John Stockton <jrs@merlyn.demon.co.uk>

The Lagrange points occur in a three-body system.  Take a system
consisting of a large mass M, orbited by a smaller mass m, and a third
mass u, where M >> m >> u.  There are five points where u can be and
have the same orbital period as m.

Three lie on the line connecting M and m.  One (L1) lies between M and
m, one (L2) lies outside the orbit of m, and one (L3) lies on the
other side of M from m.

Two are in the orbit of m, 60 degrees ahead (L4) and 60 degrees behind
it (L5).

Pictorially, we have something like this (not too scale!), with the
direction of revolution indicated for m:

                                 L4
                                  \ 
                                   \ orbit of m    ^
                                    \              |
                  L3   M         L1   m  L2        |
                                    /              |
                                   /
                                  /
                                 L5

The Lagrangian points are often considered as places where objects,
such as satellites can be "parked" for long periods.  For instance,
the SOHO satellite sits at the Sun-Earth L1 point in order to have a
continuous, unobstructed view of the Sun, and the Wilkinson Microwave
Anisotropy Probe observed from the L2 point.  There is a group of
asteroids, known as Trojans, which occupy the Sun-Jupiter L4 and L5
points.  There are also various groups advocating human colonization
of space which support putting a colony at the Earth-Moon L5 point.

In fact, the L1, L2, and L3 points are "unstable equilibria."  That
is, an object placed there will slowly drift away if there are any
other gravitational tugs on it (which there always will be due to
other objects in the solar system).  Thus, placing a spacecraft at the
Sun-Earth L1 or L2 point requires regular "course corrections" so that
it doesn't move too far from the L1 or L2 point.  The L4 and L5 points
are generally stable so that one should be able to remain at them
indefinitely.

Additional diagrams for the L points is at the WMAP site,
<URL:http://map.gsfc.nasa.gov/m_mm/ob_techorbit1.html>.