A new method is used to study a current version of the two-planet problem on the secular evolution of planetary orbits with small eccentricities and mutual inclinations, having an arbitrary orientation relative to the main (picture) plane. A model has been developed that describes a wide class of exoplanetary systems with an inclination angle of orbits different from (pi {text{/}}2.) The orbits of the planets are modeled by the Gaussian rings, the perturbing function is represented by the mutual gravitational energy of these rings in the form of a series up to terms of second order of smallness. To describe the evolution of orbits, instead of osculating Keplerian elements, a new set of variables is introduced: the unit vector ({mathbf{R}}) of normal to the plane of the ring and two Poincaré variables (left( {p,q} right);) for eight independent variables, a system of differential equations is obtained and analytically solved. The method is applied to study the secular evolution of the two-planet system Kepler-117 (KOI-209) with non-resonant orbits of exoplanets. It has been established that in this system the oscillations of the same components of the orientation vector ({mathbf{R}}) for each of the orbits, as well as the values (left( {e,i,{{Omega }}} right),) occur strictly in antiphase. The eccentricities of both orbits oscillate with the period ({{T}_{kappa }} approx 182.3;{text{years}},) and the inclinations of the orbits and the longitudes of the ascending nodes change in the libration mode with the same period ({{T}_{g}} approx {text{174}}.5;{text{years}}.) The lines of the orbital apsides rotate unevenly counterclockwise with the periods of secular rotation ({{T}_{{{{g}_{2}}}}} approx 178.3;{text{years}}) (for a light planet), and ({{T}_{{{{g}_{1}}}}} approx 8140;{text{years}}) (for a more massive planet).
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