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

Abstract We propose a closed-form normalization method suitable for the study of secular dynamics small bodies in heliocentric orbits perturbed by tidal potential planet with orbit external to body. The makes no use relegation, thus circumventing all convergence issues related that technique. is based on convenient book-keeping parameter keeping simultaneously track quantities problem. affects both Lie series and Poisson structure employed successive perturbative steps. In particular, it definition normal form remainder at every step. show results obtained assuming Jupiter as perturbing planet, we discuss validity limits method.