Teaching-oriented modeling and numerical demonstration of Newton's law of gravitation

Based on Newton's laws of motion and Kepler's empirical laws, this study presents a pedagogically oriented derivation of the inverse-square law of gravitation and develops a numerical model to simulate two-dimensional planetary motion under central gravitational interaction. The governing equations are solved using a finite-difference time-stepping scheme, enabling visualization of orbital trajectories and conservation properties. Through combined analytical derivation and numerical simulation, the study highlights the dynamical roles of energy and angular momentum conservation in shaping orbital behavior. In addition, an instructional analogy with LC oscillatory circuits is introduced to clarify the underlying dynamical structure responsible for orbital stability. By integrating theoretical reasoning, computational modeling, and cross-domain analogy, this work aims to enhance students' conceptual understanding and model-based reasoning in classical mechanics.