An exact solution to determination of an open orbit

We present an exact solution of the equations for orbit determination of a two body system in a hyperbolic or parabolic motion. In solving this problem, we extend the method employed by Asada, Akasaka and Kasai (AAK) for a binary system in an elliptic orbit. The solutions applicable to each of elliptic, hyperbolic and parabolic orbits are obtained by the new approach, and they are all expressed in an explicit form, remarkably, only in terms of elementary functions. We show also that the solutions for an open orbit are recovered by making a suitable transformation of the AAK solution for an elliptic case.