Johannes Kepler (1571-1630) discovered a set of laws that accurately described the motions of the planets.

Kepler was a great mathematician, but he had very poor eyesight Kepler was a great mathematician, but he had very poor eyesight. This made it difficult to plot the locations of the planets for his studies.

Kepler knew where to find extensive information on the locations of planets which had been kept for several decades.

These documents had been prepared and were in the possession of Tycho Brahe.

Tycho Brahe (1546-1601) was born in Denmark and was very well educated Tycho Brahe (1546-1601) was born in Denmark and was very well educated. He was very rude and insulting to everyone.

He lost his nose in a duel while still a student He lost his nose in a duel while still a student. After that, he wore a gold and silver replacement which he glued in place.

Tycho’s rudeness forced him to leave Denmark in 1597 after becoming the enemy of almost everyone important in the entire country.

He moved to Prague, which is close to Graz, Austria, where Kepler just happened to be living. Kepler came to work with Tycho in 1600.

They worked together trying to find a theory explaining Tycho’s data They worked together trying to find a theory explaining Tycho’s data. Tycho died a year later, and Kepler inherited Brahe’s data (he really stole it).

While Kepler was a Copernican, Brahe believed that the Sun orbited the Earth, but that the planets orbited the Sun.

Kepler set to work trying to find a principle that would explain the observed motions of the planets. This work would take most of the last 29 years of his life.

He used triangulation to plot the orbits of the planets from Tycho’s data. After many years of work he summarized the motions of the planets in three simple laws.

Kepler’s Laws of Planetary Motion - 1 Kepler’s Laws of Planetary Motion - 1. The orbital paths of the planets are elliptical, with the Sun at one focus.

2. An imaginary line connecting the Sun to any planet sweeps out equal areas of the ellipse in equal intervals of time.

3. The square of a planet’s orbital period is proportional to the cube of its orbital semi-major axis: P(years)2 = a(a.u.)3

1. The planet’s orbits are ellipses with the Sun at one focus.

The eccentricity is the ratio of the distance between the foci to the length of the major axis.

Perihelion - closest approach to the Sun Perihelion - closest approach to the Sun. Aphelion - greatest distance from the Sun.

None of the planets orbits are as eccentric as these pictures None of the planets orbits are as eccentric as these pictures. Except for Mercury and Pluto it would be difficult to tell that the orbit wasn’t a circle.

The substitution of the ellipse for the circle was a BIG DEAL The substitution of the ellipse for the circle was a BIG DEAL. The circle was Aristotle’s baby and even Galileo was a believer in circular motion.

2. An imaginary Sun to planet line sweeps out equal areas in equal times.

The planets move faster when close to the Sun and slower when farther away.

These two laws explained all the motions without the need for epicycles.

Kepler published the first two laws in Astronomia Nova (The New Astronomy) in 1609 proving the laws only for Mars.

In 1619 he wrote Harmonice Mundi (The Harmony of the Worlds) where he proved the first two laws for all the known planets and added his third law.

3. The square of a planet’s orbital period is proportional to the cube of its orbital semi-major axis. The time taken for a planet to orbit the Sun increases more rapidly than the size of its orbit (measured in astronomical units).

One astronomical unit is a measure of distance equal to the average distance of the Earth from the Sun, or the length of the semi-major axis of Earth’s orbit.