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.