牛顿引力定律的一个几何特征（英文）

A geometric feature of the Newton law of gravitation

在牛顿的引力定律中,最为重要的事实是引力的大小是反比于质点之间的距离的平方.基于引力是沿着质点的连线方向并正比于质量的乘积之前提下,证明了引力的反平方距离的事实完全等价于两个均匀球体之间的引力可以归结于位于球心处的同质量质点之间的引力.事实上,这个几何要求将导致一个二阶的线性欧拉方程,其具有物理意义的解恰好是反比于距离的平方.

In the Newton law of gravitation, the most miraculous fact is that the gravity is reciprocally proportional to the square of the distance between particles. In this paper, by assuming that the gravity s along with the line passing through particles and is proportional to the product of masses of particles, we will show that the above fact is equivalent to the geometric requirement that the gravity between two homogeneous balls is equal to that between two particles of the same masses located at the centers of balls. In fact, this will lead to a second-order Euler equation whose physical solution is reciprocally proportional to the square of the distance.