Ever looked up at the night sky and wondered how we know the precise dance of the planets? It’s not magic—it’s math. Specifically, it’s the elegant interplay between Johannes Kepler’s observations and Isaac Newton’s laws of gravity.
But how do we take those centuries-old equations and turn them into a living, breathing simulation on a computer screen?
In this chapter of our journey through computational physics, we are moving from theory to practice. We will bridge the gap between abstract physics and concrete code by building a robust orbital simulator. We'll explore the stability of numerical methods and write Python code that can predict the path of a planet around the Sun with frightening accuracy.
The Physics: From Kepler’s Curves to Newton’s Force
To simulate an orbit, we first need to understand the two pillars of celestial mechanics that make it possible.
