The two centre problem is studied both in the phase plane and in spacetime, assuming first a trajectory collinear, and, as a second case, a circular one through the newtonian attractors, finding a saddle equilibrium. For the latter problem a probably new differential equation is met and solved. Time is then obtained in both cases through elliptic integrals of all kinds and Jacobian functions.
Giovanni Mingari Scarpello. Arsen Palestini. Daniele Ritelli. "Straight and Circular Motions of a Particle in the Field of Two Fixed Attractors." J. Geom. Symmetry Phys. 11 49 - 66, 2008. https://doi.org/10.7546/jgsp-11-2008-49-66