Constructive-analytical solution of the problem on secular evolution of polar satellite orbits

Double-averaged Hill's problem taking into account the oblateness of the central body is considering. This problem has a row of integrable cases, which are investigated qualitatively in the works of many scientists, since M. L. Lidov and Y. Kozai. However, it is not possible to get strict analytical solution in these cases because the integrals are complicated. The present work is devoted to investigation of case, when the equatorial plane of the central body is coincided with his orbital plane relatively perturbing body and the satellite moves on a polar orbit. More detailed qualitative investigation is executed and approximate constructive-analytical solution of the evolutional system is offered as obvious dependences of eccentricity and argument of pericenter of satellite orbit versus time. The estimation of methodical accuracy is got by comparing to the numerical solution of the evolutionary system for polar lunar artificial satellite orbits.