Qualitative and Quantitative Behaviour of Planetary Systems: Proceedings of the Third Alexander von Humboldt Colloquium on Celestial Mechanics

393 Pages·1993·31.53 MB·English

by  P. K. Seidelmann (auth.)

QUALITATIVE AND QUANTITATIVE BEHAVIOUR
OF PLANETARY SYSTEMS
EDITOR-IN-CHIEF
1. HENRARD, Dept. ofM athematics, Facultes Universitaires de Namur, Namur, Belgium
ASSISTANT EDITOR
M. MOONS, Dept. of Mathematics, Facultes Universitaires de Namur, Namur, Belgium
ASSOCIATE EDITORS
N. Borderies, Jet Propulsion Laboratory, Pasadena, P. 1. Message, University ofL iverpool, U.K.
U.S.A. A. Milani, Universita di Pisa, Italy
R. Broucke, University of Texas, Austin, U.S.A. A. E. Roy, University of Glasgow, U.K.
V. A. Brumberg, Institute ofA pplied Astronomy, D. G. Saari, Northwestern University, Evanston,
Leningrad, Russia U.S.A.
G. Contopoulos, University of Athens, Greece V. A. Sarychev, Institute ofA pplied Mathematics,
A. Deprit, National Bureau of Standards, Moscow, Russia
Gaithersburg, U.S.A. L. Sehnal, Astronomical Institute, Ondrejov,
S. Ferraz-Mello, University ofS iio Paulo, Brasil Czechoslovakia
Y. Kozai, National Astronomy Observatory, P. Vandervoort, University of Chicago, U.S.A.
Mitaka, Tokyo, Japan
CELESTIAL MECHANICS INSTITUTE
Kaare Aksnes, Institute of Theoretical Astronomy, William M. Kaula, University of California, Los
Oslo Angeles
R. H. Battin, The Charles Stark Draper Laboratory, Hiroshi Kinoshita, National Astronomy Obser-
Cambridge vatory, Tokyo
R. Broucke, University of Texas, Austin Jean Kovalevsky, CERGA, Grasse
1. M. A. Danby, North Carolina State University, Jay Lieske, Pasadena
Raleigh Richard H. Miller, University of Chicago
Morris S. Davis, University ofN orth Carolina, P. K. Seidelmann, U.S. Naval Observatory,
Chapel Hill Washington (President)
L. E. Doggett, U.S. Naval Observatory, Washington Irwin I. Shapiro, Harvard-Smithsonian Center for
R. L. Duncombe, University of Texas, Austin Astrophysics, Cambridge
J. B. Eades, E & SA Engineering & Science E. M. Standish, Jet Propulsion Laboratory,
Associates Inc., Rockville (Vice President) Pasadena (Secretary)
E. Gaposchin, MIT Lincoln Laboratory, Westford V. Szebehely, University of Texas, Austin
B. Garfinkel, Yale University Observatory, New B. Tapley, University of Texas, Austin
Haven C. A. Williams, University of South Florida, Tampa
John L. Junkins, Texas A&M University, College (Treasurer)
Station
John Hadjidemetriou, Department of Theoretical
Mechanics, Thessaloniki
ISSN 0923-2958
All Rights Reserved
© 1993 Kluwer Academic Publishers
No part of the material protected by this copyright notice may be reproduced or
utilized in any form or by any means, electronic or mechanical
including photocopying, recording or by any information storage and
retrieval system, without written permission from the copyright owner.
QUALITATIVE AND QUANTITATIVE
BEHAV IOUR OF PLANETARY SYSTEMS
Proceedings of the Third
Alexander von Humboldt
Colloquium on Celestial Mechanics
Edited by
R. DVORAK
InstituI fur Astronomie, Universitătsstemwarte, VieI/ilo, Austria
,nd
J.HENRARD
Departemem de Ma/hemarique. FNDP, Namur, Be/giwlI
Reprinted from Celestial Mechanics and Oynamical Astronomy
Volume 56, Nos. 1-2, 1993
••
SPRINGER SCIENCE+BUSlNESS MEDIA, B.V.
A C.I.P. Catalogue record for this book is available from the Library of Congress.
ISBN 978-94-010-4898-9 ISBN 978-94-011-2030-2 (eBook)
DOI 10.1007/978-94-011-2030-2
Printed on acid-free paper
AII Rights Reserved
© 1993 Springer Science+Business Media Dordrecht
Originally published by Kluwer Academic Publishers in 1993
No part of the material protected by this copyright notice may be reproduced or
utilized in any form or by any means, electronic or mechanical,
including photocopying, recording or by any information storage and
retrieval system, without written permission from the copyright owner.
TABLE OF CONTENTS
PREFACE ix
SESSION ON PLANETARY THEORIES
(Chairman: H. Eichhorn)
P.K. SEIDELMANN / Review of Planetary and Satellite Theories 1
C. MARCHAL / The Mystery of Pluto's Mass - The Ring Hypothesis 13
H. YOSHIDA / Recent progress in the theory and application of
symplectic Integrators 27
D. BENEST / Stable Planetary Orbits Around One Component in
Nearby Binary Stars 45
A. KUBALA, D. BLACK and V. SZEBEHELY / Stability of Outer
Planetary Orbits Around Binary Stars: a Comparison of Hill's and
Laplace Stability Criteria 51
T. INOUE / An Excess Motion of the Ascending Node of Mercury in the
Observations Used by Le Verrier 69
SESSION ON THE SITNIKOV PROBLEM
(Chairman: Yi-Sui Sun)
R. DVORAK / Numerical Results to the Sitnikov-Problem 71
J. HAGEL and Th. TRENKLER / A Computer Aided Analysis of the
Sitnikov Problem 81
K. WODNAR / The Original Sitnikov Article - New Insights 99
SESSION ON ASTEROIDS
(Chairman: J. Henrard)
A. LEMAITRE / Proper Elements: What are They? 103
T. MICHTCHENKO and S. FERRAZ-MELLO / The High Eccentricity
Libration of the Hildas II: Synthetic-Theory Approach 121
G. HAHN, c.1. LAGERKVIST and B.A. LINDBLAD / A Stability Study
of Asteroid Families Near the 3:1 and 5:2 Resonance with Jupiter 131
M. SIDLICHOVSKY / Chaotic Behaviour of Trajectories for the
Asteroidal Resonances 143
v
vi TABLE OF CONTENTS
J. SCHUBART / Low-Eccentricity Motion of Asteroids Near the 211
Jovian Resonance 153
Ch. FROESCHLE and H. SCHOLL: Numerical Experiments in the 311
and 1I6 Overlapping Resonance Region 163
SESSION ON RESONANCE PROBLEMS
(Chairman: S. Ferraz-Mello)
A. MORBIDELLI / An Introduction to Hamiltonian Dynamical Systems
and Practical Perturbation Methods: New Insight by Successive
Elimination of Perturbation Harmonics 177
J. LASKAR / Frequency Analysis of a Dynamical System 191
Ph. ROBUTEL / An Application of KAM Theory to the Planetary
Three Body Problem 197
J. HADJIDEMETRIOU / Resonant Motion in the Restricted Three Body
Problem 201
B. ERDI and J. KOY Acs / A Fourth-Order Solution of the Ideal
Resonance Problem 221
SESSION ON GENERAL DYNAMICAL SYSTEMS
(Chairman: P.K. Seidelmann)
Ph. BENDJOYA and E. SLEZAK / Wavelet Analysis and Applications
to Some Dynamical Systems 231
A.D. GILBERT, Cl. FROESCHLE and U. FRISCH / Wavelet Analysis
of the Standard Map: Structure and Scaling 263
M. MOONS and A. MORBIDELLI / Asteroids: 211 Resonance and
High Eccentricity 273
PJ. MESSAGE / On the Second Order Long-Period Motion of
Hyperion 277
F. DELHAISE and J. HENRARD / The Problem of Critical Inclination
Combined with a Resonance in Mean Motion in Artificial Satellite
Theory 285
SESSION ON CHAOS AND STABILITY
(Chairman: P.J. Message)
P. FARINELLA, Ch. FROESCHLE and R. GONCZI / Meteorites from the
Asteroid 6 Hebe 287
TABLE OF CONTENTS vii
Cl. FROESCHLE, Ch. FROESCHLE and E. LOHINGER / Generalized
Lyapunov-Characteristic Indicators and Corresponding
Kolmogorov like Entropy of the Standard Mapping 307
E. LOHINGER, Cl. FROESCHLE and R. DVORAK / Generalized
Lyapunov Exponents Indicators in Hamiltonian Dynamics: An
Application to a Double Star System. 315
A. MILANI / Asteroid 522 Helga is Chaotic and Stable 323
SESSION ON MISCELLANEOUS PROBLEMS
(Chairman: V. Szehebely)
G. CONTOPOULOS / Classical Periodic Orbits and Quantum
Mechanical Eigenvalues and Eigenfunctions 325
H. EICHHORN / Generalized Least-Squares Adjustments: A Timely
but Much Ignored Tool 337
J. KALLRATH, J.P. SCHLODER and H.G. BOCK / Least Squares
Parameter Estimation in Chaotic Differential Equations 353
G. VALSECCHI, E. PEROZZI, A.E. ROY and B.A. STEVES / The
arrangement in Mean Elements Space of the Periodic Orbits Close to
that ofthe Moon 373
H. SCHOLL, F. ROQUES and B. SICARDY / Resonance Trapping of
Circumstellar Dust Particles by an Alleged Planet 381
D. LAZZARO, B. SICARDY, F. ROQUES and H. SCHOLL / Orbital
Resonances and Poynting-Robertson Drag Confining Dust Particles
in ,B-Pic Disk 395
Participants in the Third Alexander von Humboldt Colloquium on Celestial Mechanics
PREFACE
The success of the two first Alexander von Humboldt Colloquia on Celestial
Mechanics (March 1984 and March 1988) encouraged us to meet again this year
from March 29 to April 4, 1992 in the " Alpengasthof Peter Rosegger"" in the
Styrian Alps (Ramsau, Austria).
This time the colloquium was devoted to the "Qualitative and Quantitative
behaviour of Planetary Systems". The papers covered a large range of questions
of current interest from the behaviour of dust particles to the stability of the
Solar System as a whole, without forgetting the motion of Asteroids and their
classification into families. KAM theory, chaotic motions, resonances, Lyapunov
characteristic exponents, perturbation theory, numerical integration were - of
course - on the menu every day, served with sauces and accents from various part
of the world: from China, from Brazil, from the United States and from all over
Europe.
To be able to organize this - now well established - meeting , we have to
thank primarily the munificence of the Austrian Ministry of Science, furthermore
the Steiermarkischen Wissenschafts- und Landesfonds and the Osterreichische
Nationalbank for financial support. Also, the Osterreichische Forschungsgemein
schaft and the University of Vienna made it possible to invite participants to this
meeting from abroad. Support in form of "Tagungsunterlagen" was given by the
Creditanstalt-Bankverein in Vienna and coffee during the whole meeting time was
donated by Homig-Kaffee Graz.
Many thanks are due to the Chairmen (unfortunately we did not have any
chairwoman this time) of the sessions. They acted as Editors of the papers presented
during "their" session, arranging for competent and fast refereeing so that the papers
could be reviewed and, when necessary, corrected in a very short time.
Our model hosts Barbara and Fritz Walcher contributed a lot to the success of
the meeting, as they did their best providing pleasant and friendly surroundings.
We all are looking forward to 1996 when we plan to meet again at the Alpengasthof
Rosegger.
R. Dvorak J. Henrard
Celestial Mechanics and Dynamical Astronomy 56: ix, 1993.
REVIEW OF PLANETARY AND SATELLITE THEORIES
P. K. SEIDELMANN
US Naval Observatory
Abstract. Planetary and satellite theories have been historically and are presently intimately related
to the available computing capabilities, the accuracy of observational data, and the requirements
of the astronomical community. Thus, the development of computers made it possible to replace
planetary and lunar general theories with numerical integrations, or special perturbation methods.
In turn, the availability of inexpensive small computers and high-speed computers with inexpensive
memory stimulated the requirement to change from numerical integration back to general theories,
or representative ephemerides, where the ephemerides could be calculated for a given date rather
than using a table look-up process. In parallel with this progression, the observational accuracy has
improved such that general theories cannot presently achieve the accuracy of the observations, and,
in turn, it appears that in some cases the models and methods of numerical integration also need to
be improved for the accuracies of the observations.
Planetary and lunar theories were originally developed to be able to predict phenomena, and
provide what are now considered low accuracy ephemerides of the bodies. This proceeded to the
requirement for high accuracy ephemerides, and the progression of accuracy improvement has led
to the discoveries of the variable rotation of the Earth, several planets, and a satellite. By means of
mapping techniques, it is now possible to integrate a model of the motion of the entire solar system
back for the history of the solar system. The challenges for the future are: Can general planetary
and lunar theories with an acceptable number of terms achieve the accuracies of observations? How
can numerical integrations more accurately represent the true motions of the solar system? Can
regularly available observations be improved in accuracy? What are the meanings and interpretations
of stability and chaos with respect to the motions of the bodies of our solar system?
There has been a parallel progress and development of problems in dealing with the motions of
artificial satellites. The large number of bodies of various sizes in the limited space around the Earth,
subject to the additional forces of drag, radiation pressure, and Earth zonal and tesseral forces, require
more accurate theories, improved observational accuracies, and improved prediction capabilities, so
that potential collisions may be avoided. This must be accomplished by efficient use of computer
capabilities.
Key words: Planetary theories - satellite theories - artificial satellites
1. Introduction
There is a real solar system as part of the real universe that is moving and changing
due to the real existing forces. We attempt to compute, observe, and understand
the real thing by means of models and approximations. Unfortunately, our theories
and computations are incomplete, and our observations are subject to systematic
and random errors.
There is a need to develop new theories for the planets, the moon, and artifi
cial satellites. Technology has advanced such that we have significantly increased
computer capabilities, both speed and memory, much better software, and alge
braic manipulators. The challenge is to use these improvements to satisfy the
requirements for new theories.
Priorto the 1950's planetary and lunar theories were developed from two body
models by expansions in tenns of small quantities and by orders of the power
of the perturbing masses. Theories by Newcomb (1898), Hill (1898), Leverrier
Celestial Mechanics and Dynamical Astronomv 56: 1-12,1993.
© 1993 Kluwer Academic Publishers.