The stability of the Solar System is a classical, long standing and challenging problem, already pointed out by Newton. In this thesis we revisit the problem in the light of Kolmogorov and Nekhoroshev theorems, with the aim of proving that they apply to realistic approximations of the Sun-Jupiter-Saturn and Sun-Jupiter-Saturn-Uranus systems. The present thesis is devoted to the study of three main problems, namely: (i) the applicability of Kolmogorov and Nekhoroshev theories to the problem of three bodies; (ii) the stability of the secular evolution of the planar Sun-Jupiter-Saturn-Uranus system; (iii) the explicit construction of the normal form for elliptic tori in planetary systems. This work gives an original contribution on the methods for studying the stability of planetary systems. It contains an analytical contribution, namely the proof of the existence of low dimensional elliptic tori for the planetary system obtained via an algorithmic constructive method, and the explicit calculation of the stability time for the Sun-Jupiter-Saturn system and for the planar secular Sun-Jupiter-Saturn-Uranus system. We emphasize that we obtain the first realistic estimates for these problems based on a well established theoretical framework.

EFFECTIVE STABILITY OF HAMILTONIAN PLANETARY SYSTEMS / M. Sansottera ; tutor: Antonio Giorgilli ; coordinator: Marco Peloso. Universita' degli Studi di Milano, 2011 Feb 11. 23. ciclo, Anno Accademico 2010. [10.13130/sansottera-marco_phd2011-02-11].

EFFECTIVE STABILITY OF HAMILTONIAN PLANETARY SYSTEMS

M. Sansottera
2011

Abstract

The stability of the Solar System is a classical, long standing and challenging problem, already pointed out by Newton. In this thesis we revisit the problem in the light of Kolmogorov and Nekhoroshev theorems, with the aim of proving that they apply to realistic approximations of the Sun-Jupiter-Saturn and Sun-Jupiter-Saturn-Uranus systems. The present thesis is devoted to the study of three main problems, namely: (i) the applicability of Kolmogorov and Nekhoroshev theories to the problem of three bodies; (ii) the stability of the secular evolution of the planar Sun-Jupiter-Saturn-Uranus system; (iii) the explicit construction of the normal form for elliptic tori in planetary systems. This work gives an original contribution on the methods for studying the stability of planetary systems. It contains an analytical contribution, namely the proof of the existence of low dimensional elliptic tori for the planetary system obtained via an algorithmic constructive method, and the explicit calculation of the stability time for the Sun-Jupiter-Saturn system and for the planar secular Sun-Jupiter-Saturn-Uranus system. We emphasize that we obtain the first realistic estimates for these problems based on a well established theoretical framework.
11-feb-2011
Settore MAT/07 - Fisica Matematica
GIORGILLI, ANTONIO
PELOSO, MARCO MARIA
Doctoral Thesis
EFFECTIVE STABILITY OF HAMILTONIAN PLANETARY SYSTEMS / M. Sansottera ; tutor: Antonio Giorgilli ; coordinator: Marco Peloso. Universita' degli Studi di Milano, 2011 Feb 11. 23. ciclo, Anno Accademico 2010. [10.13130/sansottera-marco_phd2011-02-11].
File in questo prodotto:
File Dimensione Formato  
phd_unimi_R07486.pdf

accesso aperto

Tipologia: Tesi di dottorato completa
Dimensione 1.06 MB
Formato Adobe PDF
1.06 MB Adobe PDF Visualizza/Apri
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/153106
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact