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The discovery of the icy exoplanet OGLE-2005-BLG-390Lb (just 5 times more massive than Earth) by the technique of gravitational microlensing provided the first observational hint that Earth-like planets are common in the Universe. The existence of this new world was revealed from a small blip in the brightness of the star, on just one night, but we will probably never be able to see it again by this method.
This sounds dramatic but gravitational microlensing relies on one-off chance meetings to discover exoplanets. If a star moves in front of a more distant star (relative to an observer on earth), the light from the distant star is bent by the gravitational pull of the closer star and the more distant star is magnified. This effect is called gravitational lensing and is similar to the effect produced by passing the foot of a wine glass in front of a picture (see the video below). The lens isn't made from glass or plastic but it is provided by the gravitational field of the closer star. As the closer star moves in front of the distant star the magnified image of the distant star gets brighter, reaches a peak and then gets dimmer in a smooth way.
If the closer star has one or more planets in orbit around it the shape of the brightening and dimming magnified image is not smooth, but has an extra 'blip' in it (the exact shape of the 'blip' depends mostly on how near to eclipsing the more distant star the closer one comes.). Below is a graph showing how the brightness of the distant star changes with time. You can clearly see the blip from the closer planet superimposed on the light curve of the distant star.
In 2008 the discovery of a miniture Solar System was made around the star OGLE-2006-BLG-109L, 4900 light-years from our Solar System. The star is approximately half the mass of the Sun and much cooler (4000 Kelvin). Two massive planets have been discovered in orbit with similar masses, distance from their sun, and equilibrium temperatures to Jupiter and Saturn.
The best time to look for microlensing events is when the center (or bulge) of the Milky Way Galaxy is visible from Earth because there are so many stars there, there is a higher chance of one star passing in front of another from our viewpoint. The bulge season is usually from about April through September and is best visible from the southern hemisphere.
Microlensing is most sensitive to planets that are farther from their stars and cooler than many of the extrasolar planets that have been discovered by other methods, which tend to find high mass planets in very close orbits. This means microlensing lets us find planets which have formed in a different way than most of those known. It also allows us to find planets around stars which are outside the local group of stars around the Sun. These are farther away than most of the other extrasolar planets that have been discovered. So we are studying whether planet formation in other parts of the our galaxy is similar to how they formed near the Sun.
If you have telescope time, you are now ready to try the LCOGT's microlensing project called Join Our Search for New Planets. To understand the results of this project, you will need to understand how astronomers measure the brightness of stars. They use a system called the magnitude scale which you can read more about in the background document about Magnitude and Distance Measurement.