## **A Brief History** Edit

http://www.esa.int/images/JohannesKepler,1.jpg

Johannes Kepler was an Austrian mathematician and astronomer that was the founder of three fundamental laws of planetary motion. Kepler first began working with Scientist Tychio Brahe as an assistant to Brahe’s research. After observing and reading Brahe’s planetary tables and data, Kepler made his own conclusions about the solar system. Brahe wrongly believed that the earth was the center of the solar system, but had useful data and research to learn from. Kepler took advantage of these resources, and made his own scientific reasoning of how the solar system worked. Before Kepler and Brahe's time, there was a famous astrologer Nicolai Copernicus. Copernicus rationalized through science a belief that the sun was the center of the solar system, and followed a "heliocentric" system. The heliocentric system placed each of the nine planets in a pattern orbiting the sun, and followed a belief that the planets orbited circularly. In Challenging Brahe's opinion, Kepler was a firm believer in the Copernican system. Kepler used Brahe's data to rationalize the heliocentric theorem that the sun was the center of the solar system and that the planets orbited the sun in a circular pattern. Although Copernicus and Kepler were correct in their statement that the sun was the center, they had wrongly assumed that the planets followed a circular path. For years Kepler used the heliocentric theorem as a hypothesis for how the solar system worked. He finally realized that the planets did not orbit in circles, but in shapes called ellipses (ellipses are a bit like circles, but have an oval (egg-like) shape). This realization is what led to Kepler's first law of planetary motion.

## **The Law** Edit

Kepler’s first law stated that the paths of planets are ellipses (a type of circular shape that is more like an egg then an orange), with the sun at one "focus" of the ellipse. In an ellipse, there are two foci that determine where the sun is. These foci can be thought of as centers (even if they are not the technical real center), because the line from the foci to the rim of the ellipse is similar to that of a center of a circle. In a circle, the radius is always the same. In an ellipse, the sum of the distances from both foci to any point on the outside of the ellipse is the same as for any other point on the outside. An ellipse has a different shape from a circle, and can have two foci with equal distances. In the first diagram at right and above (not to scale), you can see how the ellipse has two equal distances from both foci (represented by a and b). The variables a and b are equal (or constant). This is represented by the equation a + b = constant. The sun can be at either focus of the ellipse. The elliptical pattern contains the two foci, from which the distance of any point on the ellipse is equal to the distance to either of the foci. Kepler's law states that planets rotate around the sun in this elliptical pattern, **and the pattern holds tr**ue for every planet in the solar system.

## **What Will You See on the Regents?** Edit

Which object is located at one focus of the elliptical orbit of Mars?

- the Sun
- Betelgeuse
- Earth
- Jupiter

Correct Answer: 1. (Mars (or any other planet) follows an elliptical pattern around the sun.) **The sun** will always be at one focus of the elliptical orbit. The sun being the center of the solar system will always be a focus of the elliptical orbit, and any planet orbits the sun in an elliptical pattern.

Correct Answer: 2. We can automatically cross out answer choices 3 and 4 because we know Kepler stated that planets orbit the sun in an elliptical pattern and not a circular one. We also know that the sun is always at one focus of the ellipse, and not at the very center of the shape. 2 has to be the answer because both foci are represented in the diagram, and the sun is at one of the foci.

## **References and Resources** Edit

http://csep10.phys.utk.edu/astr161/lect/retrograde/copernican.html – The Heliocentric system and information about Nicolai Copernicus

http://www.regentsprep.org/physics – Provides practice problems

http://scienceworld.wolfram.com/biography/Kepler.html – Provides a brief biography of Johannes Kepler.

http://csep10.phys.utk.edu/astr161/lect/history/kepler.html – Provided diagrams and information pertaining to Kepler’s First Law.

http://www.nineplanets.org/overview.html – Basic information about the solar system.

The Barron’s Review Physics Regents Book by Miriam A. Lazar – Has practice problems and the definition and diagrams of Kepler’s Laws.

http://www.esa.int/images/JohannesKepler,1 – Source of Picture of Johannes Kepler.

http://www.einstein-website.de/images/Kepler-E1 - Kepler's Law diagram

Ellipse Diagram, Kepler's First Law diagram and Practice Problem - Recreated by me (with sourcing).