Lagrangian points L1 L2 L3 L4 L5

Lagrange point is a vantage point of space, described by Joseph-Louis Lagrange in 1772.
The Italian-French mathematician, discovered the existence of equilibrium positions where the gravitational field between two massive objects, such as the Sun and Earth, are compensated.
A Lagrange point is a position in space where the gravitational fields of two bodies in orbit around each other and substantial weight, combine to provide a balance to a third body negligible mass. Of this balance, the relative positions of the three bodies are fixed. And a satellite Earth placed on one of these points do more moves and turns together, permanently, with the Earth around the Sun.
For example, the L2 point is located in the opposite direction to the Sun (see right image), which allows the satellite to keep its solar panels turned toward the sun and pointing his telescope to the outer solar system. This position for an observation satellite, minimizes unwanted electromagnetic emissions from the Sun and Earth. The L2 point is ideal for observing the deep Universe. L1 is located between two celestial objects in the same alignment as the two objects. If the two objects are the Sun and Earth, a satellite undergoes solar gravity more strongly than that of Earth.
It runs more quickly around the Sun than does Earth, but Earth's gravity in part counteracts the Sun, which slows it down. If the objects are close to the Earth, this effect is more important. From a certain point, the L1 point, the angular velocity of the object is equal to that of Earth. On this point to 1.502 million km from Earth, is since 1995 the solar observation satellite, SOHO (Solar and Heliospheric Observatory).

L2 is located at 1.492 million square kilometers of land on the line defined by the Earth and Sun. The satellite should rotate slower than the Earth because the gravitational force the sun is lower, but the gravitational field of the Earth tends to accelerate. At the L2 point, the object orbits the Sun at the same angular velocity as the Earth. On this point is since June 2001, the WMAP (Wilkinson Microwave Anisotropy Probe).
The GAIA satellite will settle there in 2011 and James Webb in 2013. On July 3, 2009, Planck has reached this point L2 and was placed on a course called Lissajous orbit. L3 is located on the line defined by two objects, but beyond the largest object, here the Sun (see right image). A satellite located opposite the Earth from the Sun, about 150 million km, would be in equilibrium.
In reality this is not exactly the opposite, because the center of rotation is not the Sun, but the centroid or center of mass of the couple Earth / Sun.
This item is inappropriate to comment because it is permanently hidden by the Sun. L4 and L5 are located on the vertices of two equilateral triangles whose base is formed by the line of the two objects.
Lagrange point L4 is ahead of the smaller mass in its orbit around the large and the Lagrangian point L5 is late. These points are sometimes called triangular Lagrange points or points "trojans".
Remarkably, the latter two points are on stable orbits and satellites do not need driven, they do not depend on the relative masses of two bodies.
Scientists have estimated that about 2 million asteroids of more than one kilometer in diameter could be in the L4 and L5 points of Jupiter.

The L2 point is a great place to observe the universe, it is located in a very stable thermal environment, to 1.492 million km from Earth on the line defined by the Earth and the sun.
As against this point is slightly unstable gravitationally, which is an advantage for an artificial satellite as it is protected from dust, absent in this neighborhood. However artificial satellites must correct their trajectory regularly in order to keep this privileged position in space.
Since 2001, are on this orbit, the satellite WMAP, the satellite Planck Surveyor and Herschel since May 2009, Gaia and James Webb Space Telescope will also be positioned on that.

Kepler's laws of celestial mechanics require that a body (satellite, asteroid...) can not be on a different orbit of the Earth by example and have the same rotation period of 1 year.
Lagrange proved that it is not entirely accurate, there are these famous privileged points, called Lagrange points.
The Lagrange points are places in space where a satellite can remain stationary relative to the other two objects. Among these 5 points, only L4 and L5 are stable, which means that matter and dust tend to accumulate in these areas.
L1, L2 and L3 are unstable, they can not retain the natural satellites, artificial satellites can only periodically correcting their orbits remain in these areas.

Found in the couple Jupiter-Sun, hundreds of Trojan asteroids that took agglutinate.
They are also found in some couples Neptune and Mars-Sun-Sun.
We discovered a Trojan for Mars, the asteroid 5261 Eureka.
There are also objects in the system Trojans Saturn satellite of Saturn.
Saturn-Tethys with a 2 Trojans Telesto and Calypso, respectively 29 and 26 km in diameter at the points L4 and L5.
Saturn-Dione with Helena, a moon of 33 km in diameter, to the point L4 and L5 Pollux point.