## International Year of Astronomy - Johannes Kepler

**Johannes Kepler (1571
- 1630)**

The 17^{th} century German mathematician and

astronomer Johannes Kepler is best known for his three laws of planetary

motion. These served as a foundation for Isaac Newton's law of universal

gravitation first formulated later that century.

In the early 1600s, Kepler served as the imperial

mathematician under Holy Roman Emperor Rudolph II, filling a position left

vacant by another famous astronomer of the day, Tycho Brahe.

A supporter of the Copernican System (with the planets

orbiting the Sun and not Earth), Kepler took advantage of Brahe's extensive

observations of the planet Mars and tried to fit them to the Copernican model.

The changing position of the Mars in the night sky was best fit if Mars was

assumed to orbit the Sun following an elliptical orbit-not a circular orbit as

was the doctrine-with the Sun at one of the foci of the ellipse. Kepler assumed

that this also holds true for the rest of the planetary orbits:

1) All planets move

in ellipses, with the Sun at one focus.

Kepler also noticed that Mars moved the fastest on the side

of its orbit closer to the Sun (near perihelion) and slowest on the side

farther from the Sun (near aphelion). Expressed in terms of geometry:

2) Planets sweep out equal areas in equal times.

In 1610, Kepler corresponded with and endorsed the

observations of another brilliant astronomer of the day, Galileo Galilei.

Years later, while searching for harmony in the proportions

of the natural world, Kepler discovered the mathematical relation between the

planets' orbital period and their mean distance to the Sun:

3) The square of the

orbital period P (in years) equals

the cube of the mean distance to the Sun *a
(in astronomical units), or *

*P*

=

^{2}=

*a*

^{3}.
Kepler's 3^{rd} law can be explained in terms the

inverse square law of universal gravitation-planets near the Sun feel a greater

pull and so orbit much faster than planets farther away.

** **

**The Kepler Mission**

NASA named its Earth-like planet finder mission in honor of

Johannes Kepler. The *Kepler Mission*

is a space photometer that will observe the brightness of over 100,000 stars in

the Milky Way over 3.5 years to detect periodical transits (eclipses as seen by

the mission) of a star by its planets. It is expected to discover hundreds of

Earth-size and smaller planets in or near the habitable zone of those stars and

determine how many of the billions of stars in our galaxy have such planets.

Additional Information

http://www.johanneskepler.com

http://kepler.nasa.gov/

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