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In this paper, we present a new ansatz for approximated solving equations ofmotion of the infinitesimal mass m in case of bi-elliptic restricted problem offour bodies (BiER4BP) (where three primaries M1, M2, M3 are rotating aroundtheir common centre of mass on elliptic orbits with hierarchical configurationM3 < M2 << M1). A new type of the solving procedure is implemented here toobtain the coordinates of the infinitesimal mass m. Meanwhile, the system ofequations of motion has been successfully explored with respect to theexistence of semi-analytical (approximated) way for presentation of thesolution. We obtain as follows: 1) the solution for coordinates {x, y} = {0, 0}is approximately satisfied both the first and second equations of motion if wetake into consideration assumption {M3, M2} << M1, 2) the expression forcoordinate z(f) is given by the equation of 2-nd order, which describesSitnikov-type approximated solution. It means that test particle is movingalong the z-axis, outward the common barycenter of the system (butperpendicular to the plane of the mutual rotation of all the primaries).

Sitnikov-type solution for the motion of infinitesimal mass in BiER4BP