质体/小天体重力场椭球谐展开算法研究

重力场是质体/天体的一种重要物理特性，可以反映质体/天体内部物质密度分布和变化状态，利用重力场信息能够进行航天器轨道确定、天体内部结构与矿产资源探测以及导航定位等。重力场正演计算是一个非常重要的问题，不仅可以预测重力场分布情况，也是重力资料解释等反演问题的基础；其计算方法一般包括空域和谱域方法，而谱域又包含傅里叶域和球谐域，目前已有的文献主要集中于空域、傅里叶域与球谐域方法。计算重力场的椭球谐谱方法不仅比球谐谱方法收敛速度更快，其参考椭球也比球谐谱方法的收敛球更加契合地质体或小天体的外部形状。本项目拟借助调和分析等相关数学物理方法，研究多面体模型重力场椭球谐展开、二维地质体重力场椭圆谐展开、任意形状三维质体/小天体球谐与椭球谐展开算法以及重力场高阶椭球谐展开理论，系统建立外部重力场椭球谐展开算法和理论体系，具有较为广泛的应用前景。

The gravity field is an important physical characteristic of the two- (2D) or three- dimensional (3D) body and can reflect the distribution and variation of the material density inside the body. The information of the gravity field can be used to the spacecraft orbit determination, the celestial body internal structure and mineral resource explorations, as well as the navigation and positioning, and so on. The forward computation of the gravity field of 2D/3D bodies is a very important issue, which can not only predict the distribution of gravity field, but also be the basis of the inverse problems of gravity data interpretation, so it has important theoretical significance and application value. Generally, the forward computation method of gravity field includes the space- and spectral-domain approaches, and the spectral-domain includes Fourier- and spherical harmonic spectrum-domains. In the literature, the space-, Fourier- and spherical harmonic spectrum-domain methods are often used; however. the spheroidal/ellipsoidal harmonic spectrum method for computing the gravity field not only converges faster than the spherical harmonic spectrum method, but also the reference ellipsoid is more consistent with the external shape of the geological body or small celestial body than the spherical harmonic spectrum method. This project mainly focuses on the spheroidal/ellipsoidal harmonic expansions of the gravity field of geological and small celestial bodies, including the spheroidal/ellipsoidal harmonic expansions of the gravity field of polyhedral bodies, the elliptical harmonic expansions of the gravity field of 2D geological bodies, the spheroidal/ellipsoidal harmonic expansions of the gravity field of 3D bodies with general shape and the spheroidal/ellipsoidal harmonic algorithms of the gravity field with higher order, and thus has a wide application prospect.