  We describe the geometry of geodesics on a Lorentz ellipsoid: give explicit
formulas for the first integrals (pseudo-confocal coordinates), curvature,
geodesically equivalent Riemannian metric, the invariant area-forms on the
time- and space-like geodesics and invariant 1-form on the space of null
geodesics. We prove a Poncelet-type theorem for null geodesics on the
ellipsoid: if such a geodesic close up after several oscillations in the
"pseudo-Riemannian belt", so do all other null geodesics on this ellipsoid.
