| Summary: | This article is devoted to the study of the stability of movement of a satellite of finite size around the natural satellites of the planets in the solar system, using the new concept of ER3BP with variable eccentricity. This concept was introduced earlier for the <i>variable</i> spin state of a secondary planet correlated implicitly to the motion of the satellite for its trapped orbit near the secondary planet (which is involved in the Kepler duet “Sun-planet”). But it is of real interest to explore another kind of this problem, <i>plane</i> ER3BP “planet-moon-satellite”. Here, we consider two primary celestial bodies, a planet and a moon, the latter revolves around its common barycenter in a quasi-elliptical orbit in a <i>fixed plane</i> (invariable plane) around the planet with a slowly varying eccentricity on a large time scale due to tidal phenomena. This study presents both new theoretical and numerical results for various cases of the “planet-moon-satellite” trio.
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