Analytical Proper Elements for the Hilda Asteroids I: Construction of a Formal Solution |
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| Authors: | O Miloni S Ferraz-Mello C Beaugé |
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| Institution: | (1) Instituto de Astronomia, Geofísica e Ciências Atmosféricas, Universidade de São Paulo, Rua do Matão 1226, 05508-900 São Paulo, Brasil;(2) Observatório Astronómico, Universidad Nacional de Córdoba, Laprida 854, 5000 Córdoba, Argentina |
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| Abstract: | In this paper, we present the mathematical basis for the calculation of proper elements for asteroids in 3:2 mean-motion resonance with Jupiter from their osculating Keplerian elements. The method is based on a new resonant Lie-series perturbation theory (Ferraz-Mello, 1997, 2002), which allows the construction of formal solutions in cases where resonant and long-period angles appear simultaneously. For the disturbing function, we used the Beaugé’s expansion (Beaugé, 1996), adapted to include short period terms. In this paper, the theory is restricted to the planar case and only the perturbations due to Jupiter are considered. |
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| Keywords: | Hilda asteroids perturbation theory proper elements |
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