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.