arXiv:2611.03701v1 Announce Type: new Abstract: A naturalization, in the sense of Deprit, of Vinti's dynamical system makes the construction of a first order analytical satellite perturbation solution without critical divisors possible. The process gives hints on how to recast Brouwer's classical solution in a form that is free from small divisors too. The functionality of classical perturbation solutions is in this way extended to the close vicinity of the critical inclination. The new analytical solution bears terms that may grow unbounded, but their negative effects do not disclose in time intervals in which this kind of solution may be useful in practice.
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