n次方反比力场中物体运动的普适标度比规律

The Universe Scale Law for n-th Power Inverse Law in Gravitational Field

本文从平方反比力场出发,建立行星运动学方程,通过标度变换,并利用标度无关性这一基本原理得到运动轨道关于标度变换系数的一阶拟线性方程,然后运用一阶拟线性方程的特征线解法得到行星的运动规律。最后将此方法推广到n次方反比力场,得到物体运动的普适标度比规律。

Based on the inverse square law in gravitational field,the kinetic equation for planet is obtained.First second order quasilinear system of equation for the coefficient of scale conversion is developed by applying scaling invariance theory.Law of motion for planet is presented based on characteristic line method.This method is extended to the n-th power inverse law in gravitational field,and universal scaling invariance law for planet motion is given.