# Johannes Kepler

## Johannes Kepler

Born-December 27, 1571 Weil der Stadt, Germany

Died-November 15, 1630 Regensburg, Germany

<<<<<<<<To the left is a portrait of Johannes Kepler

## Kepler's Laws

Kepler's 1st Law: Orbits are Elliptical

With Tycho Brahe's observations, Kepler set out to determine if the paths of the planets could be described with a curve. By trial and error, he discovered that an ellipse with the Sun at one focus could accurately describe the orbit of a planet about the Sun.

Ellipses are described mainly by the length of their two axes. A circle has the same diameter whether you measure it across or up and down. But an ellipse has diameters of different lengths. The longest one is called the major axis, and the shortest one is the minor axis. The ratio of these two lengths determines the eccentricity (e) of the ellipse; it's a measure of how elliptical it is. Circles have e=0, and very stretched-out ellipses have an eccentricity nearly equal to 1.

Planets do move on ellipses, but they are nearly circular. Comets are a good example of objects in our solar system that may have very elliptical orbits.

Kepler's second law he again discovered by trial and error. Kepler realized that the line connecting the planet and the Sun sweeps out equal area in equal time. What Kepler found is that it takes the same amount of time for the blue planet to go from A to B as it does to go from C to D. But the distance from C to D is much larger than that from A to B. It has to be so that the green regions have the same area. So the planet must be moving faster between C and D than it is between A and B. This means that when planets are near the Sun in their orbit, they move faster than when they are further away.

Kepler's 3rd Law: P2 = a3

Kepler's 3rd law is a mathematical formula. It means that if you know the period of a planet's orbit (P = how long it takes the planet to go around the Sun), then you can determine that planet's distance from the Sun (a = the semimajor axis of the planet's orbit).

It also tells us that planets that are far away from the Sun have longer periods than those close to the Sun. They move more slowly around the Sun.