  We present for the first time an explicit, complete and closed-form solution
to the three-dimensional problem of two fixed centres, based on Weierstrass
elliptic and related functions. With respect to previous treatments of the
problem, our solution is exact, valid for all initial conditions and physical
parameters of the system (including unbounded orbits and repulsive forces), and
expressed via a unique set of formulae. Various properties of the
three-dimensional problem of two fixed centres are investigated and analysed,
with a particular emphasis on quasi-periodic and periodic orbits, regions of
motion and equilibrium points.
