In the current research, a novel approach or solving procedure for equations of the trapped motion for small mass m near the primary m_planet in case of the elliptic restricted problem of three bodies (ER3BP) is presented. We consider two primaries M_Sun and m_planet which are orbiting around their barycenter on elliptic orbits. Our aim of investigating such the class of motions is to obtain the coordinates of the aforementioned satellite (in the synodic co-rotating Cartesian coordinate system \( \overrightarrow{r} \)={x, y, z}) which will always maintain its orbit located near the second of these primaries, m_planet. We obtain a family of semi-analytical (approximated) solutions as follows: 1) equation for x is given via coordinate y and true anomaly f, with help of the additional variable parameter α, which determines a Riccati-type character of solution for coordinate z (which means possibility of sudden jumping of the magnitude of solution), 2) expression for y is given via coordinate x, true anomaly f, and the chosen parameter α, 3) coordinate z is to be quasi-oscillating with small amplitude depending on true anomaly f which is tracing the motion of small mass (satellite) around primary m_planet. Besides, the additional ways of semi-analytical solving equations of motion are illuminated.

在目前的研究，一种新的方法或解决程序为方程被困运动为小质量米主邻近米_行星在三个机构（ER3BP）的椭圆受限问题的情况下被呈现。我们考虑了两个原初M _Sun和m_行星，它们绕其重心绕椭圆轨道运行。我们研究这种运动类别的目的是获得上述卫星的坐标（在Synodic同向旋转笛卡尔坐标系\（\ overrightarrow {r} \） = { x，y，z}），它将始终保持其轨道位于这些原边中的第二个附近，即m _planet。我们获得如下族的半解析（近似）解：1）x的方程是通过坐标y和真实异常f给出的，借助附加变量参数α，它确定了坐标的解的Riccati型特征z（这意味着可能突然解出解的大小），2）通过坐标x，真实异常f和选择的参数α给出y的表达式，3）坐标z将根据真实的异常f以小的幅度准振荡，该异常f跟踪小质量（卫星）绕主_行星m的运动。此外，还阐明了运动的半解析求解方程式的其他方法。