E Roghanizad - Satellite Research Institute, Iranian Space Research Center, Tehran, Iran.
M Chiniforoushan - Space Systems Design and Development Center, Iranian Space Research Center, Tehran, Iran.

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.

The existence of specified-energy orbit connecting two given points is studied, as well as the number and the equation of such orbits, under assumptions of the two body problem