以數理分析克卜勒三大行星律─牛頓的萬有引力定律

Abstract

本論文分成兩部分：第一部分（第二章至第四章）描述牛頓的生平，以及牛頓發現萬有引力定律的過程；第二部分（第五章至第八章）重新證明牛頓的萬有引力定律當中，四個非常重要的定理，這四個定理的結果，確認了萬有引力定律和克卜勒三大行星律的等價性。牛頓在他的著作《原理》中的證明艱澀難懂，一般人無法欣賞，本文將以較為簡單易懂的方式重新證明，如此，一般人也可以體會這些定裡的美妙所在。

There are two parts in this thesis : In the first part (ch.2 - ch.4), we introduce Newton’s lifetime and how he invents the law of universal gravitation ; In the second part (ch.5 - ch.8), we re-prove the four important theorems of Newton’s law of universal gravitation by which Newton confirmed the equivalence of Kepler’s law of planets and the law of universal gravitation. One of the aim of our work is to explain Newton’s theorems to common reader. Hopefully, everyone can enjoy the beauty of Newton’s work.