The inclinations of exoplanets detected via radial velocity method are essentially unknown. We aim to provide estimations of the ranges of mutual inclinations that are compatible with the long-term stability of the system. Focusing on the skeleton of an extrasolar system, i.e. considering only the two most massive planets, we study the Hamiltonian of the three-body problem after the reduction of the angular momentum. Such a Hamiltonian is expanded both in Poincaré canonical variables and in the small parameter D2, which represents the normalised angular momentum deficit. The value of the mutual inclination is deduced from D2and, thanks to the use of interval arithmetic, we are able to consider open sets of initial conditions instead of single values. Looking at the convergence radius of the Kolmogorov normal form, we develop a reverse KAM approach in order to estimate the ranges of mutual inclinations that are compatible with the long-term stability in a KAM sense. Our method is successfully applied to the extrasolar systems HD 141399, HD 143761 and HD 40307.
|Titolo:||A reverse KAM method to estimate unknown mutual inclinations in exoplanetary systems|
|Parole Chiave:||Celestial Mechanics; Exoplanets; KAM theory; n-Body planetary problem; Modeling and Simulation; Mathematical Physics; Astronomy and Astrophysics; Space and Planetary Science; Computational Mathematics; Applied Mathematics|
|Settore Scientifico Disciplinare:||Settore MAT/07 - Fisica Matematica|
|Data di pubblicazione:||2018|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1007/s10569-018-9829-5|
|Appare nelle tipologie:||01 - Articolo su periodico|