated. Long term simulations show more than 100% difference in the dynamics if the bodies are initially close, while the differences are negligible if the bodies are initially far apart. For simulations with two triaxial ellipsoids, the computational efficiency of the surface integral method is comparable to fourth order approximations with gubas, and superior to potentials truncated to order eight or higher.

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