Title: How to Establish an Orbit with Specified Mechanical Energy between Two Points in the Two Body Problem

Considering a specified pair of points in the space and a determined value of mechanical energy, the existence of trajectory passing through the points of interest and the number of such orbits, subject to the conditions of the two body problem, is comprehensively investigated in this paper. It is demonstrated that the connecting trajectory does not always exist and the number of passing orbits is generally zero, two or four. Furthermore, the exact equation of the connecting orbit, if there is any, is provided. In order to do so, an analytical closed form solution is presented which results in the initial flight path angle to reach the considered target point. Finally, the complete process of checking the existence, determining the number and specifying the equation of the passing orbit is introduced as an algorithm.