牛顿万有引力定律不仅是经典力学的核心内容，也是连接天体运动与地面物理现象的重要桥梁.本文基于牛顿运动定律与开普勒三定律，推导出引力平方反比关系，并构建数值模型模拟行星在引力作用下的二维轨道演化.通过位置、速度、加速度随时间的变化曲线及其相图，清晰展示了万有引力导致的周期性轨道行为和向心加速度特性.进一步，本文将物理建模与可视化图像结合，强调了引力定律的动力学本质和教学推广价值，旨在帮助学生深化对牛顿引力机制与守恒规律的理解.

Newton’s law of universal gravitation is a fundamental part of classical mechanics and serves as a key link between celestial motion and physical phenomena on earth. This paper, based on Newton’s laws of motion and Kepler’s three laws, derives the inverse-square form of the gravitational force. A numerical model is then constructed to simulate the two-dimensional orbital motion of a planet under gravitational interaction. The changes in position, velocity, and acceleration over time, as well as their phase diagrams, are used to show the periodic nature of the orbit and the centripetal acceleration caused by gravity. By combining physical modeling with visual representations, the paper highlights the dynamic nature of the gravitational law and its value in teaching. The goal is to help students better understand Newtonian gravity and the related conservation laws.