  The relative equilibria for the spherical, finite density 3 body problem are
identified. Specifically, there are 28 distinct relative equilibria in this
problem which include the classical 5 relative equilibria for the point-mass
3-body problem. None of the identified relative equilibria exist or are stable
over all values of angular momentum. The stability and bifurcation pathways of
these relative equilibria are mapped out as the angular momentum of the system
is increased. This is done under the assumption that they have equal and
constant densities and that the entire system rotates about its maximum moment
of inertia. The transition to finite density greatly increases the number of
relative equilibria in the 3-body problem and ensures that minimum energy
configurations exist for all values of angular momentum.
