Kepler's Laws of Planetary Motion — Quick Reference

Law of Orbits

• Planets move in elliptical orbits with the Sun at one focus.
• Ellipse basics:
  • Major axis: passes through the center, longest diameter; also called the transverse diameter.
  • Minor axis: shortest diameter.
  • Semi-major axis $a$: from center to edge along the major axis.
  • Semi-minor axis $b$: from center to edge along the minor axis.
  • Foci: two; Sun is at one focus.
• Key terms:
  • Perihelion: closest approach to the Sun.
  • Aphelion: farthest distance from the Sun.

Law of Areas

• The line joining the Sun and a planet sweeps out equal areas in equal times.
• Consequence: when the planet is closer to the Sun, it moves faster; when farther, it moves slower.

Law of Period

• The square of the orbital period $T^2$ is proportional to the cube of the semi-major axis $a^3$.
• In simplified units (years, AU): $T^2 = a^3$.
• Consequence: farther planets take longer to orbit.

Additional Notes and Context

• Kepler used Tycho Brahe's observational data to develop these laws.
• The three laws describe orbits of other objects as well: comets, moons, or binary stars.