开普勒三定律和万有引力定律的几何证明

GEOMETRIC PROOF OF KEPLER’S THREE LAWS AND THE LAW OF UNIVERSAL GRAVITATION

在高中教材中“由开普勒定律推导出万有引力定律”“由万有引力定律推导开普勒定律”,采用的是近似方法求解,结果不能令人信服。在大学教材或者相关文献中都是通过微积分知识求解,学生不易理解。本文采用哈密顿速度矢量图,结合简单的几何知识,巧妙地解决了上述问题。

In high school textbooks,“the law of universal gravitation is derived from Kepler’s law”and“Kepler’s law is derived from the law of universal gravitation”,which are solved by approximate method,and the result is not convincing.In university textbooks or related literature,it is solved by calculus knowledge,which is not easy for students to understand.In this paper,Hamilton velocity vector diagram and simple geometric knowledge are used to skillfully solve the above problems.