Sokolov, V. G. On approximations to the initial parts of perturbed trajectories with two Keplerian orbits. (Russian. English summary) Zbl 0539.70024 Byull. Inst. Teor. Astron. 15, No. 6, 329-333 (1984). Summary: Intermediate orbits in which the initial position vector and its successive time derivatives to the third order inclusive coincide with those of the real perturbed trajectories have been constructed. The intermediate motion is determined by the motion along the Keplerian orbit (epicycle) the focus of which moves along another Keplerian orbit (deferent) with fixed focus. The intermediate orbits have the third order tangency to the real trajectories, ensure good approximations to the initial parts of these trajectories and may be useful when studying motion of small bodies of the Solar system. MSC: 70F15 Celestial mechanics Keywords:moving focus; Intermediate orbits; Keplerian orbit; epicycle; fixed focus; motion of small bodies; Solar system PDFBibTeX XMLCite \textit{V. G. Sokolov}, Byull. Inst. Teor. Astron. 15, No. 6, 329--333 (1984; Zbl 0539.70024)