高斯定理在万有引力场中的推广及应用

Generalization and Application of Gauss Theorem in Gravitational Field

高斯定理是电磁学的重要知识内容,在处理对称性电场分布时极为简便,在力学中,也有类似于静电场的引力场,遇到此类问题,目前多以传统的力学解题方法求解,这将会遇到极大的困难,计算量大而繁琐。鉴于此,借助静电场中的高斯定理,加以推广至力学中,旨在寻找一种方法, 以解决在力学中对称性引力场的求解问题。通过类比万有引力场和静电场, 给出了引力场强度的概念, 从而引出万有引力场中的“高斯定理”, 并给出了证明。利用它分析了两个具体问题, 说明了利用高斯定理可以简化具有对称性的引力场的相关计算。

Gauss Theorem is an important knowledge content of electromagnetism,and it is very simple to deal with symmetrical electric field distribution.In mechanics,there are also gravitational fields similar to electrostatic fields.When such problems are encountered,most of them are solved by traditional mechanics methods,which will encounter great difficulties and require a large amount of calculation.By means of the Gauss Theorem in electrostatic field,it is extended to mechanics in order to find a way to solve the problem of symmetric gravitational field in mechanics.By comparing the gravitational field with the static electric field,the concept of the strength of the gravitational field is given,which leads to the Gauss Theorem in the gravitational field,and the proof is given.It is shown that Gauss Theorem can be used to simplify the calculation of gravitational field with symmetry.