A developing approach for solving equations of a trapped motion of small satellite near the secondary planet m(planet) (Earth) in case of the elliptic restricted problem of three bodies, ER3BP, is presented hereby. In ordinary way, this problem includes consideration of two primaries, M-Sun and m(planet) (m(planet) < < M-Sun), both are orbiting around their center of mass on Keplerian orbits. Eccentricity of orbit for the aforementioned m(planet) is considered to be quasiperiodically variable depending on long-term Milankovitch cycles or various types of seasonal irradiation processes influencing onto orbit of planet (hereafter, Earth). Our aim is first to establish and second to investigate a novel type of ER3BP with variable eccentricity of secondary planet stemming from long-term Milankovitch cycles where in the formulation of above problem, small satellite will always maintain its orbit located near the secondary planet, m(planet). Indeed, Milankovitch cycles govern the dynamics of slow changing the eccentricity of the secondary planet orbit quasiperiodically during a long-time period of secondary planet's motion around the primary. This planet moves on quasi-stable elliptic orbit with negligible deviations from purely elliptical motion. Semi-analytical solutions and numerical findings with graphical plots are presented accordingly.