In 1618, Johannes Kepler formulated three laws of planetary motion that bear his name. He used data gathered by the eccentric observational astronomer, Tycho Brahe. Legend has it that Kepler covertly acquired the data from a stubborn Tycho. The three empirical laws describe general properties of planets following elliptical orbits. The first law states that planets move in ellipses with the Sun at one focus. The second law states that a planet will sweep out the same amount of area during the same amount of time thoughout its orbit. The third states that the square of the period (planetary year) is proprtional its average distance from the Sun. These laws later turned out to be accurate consequences of Newtons law of gravity.
Four hundred years later, we are still using Kepler’s laws to search for more planets beyond our solar system. On March 6th 2009, NASA launched the first satellite designed specifically for hunting extrasolar planets (or exoplanets). The satellite is appropriately named Kepler. It contains a 1 meter diameter telescope that mesures the light intensity of stars. The advantage that Kepler has over ground 
based telescopes is that it won’t have to look though Earth’s atmosphere. The atomosphere is what causes stars to twinkle and interferes often interferes with observations. However, some astronomers are working to cancel out such atmospheric problems. The Kepler mission will search for planets around 100,000 stars for over three and a half years. This field of view is roughly the area of the sky that your hand covers when held out at arm’s length.
There are several methods for discovering exoplanets depending on how its orbit is oriented when we view it. Kepler will look for exoplanets that cross between us and their parent star. When this happens, the parent star appears slight more dim. This is precisely what Kepler is built to observe. If a star becomes dim on a regular basis then that indicates that a planet is passing in front of it. This is called the transit method.
The probablility that a planet’s orbit is oriented correctly for the transit method is only 0.5% . And the planet will only dim the star’s brightness by one ten thousandth over a few hours. With these low odds and high hurdles, Kelper’s mission looks dim. Given this small probabilty, there 
are still about 500 Earth-like planets that waiting for Kepler!
The first extrasolar planet was discovered in 1992. Since then, searching for exoplanets has significantly increased. The current count of known exoplanets is 342. Many astrophysicists hope to discover an exoplanet that is similar to our Earth. An Earthlike planet could contain water or even life! Aside from discovering alien life, an exo-Earth would also offer hints about the formation of our own solar system.
Most of the known exoplanets were found using the wobble method. If an exoplanet’s orbit is tilted slightly from our point of view, then it will not transit on front of its parent star. Detection of such a planet requires a different method. The orbit of a planet is caused by the force of gravity of the parent star pulling on the planet. However, Newton’s 3rd law requires that the planet also pulls on the star. This casues the star to wobble very slightly. As a result the light from the star will vary its frequency very slightly. This is due to the Doppler effect. You often observe the Doppler effect of sound waves when a train is coming and going.
Geoff Marcy from the University of California at Berkeley is the pioneer of this method. He discovered 70 of the first 100 exoplanets and some of his students hope to discover moons orbiting those planets.