Table of Contents

Orbital Mechanics

Keplerian Motion

A Summary of Kepler's Laws

Johannes Kepler (1571-1630)

Johannes Kepler was born near Stuttgart in 1571 and educated at the University of Tübingen. His original intention was to become a Lutheran minister; however, his deep interest in astronomy led him to change his plans.

In 1594, while in his early twenties, Kepler accepted a lectureship at the University of Gratz in Austria.

In 1599, he became assistant to the famous Danish-Swedish astronomer Tycho Brahe, who had moved to Prague as court astronomer to Kaiser Rudolph II.

In 1601, Brahe suddenly died, and Kepler inherited both his master's position and his vast and very accurate collection of astronomical data on the motion of the planets.

With extraordinary persistence and after much computational labour, trial and error, and false solutions, Kepler was finally able, in 1609, to formulate his first two laws of planetary motion. Ten years later, in 1619, he formulated his third law of planetary motion.

Kepler's Perfect Platonic Solids

This is a copy of one of Kepler's first attempts at building an accurate mathematical model of the solar system using geometric shapes. The large outer hemisphere is the orbit of Saturn with the next bowl being the orbit of Jupiter.

Kepler created several prototypes out of paper and was planning to have the final version cast in solid silver. He originally planned it to double as a punchbowl, dispensing various beverages at parties and social events.

The smaller drawing is an enlargement of the spheres inside the bowl, consisting of Jupiter, Mercury, Venus, Earth, and Mars.

Mathematically this model was both elegant and powerful. For example, it explained why there are only six planets. How could there be a seventh planet, when Euclid had proven that there were only five Platonic solids?

Of course, the model is completely false. The interplanetary distances it predicts are not sufficiently accurate, and Kepler was scientist enough to accept this.

Kepler's 3 Laws of Planetary Motion

Kepler's 1st Law of Planetary Motion

The planets travel in closed paths around the Sun in orbits that are elliptical in shape. The Sun is at one focus of the ellipse.

Using observational data of the orbit of Mars collected by Tycho Brahe, and after a prodigious amount of trail and error, false starts, and laborious calculations, Kepler finally determined that planets travel in elliptical orbits.

Kepler's 2nd Law of Planetary Motion

The Law of Equal Areas

The radius vectors of the planets sweep out equal areas in equal intervals of time.

This is now known to be a consequence of the Law of Conservation of Angular Momentum.

Kepler's 3rd Law of Planetary Motion

The Harmonic Law (p² =a³)

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