Viscoelastic tides: models for use in Celestial Mechanics |
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| Authors: | C Ragazzo L S Ruiz |
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| Institution: | 1.Dpto. Matemática Aplicada - IUMA,Universidad de Zaragoza,Zaragoza,Spain;2.Centro Universitario de la Defensa,Zaragoza,Spain |
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| Abstract: | In this note, by using Smale’s \(\alpha \)-theorem on the convergence of Newton’s method, the \(\alpha \)-sets of convergence of some starters of solving the elliptic Kepler’s equation are derived. For each starter we compute the exact \(\alpha \)-set in the eccentricity-main anomaly \((e,M)\in 0,1)\times 0,\pi ]\), showing that these sets are larger than those derived by Avendaño et al. (Celest Mech Dyn Astron 119:27–44, 2014). Further, new convergence tests based on the Newton–Kantorowitch theorem are given comparing with the derived from Smale’s \(\alpha \)-test. |
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