Non-Restricted Double-averaged Three Body Problem in Hill's Case

摘要: A limiting case of the problem three bodies (m 0,m 1,m 2) is considered. The distance between bodiesm 0 andm 1 assumed to be much less than that their barycenter and bodym 2 so one may use Hill's approximation for potential interaction bodiesm 1 andm 2. In absence resonant relations potential, double-averaged by mean longitudes ofm 1 andm 2, describes secular evolution orbits in first perturbation theory. As Harrington has shown, this integrable. present paper a qualitative investigation comparison with analogous restricted are carried out. set initial data found, which collision takes place. region parameters determined, plane retrograde motion unstable. special example results approximate analysis compared those numerical integration exact equations body problem.