Johannes Kepler was a German astronomer and mathematician best known for developing three namesake ** laws of planetary motion**. Kepler was a student and assistant of

**astronomer**

*Danish***. By analyzing Brahe’s data collected by observing**

*Tycho Brahe***, Kepler was able to formulate his laws of planetary motion.**

*Mars**By analyzing questions, you can see patterns emerge, patterns that will help you answer more tossups. Qwiz5 is all about those patterns. In each installment of Qwiz5, we take an answer line and look at its five most common clues. Here we explore five clues that will help you answer a tossup on Johannes Kepler*

__FIRST LAW__

Planets move in an ** elliptical** orbit around the sun. The sun is a

**of the ellipse. This is a modification of**

*focus***’s**

*Copernicus***which held that planets move in circular orbits with the sun at the center of the circle.**

*heliocentric theory*__SECOND LAW__

A line connecting a planet and the sun will ** sweep out equal areas in equal time**. Kepler’s Second Law is a derivation of the law of conservation of

**.**

*angular momentum*__THIRD LAW__

The ** square** of a planet’s

**is proportional to the**

*orbital period***of its**

*cube***. It is sometimes known as the**

*semi-major axis***, and Isaac**

*Harmonic Law***later modified it to account for**

*Newton***.**

*universal gravitation*__MYSTERIUM COSMOGRAPHICUM__

Kepler’s best known work is the ** Mysterium Cosmographicum** in it, he outlines his theory that the universe is a sphere consisting of a series of

**.**

*nested platonic solids*__KEPLER’S CONJECTURE__

Kepler developed a mathematical conjecture dealing with ** sphere packing**. He determined the using either

**or**

*hexagonal close packing***will result in the most efficient possible arrangement of**

*face-centered cubic packing***.**

*74.04%******

*Quizbowl is about learning, not rote memorization, so we encourage you to use this as a springboard for further reading rather than as an endpoint. Here are a few things to check out: *

* The Physics Classroom has a good explanation of ** Kepler’s Laws of Planetary Motion**.

* Wolfram Mathworld (which is a GREAT math resource) has a nice explanation of ** Kepler’s Conjecture**.

* How did ** Tycho Brahe** die? Poisoned by his prosthetic nose? Died when his bladder burst after failing to relieve himself in a timely manner? Murdered by a jealous Kepler? Scientific American investigated…

* Watch a simple visual depiction of Kepler’s Laws below:

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