The planets, moons, comets and asteroids of our solar system (and planets around other stars) trace orbits around their stars and planets. These orbits are mostly elliptical. Objects closer to their stars and planets have faster orbits, while more distant ones have longer orbits. Who figured all this out? Oddly enough, it's not a modern discovery. It dates back to the time of the Renaissance, when a man named Johannes Kepler (1571-1630) looked at the sky with curiosity and a burning need to explain the motions of the planets.

### Getting to Know Johannes Kepler

Kepler was a German astronomer and mathematician whose ideas fundamentally altered our understanding of planetary motion.His best-known work began when Tycho Brahe (1546-1601) settled in Prague in 1599 (then the site of the court of the German emperor Rudolf) and became court astronomer, he hired Kepler to carry out his calculations. Kepler had studied astronomy long before he met Tycho; he favored the Copernican world-view and corresponded with Galileo about his observations and conclusions. He wrote several works about astronomy, including *Astronomia Nova*, *Harmonices Mundi*, and *Epitome of Copernican Astronomy*. His observations and calculations inspired later generations of astronomers to build on his theories. He also worked on problems in optics, and in particular, invented a better version of the refracting telescope. Kepler was a deeply religious man, and also believed in some tenets of astrology for a period during his life.

*(Edited by Carolyn Collins Petersen)*

### Kepler's Task

Kepler was assigned by Tycho Brahe the task of analyzing the observations that Tycho had made of Mars. Those observations included some very accurate measurements of the position of the planet which did not agree with either Ptolemy or Copernicus's findings. Of all the planets, the predicted position of Mars had the largest errors and therefore posed the greatest problem. Tycho's data were the best available before the invention of the telescope. While paying Kepler for his assistance, Brahe guarded his data jealously.

### Accurate Data

When Tycho died, Kepler was able to obtain Brahe's observations and attempted to puzzle them out. In 1609, the same year that Galileo Galilei first turned his telescope towards the heavens, Kepler caught a glimpse of what he thought might be the answer. The accuracy of the observations was good enough for Kepler to show that Mars' orbit would precisely fit an ellipse.

### Shape of the Path

Johannes Kepler was the first to understand that the planets in our solar system move in ellipses, not circles. He then continued his investigations, finally arriving at three principles of planetary motion. Known as Kepler's Laws, these principles revolutionized planetary astronomy. Many years after Kepler, Sir Isaac Newton proved that all three of Kepler's Laws are a direct result of the laws of gravitation and physics which govern the forces at work between various massive bodies.

### 1. Planets move in ellipses with the Sun at one focus

Here, then are Kepler's Three Laws of Planetary Motion:

Kepler's first law states "all planets move in elliptical orbits with the Sun at one focus and the other focus empty". Applied to Earth satellites, the center of the Earth becomes one focus, with the other focus empty. For circular orbits, the two foci coincide.

### 2. The radius vector describes equal areas in equal times

### 3. Squares of periodic times are to each other as cubes of the mean distances

Kepler's 3rd law, the law of periods, relates time required for a planet to make 1 complete trip around the Sun to its mean distance from the Sun. "For any planet, the square of its period of revolution is directly proportional to the cube of its mean distance from the Sun." Applied to Earth satellites, Kepler's 3rd law explains that the farther a satellite is from Earth, the longer it will take to complete and orbit, the greater the distance it will travel to complete an orbit, and the slower its average speed will be.