The Restless Universe Applications of Gravitational N-Body Dynamics to Planetary Stellar and Galactic Systems

390 Pages·2001·25.876 MB·\390

by  Bonnie Steves (Author)

THE RESTLESS UNIVERSE
APPLICATIONS OF
GRAVITATIONAL N-BODY DYNAMICS
TO PLANETARY, STELLAR AND GALACTIC SYSTEMS
Proceedings of the Fifty Fourth Scottish
Universities Summer School in Physics,
Blair Atholl, 23 July 5 August 2000.
-
A NATO Advanced Study Institute
Edited by
B A Steves - Glasgow Caledonian University
A J Maciejewski - Nicolaus Copernicus University
Series Editor
P Osborne - University of Edinburgh
Copublished by
Scottish Universities Summer School in Physics &
Institute of Physics Publishing, Bristol and Philadelphia
Copyright © 2001 The Scottish Universities Summer School in Physics
Copyright @ 2001
The Scottish Universities Summer School in Physics
No Part of this book may be reproduced in any form
by photostat, microfilm or any other means without
written permission from the publishers.
British Library cataloguing-in-Publication Data:
A catalogue record for this book is available
from the British Library
ISBN 0- 7503-0822-2
Library of Congress Cataloging-in-Publication Data are available.
Copublished by
SUSSP Publications
The Department of Physics, Edinburgh University,
The King’s Buildings, Mayfield Road, Edinburgh EH9 352, Scotland.
and
Institute of Physics Publishing, wholly owned by
The Institute of Physics, London.
Institute of Physics Publishing, Dirac House, Temple Back, Bristol BS1 6BE, UK.
US Editorial Office: Institute of Physics Publishing, The Public Ledger Building,
Suite 1035, 150 Independence Mall West, Philadelphia, PA 19106, USA.
Printed in Great Britain by J W Arrowsmith Ltd, Bristol.
Copyright © 2001 The Scottish Universities Summer School in Physics
SUSSP Proceedings
1 1960 Dispersion Relations
2 1961 Fluctuation, Relaxation and Resonance in Magnetic Systems
3 1962 Polarons and Excitons
4 1963 Strong Interactions and High Energy Physics
5 1964 Nuclear Structure and Electromagnetic Interactions
6 1965 Phonons in Perfect and Imperfect Lattices
7 1966 Particle Interactions at High Energy
8 1967 Methods in Solid State and Superfluid Theory
9 1968 Physics of Hot Plasmas
10 1969 Quantum Optics
11 1970 Hadronic Interactions of Photons and Electrons
12 1971 Atoms and Molecules in Astrophysics
13 1972 Properties of Amorphous Semiconductors
14 1973 Phenomenology of Particles at High Energy
15 1974 The Helium Liquids
16 1975 Non-linear Optics
17 1976 Fundamentals of Quark Models
18 1977 Nuclear Structure Physics
19 1978 Metal Non-metal Transitions in Disordered Solids
20 1979 Laser-Plasma Interactions: 1
21 1980 Gauge Theories and Experiments at High Energy
22 1981 Magnetism in Solids
23 1982 Lasers: Physics, Systems and Techniques
24 1982 Laser-Plasma Interactions: 2
25 1983 Quantitative Electron Microscopy
26 1983 Statistical and Particle Physics
27 1984 Fundamental Forces
28 1985 Superstrings and Supergravity
29 1985 Laser-Plasma Interactions: 3
30 1985 Synchrotron Radiation Sources and their Applications
31 1986 Localisation and Interaction
32 1987 Computational Physics
33 1987 Astrophysical and Laboratory Spectroscopy
34 1988 Optical Computing
35 1988 Laser-Plasma Interactions: 4
/continued
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Copyright © 2001 The Scottish Universities Summer School in Physics
sus
SP Proceedings
(continued)
36 1989 Physics of the Early Universe
37 1990 Pattern Recognition and Image Processing in Physics
38 1991 Physics of Nanostructures
39 1991 High Temperature Superconductivity
40 1992 Quantitative Microbeam Analysis
41 1992 Nonlinear Dynamics and Spatial Complexity in Optical Systems
42 1993 High Energy Phenomenology
43 1994 Determination of Geophysical Parameters from Space
44 1994 Quantum Dynamics of Simple Systems
45 1994 Laser-Plasma Interactions 5: Inertial Confinement Fusion
46 1995 General Relativity
47 1995 Laser Sources and Applications
48 1996 Generation and Application of High Power Microwaves
49 1997 Physical Processes in the Coastal Zone
50 1998 Semiconductor Quantum Optoelectronics
51 1998 Muon Science
52 1998 Advances in Lasers and Applications
53 1999 Soft and J?ragile Matter
54 2000 The Restless Universe
55 2001 Heavy Flavour Physics
vi
Copyright © 2001 The Scottish Universities Summer School in Physics
Lecturers
Sverre Aarseth Institute of Astronomy, Cambridge, UK
Alessandra Celletti Universith di Roma Tor Vergata
Hugh Couchman McMaster University, Ontario
Rudolf Dvorak University of Vienna, Austria
Claude Froeschlh Observatoire de la Cote d'Azur
Douglas Heggie University of Edinburgh
Martin Hendry University of Glasgow
Andrzej J Maciejewski Nicolaus Copernicus University, Torun
Christian Marchal D.E.S. ONERA, Chatillon, France
Michael Merrifield University of Nottingham
David Merritt Rutgers University, New Jersey
Philip James Message University of Liverpool
Andrea Milani Universita di Pisa
Tom Quinn University of Washington, Seattle
Carles Sim6 Universitat de Barcelona
Bonnie A Steves Glasgow Caledonian University
David Vokroulickj, Charles University, Prague
Joerg Waldvogel ETH-Zentrum, Zurich
Martin Weinberg University of Massachusetts
Gustavo Yepes Universidad Aut6noma de Madrid
Postal and e-mail addresses for lecturers, students and committee members can be found at
.
http://www.astro.gla,ac.uk/users/martin/nato/natoconf.html
vii
Copyright © 2001 The Scottish Universities Summer School in Physics
Executive Committee
Dr B A Steves Glasgow Caledonian Univ. Co-Director and Co-Editor
Prof. A E Roy University of Glasgow Treasurer
Dr M Hendry University of Glasgow Secretay
International Advisory Committee
Dr B A Steves Glasgow Caledonian Univ. Co-Director and Co-Editor
Prof. A J Maciejewski Nicolaus Copernicus Univ. Co-Director and Co-Editor
Prof. C1 Froeschlk Observatoire de Nice, France
Prof. D Heggie University of Edinburgh, Scotland
Dr M Hendry University of Glasgow, Scotland
Prof. A Milani Universita di Pisa, Italy
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Copyright © 2001 The Scottish Universities Summer School in Physics
Preface
The gravitational N-body problem dominates much of theoretical astrophysics. It
arises in problems ranging from the motion of artificial and natural satellites to the
behaviour of stars in star clusters and galaxies and the formation of large-scale structure in
the universe. Since the early years of the twentieth century, the techniques and scientific
issues involved in gravitational dynamics have diversified widely. Recently, however, there
have been signs for the need to exchange ideas and techniques between the disciplines of
celestial mechanics, stellar dynamics and galactic dynamics as many of the established
techniques in one field are being rediscovered or reinvented for use in another field. This
especially concerns theoretical achievements allowing better understanding of dynamics
in multidimensional phase space and global properties of investigated systems.
This state of the art textbook provides an invaluable reference volume for all students
and researchers in these subjects. Based on the recent joint NATO Advanced Study Insti-
tute and Scottish Universities Summer School in Physics entitled ‘The Restless Universe:
Applications of Gravitational N-Body Dynamics to Planetary, Stellar and Galactic Sys-
tems’, the book, written by the lecturers at the School, is aimed at young scientists at
PhD level who wish to learn of recent developments in their fields. By the nature of the
different themes involved in N-body gravitational dynamics, the book is also relevant to
research specialists in each field providing them with an up-to-date synoptic view of their
own discipline, while enabling them to obtain a review of gravitational N-body dynamics
from the viewpoint of the other disciplines.
A major aim of the volume, like that of the School, is to lead the reader from a
strong element of review in tutorial form to a clear picture of the state-of-the-art of
research being conducted in the application of gravitational N-body dynamics in the
following fields. Within the Solar System (the traditional realm of celestial mechanics),
studies of the three, four or few body problems come into their own. Recent numerical
and analytical methods such as the use of fast Lyapunov indicators are being used to
study chaos and resonance in the three body problem. While exciting applications of
these new analyses are found in such studies as the distribution and impact probabilities
of Near Earth Asteroids, the formation and evolution of planetary systems and more
particularly in the dynamics of small bodies in the solar system, in recent years it has
become apparent that the developing theory of chaotic motion in celestial mechanics has
also serious application in the relaxation of galactic structures.
Stellar dynamics is the application of the N-body problem to the formation, evolution
and dynamics of galaxies, star clusters, and multiple star systems of few bodies. It
therefore finds common ground with both cosmology and celestial mechanics. Specially
tailored algorithms and specially designed computer hardware are developed to handle
the N- body problem to high accuracy and high speed. Such techniques, for example, are
becoming increasingly important in the study of galaxy formation where direct numerical
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Copyright © 2001 The Scottish Universities Summer School in Physics
simulations of galaxy formation are fast approaching the resolution required to model
galaxy morphology.
Cosmology studies the formation and evolution of galaxies in the context of the stan-
dard Big Bang model, and so draws together several other strands of cosmology, including
the analysis of large scale structure and the physics of the early Universe. Numerical sim-
ulations of large-scale structure we raising important questions about the relationship
between galaxy evolution and the background cosmological model. Dynamical studies of
the matter distribution in galaxy clusters, and their large scale streaming motions, are
also being used to constrain the mean mass density of the universe and determine its
eventual fate. Many of the well-established techniques of celestial mechanics and stellar
dynamics are being rediscovered or reinvented to help study these problems.
The SUSSP54/NATO AS1 was held in the Atholl Arms Hotel, Blair Atholl, Scotland.
The two week long AS1 brought together 80 scientists from more than 30 countries. Blair
Atholl in Perthshire was an ideal location for the School. It fitted the NATO criteria
of being comparatively secluded and quiet, yet major towns were only one hour’s train
journey away. The Atholl Arms Hotel, built in 1832, is completely refurbished in the style
of a traditional highland hotel. Located in the heart of the Scottish highlands it enabled
us to provide a variety of outdoor pursuits and cultural interests amidst spectacular
mountain scenery.
We would like to thank Professor Archie Roy, Dr Martin Hendry and Ms. Gail
Penny (University of Glasgow), Dr Winston Sweatman (Napier University) and Mr Peter
Duncan (Glasgow Caledonian University) for their unstinting help which contributed so
much to the success of the School. The proprietor and hotel staff of the Atholl Arms
Hotel are also in our debt for the high standard of service they provided. We are also
indebted to the NATO Scientific Affairs Division and the SUSSP Committee for their
valuable help and sponsorship. Further information on the School, including addresses
of all participants, can be found at the web address:
http://www.astro.gla.ac.uk/users/martin/nato/natoconf.htm.l
Bonnie A Steves and Andrzej J Maciejewski
CO-Directors, March 2001
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Copyright © 2001 The Scottish Universities Summer School in Physics
Contents
Solar system dynamics
N-body simulations of the Solar System, planet formation,
and galaxy clusters.. ............................................................. .l
Thomas Quinn
On the Trojan problem.. ....................................................... .21
Rudolf Dvorak and Elke Pilat-Lohinger
Ideal resonance and Melnikov’s theorem. ..................................... .43
Philip J Message
The Yarkovsky effect in the dynamics of the Solar System... .............. .53
David Vokrouhlicky’
Are science and celestial mechanics deterministic?
Henri PoincarB, philosopher and scientist ..................................... 79
Christian Marchal
Stellar kinematics and dynamics
Regularization methods for the N-body problem ........................... .93
Sverre J Aarseth
Escape in Hill’s problem.. ..................................................... .lo9
Douglas C Heggie
Galactic dynamics
Galaxies: from kinematics to dynamics., .................................... .129
Michael R Merrifield
Non-integrable galactic dynamics. ............................................ .145
David Merritt
Evolution of galaxies due to self-excitation. ................................. ,167
Martin D Weinberg
f cont
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Copyright © 2001 The Scottish Universities Summer School in Physics
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Cosmology Large scale structure dynamics
Dynamical methods for reconstructing the large scale galaxy density
and velocity fields.. ............................................................ ,191
Martin Hendy
Cosmological numerical simulations: past, present and future .............2 17
Gustavo Yepes
Gravitational N-body simulation of large-scale cosmic structure. .........,2 39
H M P Couchman
General dynamics
Periodic orbits of the planar N-body problem with equal masses
and all bodies on the same path... ........................................... ,265
Carles Simd
Central configurations revisited ......................... 285
Jorg Waldvogel
Surfaces of separation in the Caledonian Symmetrical
Double Binary Four Body Problem.,. .................. 301
Bonnie A Steves and Archie E Roy
The Fast Lyapunov Indicator ................................................. ,327
Claude Froeschle', Massimiliano Guzzo and Elena Lega
Determination of chaotic attractors in short discrete time series ..........3 39
Alessandra Celletti, Claude Froeschle', Igor V Tetko and Alessandro E P Villa
Non-integrability in gravitational and cosmological models. ................3 61
Andrzej J Maciejewski
Index... ......................................................................... ,387
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Copyright © 2001 The Scottish Universities Summer School in Physics