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Higher-order stability of the restricted problem and the solar system

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Abstract

A generalization is expressed of the Poisson theorem referring to the invariance of the planetary semi-major axes using the restricted problem model. In particular, it is shown that first and second approximation in terms of a change in the initial states of planets describing closed motions in the solar system remain invariant in modulus after any number of revolutions. But third-order terms contain secular parts and, thus, they undergo a secular change in their orbital motion. Such change would be apparent afterГ ε -2 Jovian years, where Γ is a constant and ε is the maximum initial deviation of each planet from its reference orbit.

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Authors and Affiliations

  1. Department of Mechanics, University of Patras, Greece

    V. Markellos, C. Goudas, G. Katsiaris & G. Georgantopoulos

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  1. V. Markellos
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  2. C. Goudas
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  3. G. Katsiaris
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  4. G. Georgantopoulos
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Markellos, V., Goudas, C., Katsiaris, G. et al. Higher-order stability of the restricted problem and the solar system. Astrophys Space Sci 45, 99–103 (1976). https://doi.org/10.1007/BF00642145

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  • DOI: https://doi.org/10.1007/BF00642145

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