In the n{body problem a central con guration is formed when the
position vector of each particle with respect to the center of mass is a common
scalar multiple of its acceleration vector. Lindstrom showed for n = 3 and for
n > 4 that if n ? 1 masses are located at xed points in the plane, then there
are only a nite number ...Â»Â»Â»Â»

In the n{body problem a central con guration is formed when the
position vector of each particle with respect to the center of mass is a common
scalar multiple of its acceleration vector. Lindstrom showed for n = 3 and for
n > 4 that if n ? 1 masses are located at xed points in the plane, then there
are only a nite number of ways to position the remaining nth mass in such a
way that they de ne a central con guration. Lindstrom leaves open the case
n = 4. In this paper we prove the case n = 4 using as variables the mutual
distances between the particles.^^^^