On the families of periodically evolving orbits in Hill's averaged problem with allowance for oblateness of the central planet

Details On the families of periodically evolving orbits in Hill's averaged problem with allowance for oblateness of the central planet On the families of periodically evolving orbits in Hill's averaged problem with allowance for oblateness of the central planet

Mar 1998

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998astl...24..185v&link_type=abstract

Astronomy Letters, Volume 24, Issue 2, March 1998, pp.185-192; Pis'ma v Astronomicheskii Zhurnal, Vol. 24, p. 226

Astronomy and Astrophysics

Astronomy

Scientific paper

We study the families of periodically evolving orbits in Hill's averaged problem with allowance for a polar oblateness of the central planet. In the integrable case, where its equatorial plane coincides with the orbital plane of a distant attracting point, we construct the families of generating orbits. In addition to stationary solutions in the plane (g is the argument of the pericenter latitude, e is the eccentricity), we have also found periodic generating solutions. For small deviations from the stationary solutions, these periodic solutions are described by analytical formulas, whereas the large-amplitude solutions are obtained numerically. Continuing the generating solutions to the domain of arbitrary angles eps between the above planes, we trace the changes in the parameters of the periodically evolving orbits and find various branches of these solutions in the (eps, e) plane for various constants of the first integral of the problem - the averaged perturbing function. These branches originate from both periodic and nonresonant quasi-stationary generating solutions of the coplanar problem (eps = 0). For eps = 23.44 deg, which corresponds to the Earth-Moon-Sun model system, we note cases where one, three, and two (in a degenerate case) solutions, which correspond to periodically evolving orbits of the Earth's satellites with the semimajor axis a = 42 200 km, exist.

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