Precise and fast computation of gravitational field of general finite body and its application to gravitational study of small asteroids, small satellites, and comets

福島　登志夫（Toshio FUKUSHIMA）
国立天文台（NAOJ）

In order to obtain the gravitational field of a general finite body inside its Brillouin sphere, we developed a new method to compute the field accurately. First, the body is assumed to consist of some layers in a certain spherical polar coordinate system and the volume mass density of each layer is expanded as a Maclaurin series of the radial coordinate. Second, the line integral with respect to the radial coordinate is analytically evaluated in a closed form. Third, the resulting surface integrals are numerically integrated by the split quadrature method using the double exponential rule. Finally, the associated gravitational acceleration vector is obtained by numerically differentiating the numerically integrated potential. Numerical experiments confirmed that the new method is capable of computing the gravitational field independently of the location of the evaluation point, namely whether inside, on the surface of, or outside the body. Also, it can provide sufficiently precise field values, say of 14--15 digits for the potential and of 9--10 digits for the acceleration, respectively. Furthermore, its computational efficiency is better than that of the polyhedron approximation. This is because the computational error of the new method decreases much faster than that of the polyhedron models when the number of required transcendental function calls increases.
As an application, we obtained the gravitational field of 433 Eros from its shape model expressed as the 24x24 spherical harmonic expansion by assuming the homogeneity of the object. The developed formulation would be easily applied to the Ryugu once its surface function is roughly estimated and/or precisely determined.
参考文献：
T. Fukushima 2017, Astron. J., 154:145

エロスやイトカワのような任意形状の天体の重力場を計算する新しい方法を開発した。計算精度と計算速度の両面で、従来の多面体(polyhedron)モデルを上回るばかりでなく、非一様な密度分布の場合にも適用可能である。

Place: Shin-A 2F Conf. room A(1257) / 新A棟２階会議室A（1257号室）