Marco Sansottera
University of Milan
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Publication
Featured researches published by Marco Sansottera.
Celestial Mechanics and Dynamical Astronomy | 2009
Antonio Giorgilli; Ugo Locatelli; Marco Sansottera
We investigate the long time stability in Nekhoroshev’s sense for the Sun– Jupiter–Saturn problem in the framework of the problem of three bodies. Using computer algebra in order to perform huge perturbation expansions we show that the stability for a time comparable with the age of the universe is actually reached, but with some strong truncations on the perturbation expansion of the Hamiltonian at some stage. An improvement of such results is currently under investigation.
Mathematics and Computers in Simulation | 2013
Marco Sansottera; Ugo Locatelli; Antonio Giorgilli
We investigate the long time stability of the Sun–Jupiter–Saturn–Uranus system by considering the planar, secular model. Our method may be considered as an extension of Lagrange’s theory for the secular motions. Indeed, concerning the planetary orbital revolutions, we improve the classical circular approximation by replacing it with a torus which is invariant up to order two in the masses; therefore, we investigate the stability of the elliptic equilibrium point of the secular system for small values of the eccentricities. For the initial data corresponding to a real set of astronomical observations, we find an estimated stability time of 107 years, which is not extremely smaller than the lifetime of the Solar System (∼5Gyr).
Regular & Chaotic Dynamics | 2017
Antonio Giorgilli; Ugo Locatelli; Marco Sansottera
We investigate the long-time stability of the Sun-Jupiter-Saturn-Uranus system by considering a planar secular model, which can be regarded as a major refinement of the approach first introduced by Lagrange. Indeed, concerning the planetary orbital revolutions, we improve the classical circular approximation by replacing it with a solution that is invariant up to order two in the masses; therefore, we investigate the stability of the secular system for rather small values of the eccentricities. First, we explicitly construct a Kolmogorov normal form to find an invariant KAM torus which approximates very well the secular orbits. Finally, we adapt the approach that underlies the analytic part of Nekhoroshev’s theorem to show that there is a neighborhood of that torus for which the estimated stability time is larger than the lifetime of the Solar System. The size of such a neighborhood, compared with the uncertainties of the astronomical observations, is about ten times smaller.
Celestial Mechanics and Dynamical Astronomy | 2014
Marco Sansottera; Christoph Lhotka; Anne Lemaitre
We investigate the long-time stability in the neighborhood of the Cassini state in the conservative spin-orbit problem. Starting with an expansion of the Hamiltonian in the canonical Andoyer-Delaunay variables, we construct a high-order Birkhoff normal form and give an estimate of the effective stability time in the Nekhoroshev sense. By extensively using algebraic manipulations on a computer, we explicitly apply our method to the rotation of Titan. We obtain physical bounds of Titan’s latitudinal and longitudinal librations, finding a stability time greatly exceeding the estimated age of the Universe. In addition, we study the dependence of the effective stability time on three relevant physical parameters: the orbital inclination,
Celestial Mechanics and Dynamical Astronomy | 2017
Marco Sansottera; Marta Ceccaroni
Monthly Notices of the Royal Astronomical Society | 2015
Marco Sansottera; Christoph Lhotka; Anne Lemaitre
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Physica D: Nonlinear Phenomena | 2017
Tiziano Penati; Marco Sansottera; Simone Paleari; V. Koukouloyannis; P. G. Kevrekidis
Communications in Nonlinear Science and Numerical Simulation | 2018
Tiziano Penati; Marco Sansottera; Veronica Danesi
i, the mean precession of the ascending node of Titan orbit,
Physica D: Nonlinear Phenomena | 2016
Marco Sansottera; Antonio Giorgilli; Timoteo Carletti
arXiv: Dynamical Systems | 2014
Marco Sansottera; L. Grassi; Antonio Giorgilli
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