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.

在本文中，我们提出了一个新的ansatz，用于求解无限小质量（卫星）的被困轨道的运动方程，如果三个物体的椭圆受限制，则该ansatz会被锁定在空间陷阱中并在行星附近移动， ER3BP（带Keplerian椭圆形太阳和行星彼此围绕的原轨道）。在这里执行一种新型的求解过程，以获取其轨道位于行星附近的无穷小质量（卫星）的坐标。将运动方程组用于获得半解析和解析解。得出两个笛卡尔坐标（在原行星与行星相互旋转的平面上）取决于真实的异常和确定解的准周期特征的函数，而第三个坐标（垂直于平面）原边旋转的角度）在一定时期内随着真正的异常而变化。