This paper introduces a new set of compatible orbits, called the "Two-way orbits", whose ground track path is a closed-loop trajectory that intersect itself, in some points, with tangent intersections. The spacecraft passes over these tangent intersections once in a prograde and once in a retrograde mode. The general mathematical model to design the Two-way orbits is presented for the specific case where the tangent points are experienced at the orbit extremes: perigee and apogee. As for the general case, the Two-way orbits conditions are formulated and numerically solved. Results show that, in general, Two-way orbits could be formed at a general tangency point. Using these Two-way orbits, this paper also introduces the Two-way Constellations, that have one spacecraft prograde and one retrograde, passing simultaneously over the tangent intersections.
