TO THE ORBITAL DYNAMICS WITH VARIABLE ECCENTRICITY

In this work, we study the orbital dynamics of the non-stationary gravitating system. We consider eccentricity as a function of time, because of its plenty interesting implications for evolution of young planetary systems. Eccentricities can be indicative of long-term orbital stability for various planetary and other gravitating systems of Universe. In particular, the recent studies of dynamical mass of some exoplanet showed there is strong covariance between planet eccentricities and total system mass: higher planet eccentricities imply a substantially larger total mass with long-term orbital stability.   It should be noted that the orbital eccentricity is most often from the radial velocity observations of a bright host star and can also be inferred to a lesser extent from the duration of a planetary transit he primary purpose of some studies of exoplanets could then be seen as placing constraints on the variable flux from the measurable parameter of eccentricity as a proxy for the presently unknown obliquity of the exoplanet. It means that eccentricity is one of the key parameters in dynamical formation and evolution of the non-stationary gravitating systems. We use the method of the inverse problem that provides a significant analytical tool for study of different problems in the field of celestial mechanics.  This method plays an important value for solution of the problems of celestial mechanics connected to the finding of potentials and force fields on the grounds of the given sets of orbits and on the basis of the available first integrals of the motion.   This inverse method approach gives very more profound analytical vision for study of different dynamical systems and to understand its general structure. And this method allows to reconstruct the form of the non-stationary potential field with additional friction force with a known integral of motion for the given monoparametric family of evolving orbits. We assume as reasonable to study such inverse problem for orbits with variable eccentricity in order to understand better the outcomes for long-term architecture and evolution of different gravitating systems of Universe. We assume, that the non-stationary problem with additional friction force сan be useful for study of dynamical evolution of exoplanets or other astrophysical objects, which have been targeted for study for the last decades. In result of such research approach we found two forms of the non-stationary space symmetrical ‘potential’ function generating motion on given monoparametric family of evolving in time planar orbits with variable eccentricity.