Chaos And Stability In Planetary Systems
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Chaos And Stability In Planetary Systems
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Author : Rudolf Dvorak
language : en
Publisher: Springer
Release Date : 2009-09-02
Chaos And Stability In Planetary Systems written by Rudolf Dvorak and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-02 with Science categories.
This book is intended as an introduction to the field of planetary systems at the postgraduate level. It consists of four extensive lectures on Hamiltonian dynamics, celestial mechanics, the structure of extrasolar planetary systems and the formation of planets. As such, this volume is particularly suitable for those who need to understand the substantial connections between these different topics.
Chaos And Stability In Planetary Systems
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Author : Rudolf Dvorak
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-01-13
Chaos And Stability In Planetary Systems written by Rudolf Dvorak and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-13 with Science categories.
This book is intended as an introduction to the field of planetary systems at the postgraduate level. It consists of four extensive lectures on Hamiltonian dynamics, celestial mechanics, the structure of extrasolar planetary systems and the formation of planets. As such, this volume is particularly suitable for those who need to understand the substantial connections between these different topics.
Dynamical Chaos In Planetary Systems
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Author : Ivan I. Shevchenko
language : en
Publisher: Springer Nature
Release Date : 2020-08-31
Dynamical Chaos In Planetary Systems written by Ivan I. Shevchenko and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-31 with Science categories.
This is the first monograph dedicated entirely to problems of stability and chaotic behaviour in planetary systems and its subsystems. The author explores the three rapidly developing interplaying fields of resonant and chaotic dynamics of Hamiltonian systems, the dynamics of Solar system bodies, and the dynamics of exoplanetary systems. The necessary concepts, methods and tools used to study dynamical chaos (such as symplectic maps, Lyapunov exponents and timescales, chaotic diffusion rates, stability diagrams and charts) are described and then used to show in detail how the observed dynamical architectures arise in the Solar system (and its subsystems) and in exoplanetary systems. The book concentrates, in particular, on chaotic diffusion and clearing effects. The potential readership of this book includes scientists and students working in astrophysics, planetary science, celestial mechanics, and nonlinear dynamics.
Stability And Chaos In Celestial Mechanics
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Author : Alessandra Celletti
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-03-10
Stability And Chaos In Celestial Mechanics written by Alessandra Celletti and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-03-10 with Science categories.
This overview of classical celestial mechanics focuses the interplay with dynamical systems. Paradigmatic models introduce key concepts – order, chaos, invariant curves and cantori – followed by the investigation of dynamical systems with numerical methods.
Chaos Resonance And Collective Dynamical Phenomena In The Solar System
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Author : Sylvio Ferraz-Mello
language : en
Publisher: Springer Science & Business Media
Release Date : 1992-05-31
Chaos Resonance And Collective Dynamical Phenomena In The Solar System written by Sylvio Ferraz-Mello and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-05-31 with Science categories.
This symposium was devoted to a new celestial mechanics whose aim has become the study of such `objects' as the planetary system, planetary rings, the asteroidal belt, meteor swarms, satellite systems, comet families, the zodiacal cloud, the preplanetary nebula, etc. When the three-body problem is considered instead of individual orbits we are, now, looking for the topology of extended regions of its phase space. This Symposium was one step in the effort to close the ties between two scientific families: the observationally-oriented scientists and the theoretically-oriented scientists.
The Orbital Dynamics And Long Term Stability Of Planetary Systems
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Author : Katherine Michele Deck
language : en
Publisher:
Release Date : 2014
The Orbital Dynamics And Long Term Stability Of Planetary Systems written by Katherine Michele Deck and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with categories.
A large population of low-mass exoplanets with short orbital periods has been discovered using the transit method. At least 40% of these planets are actually part of compact systems with more than one planet. The closeness of the planetary orbits in these multi-planet systems leads to strong dynamical interactions that imprint themselves on the transit light curve as transit timing variations (TTVs). By modeling the orbital evolution of these planetary systems, one can fit the observed variations and strongly constrain the masses and orbits of the interacting planets, parameters which, given the faintness of the host stars, cannot be determined using other techniques. This type of analysis is performed for KOI- 984, a system with a single transiting planet perturbed by a non-transiting companion. By modeling the gravitational interaction between the planets using our code TTVFast, we are able to infer the masses and orbits of the two planets and to show that the orbits are distinctly non-coplanar. This discovery, a first for the low-mass multi-planet systems, indicates that dynamical processes that excite mutual inclinations can be important for such systems. The dynamical interactions that lead to observable TTVs can also lead to orbital instability and chaos. The Kepler 36 system has the closest confirmed pair of planets to date, with unique TTVs that tightly constrain the orbits, in turn allowing for detailed analysis of the long-term dynamics of the system. We find the system to be strongly chaotic, characterized by the very human timescale of -10 years. We are able to understand the source of this rapid chaos, and to show that despite its presence, the system can be long-lived. But how compact can two planetary orbits be before being unstable? We consider more generally the long-term stability of two-planet systems within the framework of first-order resonance overlap. We determine a stability criterion for close pairs of planets which we then compare to other analytic criteria and to numerical integrations. This work provides a step towards understanding the long-term evolution of more complex planetary systems.
Chaos In Gravitational N Body Systems
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Author : J.C. Muzzio
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Chaos In Gravitational N Body Systems written by J.C. Muzzio and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
The Workshop on Chaos in Gravitational N -Body Systems was held in La Plata, Argentina, from July 31 through August 3, 1995. The School of Astronomy and Geophysics of La Plata National University, best known as La Plata Observatory, was the host institution. The Observatory (cover photo) was founded in 1883, and it has nowadays about 120 faculty members and 70 non-faculty members devoted to teaching and research in different areas of astronomy and geophysics. It was very nice to see how many people, from young students to well recognized authorities in the field, came to participate in the meeting. This audience success was due to the increasing understanding of the neces sity to gather together people from Celestial Mechanics and Stellar Dynamics to explore the problems that exist at the frontier of these two disciplines and their common interest in chaotic phenomena and integrability (the famous Argentine beef was, certainly, also an attraction!). All the papers of the present volume were refereed. Most were accepted after some revision, while some needed no change at all (compli ments to their authors!) and, sadly, a few could not be included. About half a dozen authors did not submit their contributions for publication, mainly because they were already in print elsewhere. Therefore, the special issue of Celestial Mechanics and Dynamical Astronomy includes all the invited lectures of the workshop, while the proceedings volume includes those same lectures plus the bulk of, but Bot all, the contributions to the meeting.
Chaotic Dynamics In Planetary Systems
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Author : Sylvio Ferraz-Mello
language : en
Publisher: Springer Nature
Release Date : 2023-12-31
Chaotic Dynamics In Planetary Systems written by Sylvio Ferraz-Mello and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-12-31 with Science categories.
The main theme of the book is the presentation of techniques used to identify chaotic behavior in the evolution of conservative mechanical systems and their application to astronomical systems. It results from graduate courses given by the author over the years both at university and at several international summer schools. Along the book surfaces of section, Lyapunov characteristic exponents, frequency maps, MEGNO, dense grid maps, etc., are presented and discussed in connection with the applications. The initial chapter is devoted to the presentation of the main ideas of the chaotic dynamics of conservative systems in plain language so that they can be accessible to a wide range of professionals and students of physical sciences. The applications are mainly related to the motions in the solar system and extrasolar planetary systems. Another chapter is devoted to the applications to asteroids showing how the asteroidal belt is sculpted by chaos and resonances. The contrasting existence of gaps in the distribution of the asteroids and groups of asteroids in resonances is thoroughly discussed. The interest in applications to planetary systems is growing since the discovery of systems of resonant planets around some stars of the solar neighborhood. Exoplanets added a lot of cases to a problem that was before restricted to the planets of our solar system. The book includes an account of results already existing about compact systems.
Newton S Clock
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Author : Ivars Peterson
language : en
Publisher: Macmillan + ORM
Release Date : 1993-07-15
Newton S Clock written by Ivars Peterson and has been published by Macmillan + ORM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-07-15 with Science categories.
With his critically acclaimed best-sellers The Mathematical Toursist and Islands of Truth, Ivars Peterson took readers to the frontiers of modern mathematics. His new book provides an up-to-date look at one of science's greatest detective stories: the search for order in the workings of the solar system. In the late 1600s, Sir Isaac Newton provided what astronomers had long sought: a seemingly reliable way of calculating planetary orbits and positions. Newton's laws of motion and his coherent, mathematical view of the universe dominated scientific discourse for centuries. At the same time, observers recorded subtle, unexpected movements of the planets and other bodies, suggesting that the solar system is not as placid and predictable as its venerable clockwork image suggests. Today, scientists can go beyond the hand calculations, mathematical tables, and massive observational logs that limited the explorations of Newton, Copernicus, Galileo, Kepler, Tycho Brahe, and others. Using supercomputers to simulate the dynamics of the solar system, modern astronomers are learning more about the motions they observe and uncovering some astonishing examples of chaotic behavior in the heavens. Nonetheless, the long-term stability of the solar system remains a perplexing, unsolved issue, with each step toward its resolution exposing additional uncertainties and deeper mysteries. To show how our view of the solar system has changed from clocklike precision to chaos and complexity, Newton's Clock describes the development of celestial mechanics through the ages--from the star charts of ancient navigators to the seminal discoveries of the 17th centure; from the crucial work of Poincaré to the startling, sometimes controversial findings and theories made possible by modern mathematics and computer simulations. The result makes for entertaining and provocative reading, equal parts science, history, and intellectual adventure.
Chaos In Nature
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Author : Christophe Letellier
language : en
Publisher: World Scientific
Release Date : 2013
Chaos In Nature written by Christophe Letellier and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Mathematics categories.
Chaos theory deals with the description of motion (in a general sense) which cannot be predicted in the long term although produced by deterministic system, as well exemplified by meteorological phenomena. It directly comes from the Lunar theory — a three-body problem — and the difficulty encountered by astronomers to accurately predict the long-term evolution of the Moon using “Newtonian” mechanics. Henri Poincaré's deep intuitions were at the origin of chaos theory. They also led the meteorologist Edward Lorenz to draw the first chaotic attractor ever published. But the main idea consists of plotting a curve representative of the system evolution rather than finding an analytical solution as commonly done in classical mechanics. Such a novel approach allows the description of population interactions and the solar activity as well. Using the original sources, the book draws on the history of the concepts underlying chaos theory from the 17th century to the last decade, and by various examples, show how general is this theory in a wide range of applications: meteorology, chemistry, populations, astrophysics, biomedicine, etc.