Kepler’s Law

There are actually three, Kepler’s laws that is, of planetary motion: 1) every planet’s orbit is an ellipse with the Sun at a focus; 2) a line joining the Sun and a planet sweeps out equal areas in equal times; and 3) the square of a planet’s orbital period is proportional to the cube of the semi-major axis of its orbit. As it’s the third which is most often used, Kepler’s law usually means Kepler’s third law (of planetary motion).

Tycho Brahe’s decades-long, meticulous observations of the stars and planets provided Kepler with what today we’d call a robust, well-controlled dataset to test his hypotheses concerning planetary motion (this way of describing it is, dear reader, a deliberate anachronism). In particular, Tycho’s observations of the position of Mars in the Uraniborg night sky were the primary source of hard data Kepler used to derive, and test, his three laws.

Kepler’s laws have an important place in the history of astronomy, cosmology, and science in general. They marked a key step in the revolution which moved the center of the universe from the Earth (geocentric cosmology) to the Sun (heliocentric), and they laid the foundation for the unification of heaven and earth, by Newton, a century later (before Newton the rules, or laws, which governed celestial phenomena were widely believed to be disconnected with those controlling things which happened on Earth; Newton showed – with his universal law of gravitation – that the same law rules both heaven and earth).

Although Kepler’s laws are only an approximation – they are exact, in classical physics, only for a planetary system of just one planet (and then the focus is the baricenter, not the Sun) – for systems in which one object dominates, mass-wise, they are a good approximation.

Further Reading: Kepler’s Three Laws of Planetary Motion, and Understanding Solar System Dynamics: Orbits and Kepler’s Laws (both from NASA) are good, and this University of Virginia webpage is fun!

Several Universe Today articles cover one aspect of Kepler’s Law or another, among them Let’s Study Law: Kepler Would Be So Proud!, and Happy Birthday Johannes Kepler

Astronomy Cast has three episode relevant to Kepler’s law: Gravity, and two Questions Shows Jan 27th, 2009, and May 19th, 2009; check them out!