💫 Kepler's law

Kepler’s law of equal areas

Johannes Kepler is without doubt one of the founding fathers of astronomy. Above all, he became famous for his three laws:

1. The shape of each orbit is an ellipse, with the sun at one focus of the ellipse.
2. The planets move faster when they are closer to the sun, in such a way that a line drawn from the sun to any planet sweeps out equal areas in equal times.
3. The outer planets move slower than the inner ones, in such a way that the cube of the length of the ellipses semi-major axis is proportional to the square of the period of the orbit.

This app plots the orbit of a planet in an eccentric orbit to illustrate the sweeping out of equal areas in equal times, with sun at focus. The eccentricity of the orbit is random and determined by the initial velocity. The program uses normalised units ($G =1$).

🎯 Demonstration of Kepler’s law of equal areas
🧠 Inspired by origin VPython program by Peter Borcherds, University of Birmingham, England
🐍 A VPython demo is available as well, see keplers_law.py

Live experiment