Kepler’s Laws of Planetary Motion

A humorous cartoon of astronomer Johannes Kepler enthusiastically explaining his Third Law of planetary motion to a surprised colleague (looking uncannily like Isaac Newton), with a chalkboard diagram showing elliptical orbits and the equation T² = R³, set against a starry night sky. Educational science illustration with historical characters and annotated orbital mechanics. Artwork: NaturPhilosophie with AI

The study of planetary motion was revolutionized in the early 17th century when Johannes Kepler uncovered precise mathematical patterns governing how planets travel around the Sun.

His insights transformed Astronomy from a descriptive art into a predictive science, laying the foundation for modern celestial mechanics and influencing thinkers from Newton to contemporary astrophysicists.

A scientific diagram illustrating Kepler’s Third Law of Planetary Motion, showing the mathematical relationship between the orbital period of a planet and the semi-major axis of its elliptical orbit around the Sun, with labeled axes and proportional scaling to highlight how orbital period increases with distance. Source: ResearchGate
  1. Law of Ellipses: Planets move in elliptical orbits with the Sun at one focus.
  2. Law of Equal Areas: A line joining a planet and the Sun sweeps out equal areas in equal times (faster near perihelion, slower near aphelion).
  3. Law of Periods: The square of the orbital period T is proportional to the cube of the semi-major axis a :

T^2\propto a^3

Therefore, much larger orbits take much longer to complete.