Integral criterion for determining the existence domain of periodic orbits in the vicinity of a smaller body in three-body problem

While accomplishing space missions to the planets of the Solar System, it is impossible to obtain the operating orbit which requires the least expenditure of characteristic velocity without solving the problem of determining the existence domain of periodic solutions (motions with specified characteristics) in the vicinity of the target planet. An effective integral criterion is proposed. The criterion is based on the principle of the least action. Using the given initial conditions it allows both determining an attribution of the obtained trajectory to a class of either periodic or quasi-periodic orbits of the three-body problem and selecting some initial conditions of a spacecraft motion corresponding to the considered class orbits. These results demonstrate the high stability and selectivity of the criterion, as well as the possibility of its application to the analysis of the trajectories in the automated computation mode.

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