## Planetary Motion, Elliptical Orbits, & Understanding the Cosmos

Kepler’s first law of planetary motion radically changed our views of the cosmos by saying that planets had elliptical orbits.

Johannes Kepler went to work for Tycho Brahe near the end of Tycho’s life. When Tycho died, Kepler used Tycho’s data to deduce three laws of planetary motion. Because Tycho’s data were far more accurate than any previously collected data on planetary positions neither Ptolemy’s nor Copernicus’s models of the cosmos worked.

Kepler deduced three laws of planetary motion that did agree with Tycho’s data but diverged from traditional views of the cosmos.

### Statement of Kepler’s First Law

Kepler’s first law states that the planet’s move in elliptical orbits around the Sun and that the Sun is at one focus of the ellipse.

### Circular Versus Elliptical Orbits

Kepler had been taught that planets move in uniform circular orbits. From the time of the ancient Greeks until Kepler’s time, scientific dogma insisted that planets move in circular orbits at a constant speed. No one has seriously questioned this dogma for about 2 millennia. Kepler’s suggestion that the planets orbited the Sun in ellipses rather than circles seems innocuous now, but in Kepler’s time it was a radical suggestion.

### What is an Ellipse?

An ellipse looks like a slightly flattened circle, but not just any flattened circle is an ellipse. There is a very specific mathematical relationship for the points on an ellipse. It is not necessary to understand the mathematics to understand Kepler’s first law. It does however help to know how to draw an ellipse.

To draw a circle using a nail, pencil, and a loop of string, loop the string around the nail, and place the pencil at the other end of the loop. Moving the pencil around in a circular path gives a drawing of a circle with the nail at the center.

Drawing an ellipse requires two nails. Loop the string around both nails and move the pencil around as for drawing a circle. With two nails, however, the drawing will be an ellipse rather than a circle. The positions of the two nails will be the two focal points of the ellipse.

Draw several different ellipses by changing the positions of the nails. As the two nails move closer together, the ellipse becomes more circular. A circle is a special ellipse that has both focal points at the same point, the center of the circle. As the nails move farther apart, the ellipse becomes more flattened. A line is a special case of an ellipse that has the two focal points infinitely far apart.

In a planet’s elliptical orbit around the Sun, the Sun is at one of the focal points of the ellipse. There is nothing at the other focal point. The elliptical orbits of the planets around the Sun differ only slightly from circles, but the difference was enough to make circular orbits disagree with Tycho’s data.

Kepler’s willingness to go against 2000 years of scientific dogma and suggest that planets moved in elliptical rather than circular orbits contributed to our new understanding of how the cosmos works.