Astronomy and Astrophysics – Astronomy
Scientific paper
Apr 1988
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1988a%26a...194..309d&link_type=abstract
Astronomy and Astrophysics (ISSN 0004-6361), vol. 194, no. 1-2, April 1988, p. 309-318. In French.
Astronomy and Astrophysics
Astronomy
11
Hyperion, Orbit Perturbation, Planetary Orbits, Chebyshev Approximation, Laplace Transformation, Taylor Series, Planets, Eccentricity, Theoretical Studies, Calculations, Perturbations, Asteroids, Jupiter, Saturn, Satellites, Titan, Hyperion, Parameters, Orbits, Orbital Elements, Models, Celestial Mechanics, Motion, Astronomy
Scientific paper
The author considers the planetary problem with coplanar and non secant orbits (i.e. ρ = r/rarcmin < 1, where r and rarcmin are distances to the Sun of two consecutive planets). The classical methods used to expand the disturbing function by Fourier series in terms of the Keplerian osculating elements (a, e, λ, ω), are limited to small eccentricities, provided that ρ is not too close to unity. The author shows that it is possible to construct a usable analytic representation of aarcmin/Δ (Δ is the mutual distance between two planets), for any eccentricity allowing ρ to be less than 0.95 approximately. Examples are provided for the case of a typical asteroid disturbed by Jupiter (ρ < 0.85 and e < 0.4), and for the case of Titan-Hyperion (ρ < 0.954 and e < 0.134).
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