Modeling Planetary and Stellar Motion Using Differential Equations

Abstract

The report aims to explore the application of differential equations in modeling the motion of planets and stars within our universe, serving as an introduction to the captivating realm of celestial mechanics. We utilize differential equations to represent the movement and positions of celestial bodies within a gravitational field, grounding our analysis in Newton's laws of motion and gravitation. Moreover, we employ Kepler's laws of planetary motion to elucidate the orbits of planets around the sun. It is important to note that this report offers a simplified perspective, designed for educational purposes. In reality, celestial mechanics can be exceedingly intricate, involving n-body problems, relativistic effects, and a multitude of other factors.