What Are Lagrange Points?

 
There are five locations around a planet’s orbit where the gravitational forces and the orbital motion of the spacecraft, Sun and planet interact to create a stable location from which to make observations. These points are known as Lagrangian or ‘L’ points, after the 18th century Italian astronomer and mathematician Joseph-Louis Lagrange (born Giuseppe Luigi Lagrancia).

Joseph-Louis Lagrange found the solution to what is called the “three-body problem.” That is, is there any stable configuration, in which three bodies could orbit each other, yet stay in the same position relative to each other?
As it turns out, there are five solutions to this problem - and they are called the five Lagrange points, after their discoverer. The L1, L2, and L3 points are all in line with each other - and L4 and L5 are at the points of equilateral triangles, as we can see in the image below.

The first Sun-Earth Lagrange point, L1, is 1.5 million km from the Earth towards the Sun, and there have been many solar observatories located here, including DSCOVR, WIND, SOHO, and ACE.

There have been other satellites out at Sun-Earth L2, where JWST will be, including WMAP, Herschel, and Planck.

Some Technical Details: It is easy for an object (like a spacecraft) at one of these five points to stay in place relative to the other two bodies (e.g., the Sun and the Earth). In fact, L4 and L5 are stable in that objects there will orbit L4 and L5 with no assistance. Some small asteroids are known to be orbiting the Sun-Earth L4 and L5 points. However, L1, L2, and L3 are metastable so objects around these points slowly drift away into their own orbits around the Sun unless they maintain their positions, for example by using small periodic rocket thrust. This is why L1, L2, and L3 don't "collect" objects like L4 and L5 do.
► Go to an ESA page, where we can watch some nice animations of Lagrangian points>>http://www.esa.int/Our_Activities/Operations/What_are_Lagrange_points

► Read this NASA information>> http://jwst.nasa.gov/orbit.html