Computer Science
Scientific paper
Apr 1974
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1974cemec...9..151l&link_type=abstract
Celestial Mechanics, Volume 9, Issue 2, pp.151-173
Computer Science
4
Scientific paper
It is known that the restricted circular Three Body Problem with the perturbing function being twice averaged (by the longitudes of the point with zero-mass and the one with the least finite mass) could be integrated. Due to the complexity of one of the known integrals the full investigation of this problem so far does not exist. Only investigations of limiting cases are known. This paper shows a new limiting class of solution of this problem and gives its qualitative investigation. The space orbits of the ‘asteroids’ everywhere close to the circular orbit of the body with the least finite mass are considered. Certain qualitative singularities of the behavior of solutions, connected with the critical inclination (Krasinsky, 1972) are noted. The paper also shows an analogous class of solutions of the twice-averaged problem, dealing with the perturbing of the satellite's orbit by the ‘mascon’.
Lidov M. L.
Ziglin S. L.
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