The knowledge of the stellar age

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Table of contents

1 Introduction 
1.1 Historical overview
1.2 Problematic
1.3 Plan of the thesis
2 Extrasolar planets 
2.1 Detection methods
2.1.1 Direct Imaging
2.1.2 Transit Photometry
2.1.3 Radial velocities
2.1.4 Astrometry
2.1.5 Gravitational microlensing
2.1.6 Transit Timing Variations
2.1.7 Other methods
2.1.8 The Rossiter-McLaughlin effect
2.2 The diversity of exoplanets
2.2.1 Period distribution
2.2.2 Mass distribution
2.2.3 Eccentricity distribution
2.2.4 Spin-orbit angle distribution
2.2.5 Multiple systems
2.2.6 Statistical properties of exoplanets
2.3 Planet Formation
2.3.1 The protostellar nebulae
2.3.2 Properties of protoplanetary discs
2.3.3 Grains and planetesimals formation
2.3.4 Rocky planets formation
2.3.5 Giant planets formation
2.4 Planet migration
2.4.1 Disc migration
2.4.2 Migration via scattering of planetesimals
2.4.3 High-eccentricity induced migration
3 Basics of celestial mechanics 
3.1 The two-body problem
3.1.1 The planar case
3.1.2 Three-dimensional orbit
3.2 Perturbation theory
3.2.1 Keplerian orbits perturbed by an extra force
3.2.2 The disturbing function and Lagrange’s equations
3.2.3 Laplace-Lagrange theory of secular perturbations
3.2.4 Hierarchical systems and the Kozai mechanism
3.2.5 Resonant perturbations
3.2.6 Post-Newtonian perturbations
4 Interactions between an inclined planet and a disc 
4.1 Planets on inclined orbits
4.2 The disc potential
4.2.1 The 2D case
4.2.2 The 3D case
4.3 Frictional forces
4.3.1 Aerodynamic drag
4.3.2 Dynamical Friction
4.3.3 Comparison of the two forces
4.4 Publication I – Orbital evolution of a planet on an inclined orbit interacting with a disc
4.5 Interplay between eccentricity and inclination
4.6 Systems of two planets
5 Resonant Migratin 
5.1 Migration and the capture in resonance
5.1.1 Observational evidences
5.1.2 Disc–driven migration of two planets
5.2 Resonant migration and orbital evolution
5.2.1 Probability of capture in resonance
5.2.2 Physics of the resonant migration
5.2.3 Damping of the orbital elements by the disc
5.3 Publication II – Evolution of eccentricity and orbital inclination of migrating planets in 2:1 mean motion resonance
5.4 Complete solution in the case of strong eccentricity damping
6 Conclusions 
6.1 Summary
6.2 Perspectives