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Seminario / Locatelli

SEMINARIO DI FISICA MATEMATICA

8 Febbraio, ORE 13:45, AULA DOTTORATO

Ugo Locatelli

Titolo: A reverse KAM method to estimate unknown mutual inclinations
in exoplanetary systems.

Abstract: The orbital evolution of the major planets of the Solar system is
usually studied in the framework of the Lagrange-Laplace secular
theory (i.e, averaging the system over the fast revolution angles). In
this approximation the evolution of the eccentricities and
inclinations turns out to be quasi-periodic: the corresponding orbits
are stable [L], lying on KAM tori or, at least, being close to them
for times exceeding the age of the Universe [GLS1,GLS2]. The part
concerning with the orbits on invariant tori was completely proved
nearly twenty years ago, for a secular model of the Sun-Jupiter-Saturn
system [LG], where the behaviour of the mutual inclination is obtained
from a suitable parameter, D2, the so-called Angular Momentum Deficit.

Coming to extrasolar systems, we tackle the opposite problem: assuming
that the system is stable, we aim to bound the usually unknown mutual
inclination to a suitable range of values. Therefore, considering
exoplanets that have been detected via Radial Velocity method, we
investigate the range of values of D2 for which KAM stability applies
to the secular dynamics. Such a procedure looks to be successful in
providing limits on the (unknown) inclination for pairs of exoplanets
having very moderate eccentricities, i.e., in situations similar to
the Sun-Jupiter-Saturn system. We show our first applications to the
following systems: HD141399, HD143761 and HD40307.

Joint work with M. Sansottera (Univ. of Milan) and M. Volpi (Univ. of
Namur).

02 febbraio 2018
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