多面体模型的Eros433引力场计算与分析

Computing and analysis of gravity field of Eros433 using polyhedron model

摘要:

为更好的认识不规则小行星引力场的特点,本文采用多面体模型法对Eros433小行星的引力场进行计算,并由此分析了小行星引力场的分布特点．首先介绍了多面体模型的概念和小行星多面体模型的计算方法．然后,应用高斯公式和格林公式,通过两次积分变换将引力势函数的三重积分转化为一重积分,并将其应用到多面体模型中,推导了多面体模型的引力势函数、引力加速度和拉普拉斯算子的计算公式．最后,计算并分析了Eros433小行星引力场的分布特点,应用伪势能曲面和零速度曲线分析了小行星周围的轨道动力学环境和平衡点的位置情况,通过与JPL实验室公布的数据对比表明,本方法最大计算误差为1.52％,具有较高的精度．

Abstract:

To better understand the properties of gravity field of irregularly shaped asteroid, this paper adopted the Polyhedron modeling method to calculate the gravity filed of asteroid Eros433, and analyzed the distributing properties of this asteroid’s gravity field. Firstly this article introduced the concept of Polyhedron model and the method of calculating polyhedron model of asteroid, and then the polyhedron model of asteroid Eros433 was given. After that, Gauss Law and Green’s formula are applied to the calculation, and by twice integral transformation the triple integral of gravitational potential function can be transformed into single integral, which can be used in polyhedron model to derive the formulas of gravitational potential function, gravitational acceleration and Laplacian. Finally, the formulas derived were applied to calculate and analyze the distributing properties of gravity field of Eros433, after taking the self-rotation of asteroid into consideration, Pseudo-potential surface and Zero velocity curve are used to analyze the orbital dynamic environment around the asteroid and the position conditions of equilibrium points of asteroid.