  We consider the unrestricted problem of two mutually attracting rigid bodies,
an uniform sphere (or a point mass) and an axially symmetric body. We present a
global, geometric approach for finding all relative equilibria (stationary
solutions) in this model, which was already studied by Kinoshita (1970). We
extend and generalize his results, showing that the equilibria solutions may be
found by solving at most two non-linear, algebraic equations, assuming that the
potential function of the symmetric rigid body is known explicitly. We
demonstrate that there are three classes of the relative equilibria, which we
call "cylindrical", "inclined co-planar", and "conic" precessions,
respectively. Moreover, we also show that in the case of conic precession,
although the relative orbit is circular, the point-mass and the mass center of
the body move in different parallel planes. This solution has been yet not
known in the literature.
