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We propose a closed-form normalization method suitable for the study of thesecular dynamics of small bodies in heliocentric orbits perturbed by the tidalpotential of a planet with orbit external to the orbit of the small body. Themethod makes no use of relegation, thus, circumventing all convergence issuesrelated to that technique. The method is based on a convenient use of abook-keeping parameter keeping simultaneously track of all the small quantitiesin the problem. The book-keeping affects both the Lie series and the Poissonstructure employed in successive perturbative steps. In particular, it affectsthe definition of the normal form remainder at every normalization step. Weshow the results obtained by assuming Jupiter as perturbing planet and wediscuss the validity and limits of the method.

Closed form perturbation theory in the restricted three-body problem without relegation