Construction of periodically evolving orbits of a satellite of an oblate planet in the averaged Hill's problem with allowance for precession of the orbit of a perturbing point

Details Construction of periodically evolving orbits of a satellite of an oblate planet in the averaged Hill's problem with allowance for precession of the orbit of a perturbing point Construction of periodically evolving orbits of a satellite of an oblate planet in the averaged Hill's problem with allowance for precession of the orbit of a perturbing point

May 1998

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998astl...24..406v&link_type=abstract

Astronomy Letters, Volume 24, Issue 3, May 1998, pp.406-412; Pis'ma v Astronomicheskii Zhurnal, Vol. 24, p. 474

Astronomy and Astrophysics

Astronomy

2

Scientific paper

Our goal is to find special orbits whose elements vary with the same period due to perturbations. In the averaged Hill's problem with an oblate central planet, we constructed examples of such periodically evolving orbits for the satellite-oblate Earth-Moon-Sun system in the model of an elliptical lunar orbit that precesses with a constant inclination i_1 to the plane of the ecliptic. Based on generating orbits (i_1 = 0), we obtained peri- odic solutions of an evolving system with a period that is a multiple of the precession period of the lunar orbit for i_1 = 5 deg 15.15 using the numerical solution of a two-dimensional boundary-value problem. Our numerical results are confirmed by the calculations performed by an independent numerical-analytical method.

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