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In this paper, we present a new ansatz for solving equations of motion forthe trapped orbits of the infinitesimal mass (satellite), which is locked inthe space trap to be moving near the planet in case of the elliptic restrictedproblem of three bodies, ER3BP (with Keplerian elliptic trajectories ofprimaries Sun and planet around each other). A new type of the solvingprocedure is implemented here to obtain the coordinates of the infinitesimalmass (satellite) with its orbit located near the planet. The system ofequations of motion was applied for obtaining of the semi-analytic and analyticsolutions. It is obtained that two cartesian coordinates (in a plane of mutualrotation of primaries Sun and planet around each other) depend on the trueanomaly and a function which determines the quasi periodic character ofsolution, while the third coordinate (perpendicular to the plane of rotation ofprimaries) is quasi-periodically varying with true anomaly.

Semi-analytical solution for the trapped orbits of satellite near the planet in ER3BP