On coplanar integrable case of double-averaged Hill's problem taking into account the oblateness of central body

Double-averaged Hill's problem taking into account the oblateness of central planet is considering in the case, when its equatorial plane coincides with the plane of orbital motion relatively perturbing body. A qualitative investigation of this so named coplanar integrable case was begun by Y. Kozai and was prolonged by M. L. Lidov and M. V. Yarskaya. However, it is not possible to get strict analytical solution of this problem because the integrals are complicated. In present work some quantitative evolution’s characteristics are got and approximate constructive-analytical solution of the evolutional system is offered as obvious dependences of satellite orbital elements versus time. The estimation of methodical accuracy is got by comparing to the numerical solution of the evolutionary system for row lunar satellite orbits.