B.16 What are the Lagrangian (L) points?

The Lagrangian 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 the
gravitational force on u is contributed equally by M and 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:

                                 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.  There is a group of
asteroids, known as Trojans, which occupy the Sun-Jupiter L4 and L5
points.  There is also various groups advocating human colonization of
space which support putting a colony at the Earth-Moon L5 point.