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New relative equilibria and their implications in the Full 3-Body Problem In the gravitational 3-body problem, if the bodies are assumed to be rigid, spherical and of finite density, there are 28 distinct relative equilibria which exist, including the classical five relative equilibria for the point-mass three-body problem. The bifurcation pathways of these relative equilibria can be mapped out as the angular momentum of the system is increased, and we find that none of these relative equilibria exist or are stable over all values of angular momentum. The transition to finite density greatly increases the number of relative equilibria in the three-body problem and ensures that minimum energy configurations exist for all values of angular momentum. Analysis of these new relative equilibria lead to interesting dynamical phenomenon and limits not present in the classical point-mass 3-body problem.