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