Stability of the Solar System and Its Minor Natural and Artificial Bodies

It is this editor's distinct pleasure to offer to the readership the text of the lectures presented at our recent NATO Advanced Study Institute held in Cortina d'Ampezzo, Italy between August 6 and August 17, 1984. The invited lectures are printed in their entirety while the seminar contributions are presented as abstracts. Our Advanced Study Institutes were originated in 1972 and the reader, familiar with periodic phenomena, so important in Celestial Mechanics, will easily establish the fact that this Institute was our fifth one in the series. We dedicated the Institute to the subject of stability which itself is a humbling experience since it encompasses all fields of sciences and it is a basic element of human culture. The many definitions in existence and their practical applications could easily fill another volume. It is known in this field that it is easy to deliver lectures or write papers on stability as long as the definition of stability is carefully avoided. On the other hand, if one selects a definition, he might be criticized for using that definition and not another one. In this volume we carefully defined the specific concept of stability used in every lecture. If the reader wishes to introduce other definitions we feel that he should be entirely free and we encourage him to do so. It is also known that certain sta­ bility definitions and concepts are more applicable to certain given fields than to others.

I: Dynamics of Natural and Artificial Satellites.- The Tiny Satellites of Jupiter and Saturn and Their Interactions with the Rings.- Motion of a Geo-Centric Synchronous Satellite.- On the Brown Conjecture.- On the Evolution of the Lunar Orbit.- The Three-Body Problem With Two Small Masses: A Singular-Perturbation Approach to the Problem of Saturn’s Coorbiting Satellites.- Stability and Origin of the Minor Bodies of the Solar System.- II: Theory and Application of Stability, Bifurcation and Escape.- Existence and Stability of Circular Orbits in Axially-Symmetric Gravitational Fields.- Bifurcations and Stability in Three-Dimensional Systems.- Three-Body Problem: Some Applications of the Tests of Escape.- Methods of Stability Analysis in the Solar System.- Studies in the Stability of Hierarchical Dynamical Systems.- Stability in Celestial Mechanics.- III: Resonance and Singularities.- Resonance Sweeping in the Solar System.- Some Results of Resonance and Periodic Motions.- Sur une Equation de Hill Singuliere.- IV: Hamiltonian Mechanics and Kam Theory.- Hamiltonian Perturbations in Dynamical Systems and Applications in Planetary Systems.- Recent Extensions of Hamilton’s Law of Varying Action with Applications — the Integral Variation Method.- Recent Extensions of Hamilton’s Law of Varying Action — Mathematical Insights.- KAM Theory and Dynamical Astronomy.- Stability of Hamiltonian Systems of Two Degrees of Freedom and of Formally Conservative Mappings Near a Singular Point.- V: Chaotic Systems and Integrability.- The Lyapunov Characteristic Exponents and Applications to the Dimension of the Invariant Manifolds and Chaotic Attractors.- Dynamics of Multi-Parameter Syst ems with Interacting Oscillations.- Homoclinic Phenomena and Quasi-Integrability.- VI. Geodesic Flows, Charged Particles and Extragalactic Celestial Mechanics.- Geodesic Flows.- Extragalactic Celestial Mechanics: An Introduction.- Motions in the Magnetic Field of Two Revolving Dipoles.- VII: Abstracts of Seminar Contributions.- Types of Motion in the Oblate Planet Problem.- Future Orbital Evolution of Satellite Phobos.- Precession Dynamics in Spin-Orbit Coupling: A Unified Theory.- A Singularity Analysis of Dynamical Systems With Applications to Astronomy.- Resonant Periodic Orbits in a Rotating Galaxy.- Earth Deformations from Lageos Orbit.- The Puzzle of Lageos Semimajor Axis Decay.- On the Hill Variables and the Radial Intermediaries in Artificial Satellite Theory.- Applications of the Method of Averaging to Predict Dual-Spin Spacecraft Attitude Motion.- Orbit Determination: Preliminary Orbits.- Quasiresonant Canonical Forms for Hamiltonian Systems.- On the Equilibrium Solutions in the Circular Planar Restricted Problem of Three Rigid Bodies.- Linearization in Special Cases of the Perturbed Two-Body Problem.- Generalized Elliptic Anomalies.- Invariant Manifolds and Homoclinic Orbits for L3 in the R.T.B.P..- Models for the Splitting of Separatrices.- Kolmogorov Entropy as a Measure of Disorder in Some Non-Integrable Hamiltonian Systems.- Orbital Reversal of Particle Streams in Resonance With Jupiter.- Approximate Solutions to the Restricted Problem of Three Bodies for Small Mass Parameter.- A Perturbation Technique Based on the Integral Variation Method.- Regularization of the Triple Collision Manifold in the Planar Three-Body Problem.- A Restricted Problem of Four Bodies.- Escape of a Subsystem in a N-Body Problem. Application to the Three Body Problem..- The Orbits of Titan, Hyperion and Iapetus.- Motion About the Stable Libration Points in the Linearized, Restricted Three-Body Problem.- Stability in the Restricted Three-Body Problem With Drag.- Structure of the 3:1 Jovian Resonance.- The Restricted Elliptic Three-Body Problem for the Mass Parameter Equal to Zero.- Final Tidal Evolution of Orbit-Orbit Resonances.- Two Applications of Joukowsky’s Formula in the Inverse Problem of Dynamics.- A Canonical Approach to a Second-Order Solution for the Secular Motion of the Planets.- Translatory-Rotatory Motion of a Gyrostat in a Newtonian Force Field.- Analytical Expressions for Some Spatial Periodic Orbits of the Restricted Three-Body Problem and Their Invariant Manifolds.- On the Integrability and Non-Integrability in Boolean Dynamics.- Stability of Binary Asteroids.- Index of Names.- Index of Subjects.