The Stability of Planetary Systems: Proceedings of the Alexander von Humboldt Colloquium on Celestial Mechanics, held at Ramsau, Styria, March 25–31, 1984

450 Pages·1985·13.2 MB·English

by  R. L. D.

The Stability
of Planetary Systems
Proceedings of the Alexander von Humboldt Colloquium
on Celestial Mechanics,
held at Ramsau, Styria, March 25-31, 1984
Edited by
R. L. DUNCOMBE
Department of Aerospace Engineering. University of Texas. Austin. Texas. US.A.
R.DVORAK
Institutfiir Astronomie. Universitiit Wien. Wien. Osterreich
and
P. J. MESSAGE
Department of Applied Mathematics and Theoretical Physics.
Liverpool University. England
Reprinted from
Celestial Mechanics, Vol. 34, Nos. 1-4
D. Reidel Publishing Company
Dordrecht / Boston
ISBN-13: 978-94-010-8854-1 e-ISBN-13: 978-94-009-5331-4
DOl: 10.1007/978-94-009-5331-4
All Rights Reserved
© 1984 by D. Reidel Publishing Company, Dordreeht, Holland
Softcover reprint of the hardcover 1s t edition 1984
No part of the material protected by this copyright notice may be reproduced or
utilized in any form or by any means, electronic or inechanical
including photocopying, recording or by any information storage and
retrieval system, without written permission from the copyright owner
TABLE OF CONTENTS
The Stability of Planetary Systems
PREFACE 5
INTRODUCTORY ADDRESS
F. SCHMEIDLER / The Meaning of Celestial Mechanics Ln the Kosmos
of Alexander von Humboldt 7
ASTROMETRIC PROBLEMS
(Chairman of Session: J. Haupt)
H. EICHHORN / Inertial Systems - Definitions and Realizations* 11
R. L. DUNCOMBE, P. D. HEMENWAY, and A. L. WHIPPLE / Minor
Planet Observations and the Fundamental Reference
System 19
W. FRICKE / The Empirical Inertial System Determined in FK5
by the Dynamics of the Planetary System (Abstract) 37
P. K. SEIDELMANN, G. H. KAPLAN, K. J. JOHNSTON, and C. M. WADE /
Observations of Minor Planets with the Very Large Array 39
QUALITATIVE METHODS
(Chairman of Session: P. J. Message)
V. SZEBEHELY / Review of Concepts of Stability* 49
C. MARCHAL, J. YOSHIDA, and SUN YI-SUI / Three-Body Problem* 65
CL. FROESCHLE / The Lyapunov Characteristic Exponents -
Applications to Celestial Mechanics* 95
R. GONCZI, CH. FROESCHLE, and CL. FROESCHLE / Kolmogorov
Entropy as a Measure of Disorder in Some Non-Integrable
Hamiltonian Systems 117
V. SZEBEHELY and A. L. WHIPPLE / Generalizations of the
Jacobian Integral 125
A. HANSLMEIER / Application of Lie-Series to Regularized
Problems in Celestial Mechanics 135
M. DELVA / Integration of the Elliptic Restricted Th'ree-Body
Problem with Lie Series 145
2 TABLE OF CONTENTS
PLANETARY MOTIONS
(Chairman of Session: R. Dvorak)
P. J. MESSAGE / The Stability of Our Solar System* 155
J. CHAPRONT / Approximation Methods in Celestial Mechanics.
Applications to Pluto's Motion* 165
T. INOUE / Termes Seculaires Dans la Theorie des Perturbations 185
P. BRETAGNON / Amelioration des Theories Planetaites
Analytiques 193
H. KINOSHITA and H. NAKAI/Motions of the Perihelions of
Neptune and Pluto 203
J. LASKAR / Progress in General Planetary Theory (Abstract) 219
SATELLITE MOTIONS
(Chairman of Session: J. Chapront)
S. FERRAZ-MELLO / Satellite Orbits and Ephemerides* 223
J. KOVALEVSKY / Tidal Effects and the Motion of a Satellite
(Abstract) 243
w.
THUILLOT / The Effec~ of the Dynamical Parameters in the
Motion of the Galilean Satellites of Jupiter 24:
J. HENRARD / Libration of Laplace's Argument in the Galilean
Satellites Theory 255
M. MOONS / Planetary Perturbations on the Libration of the Moon 263
F. MIGNARD / Stability ofL4 and L5 Against Radiation Pressure 275
COSMOGONY
(Chairman of Session: G. Marchal)
W. M. TSCHARNUTER / The Formation of the Planetary System* -289
N. BORDERIES / Dynamics of Ring-Satellite Systems Around
Saturn and Uranus* 297
A. LEMAITRE / Formation of the Kirkwood Gaps in the Asteroid
Belt 329
A. MILANI and A. M. NOBILl/Resonant Structure of the Outer
Asteroid Belt 343
H. LICHTENEGGER / The Dynamics of Bodies with Variable Masses 357
R. DVORAK / Numerical Experiments on Planetary Orbits in
Double Stars 369
TABLE OF CONTENTS
PERIODIC ORBITS, RESONANCES, AND ASTEROID MOTIONS
(Chairman of Session: H. Eichhorn)
J. D. HADJIDEMETRIOU / Periodic Orbits* 379
C. A. WILLIAMS / The Problem of Small Divisors in Planetary
Motion* 395
A. H. JUPP and A. Y. ABDULLA / The Ideal Resonance Problem -
A Comparison of Two Formal Solutions I 411
R. BIEN and J. SCHUBART / Trojan Orbits in Secular Resonances 425
B. ERDI / Critical Inclination of Trojan Asteroids 435
J. SCHUBART and R. BIEN / An Application of Labrouste's
Method to Quasi-Periodic Asteroidal Motion 443
S. FERRAZ-MELLO and W. SESSIN / A Note on Resonance in
Regular Variables and Averaging 453
B. GARFINKEL I On the Brown Conjecture 459
LIST OF PARTICIPANTS 465
ANNOUNCEMENT 468
* Invited Review

Preface
The Alexander von Humboldt Colloquium on Celestial Mechanics (sub
titled "The Stability of Planetary Systems") was held in Ramsau, Styria,
in the Austrian Alps, from March the 25th to the 31st, 1984. The
dedication of the meeting to Alexander von Humboldt presented partici
pants with the challenge that the discussions during the week should
reflect the spirit of that great scientist of the last century, that
the very many interesting ideas presented and developed during the
sessions should be interpreted in the light of a broad v~ew of astron
omy and astrophysics. The topics of the meeting ranged from astrometric
questions relating to the specification of inertial reference systems,
motion of planets (including minor planets) and satellites, with the
recurring topic of the search for criteria of stability of the systems,
resonances, periodic orbits, and to the origin of the systems. Each
session began with one or more invited review papers, followed by
offered contributions and discussion. Three evening discussions were
held, devoted respectively to inertial systems, to numerical integration
techniques, and to cosmogonic problems and ring systems.
On the evening of Wednesday, March 28th, a recital of chamber
mus~c was given by Bernhard Piberauer, on the violin, and Meinhard
Prinz, on the piano. On the Friday evening, March 30th, participants
were entertained at a Styrian Evening, hearing Styrian and Alpine folk
songs performed by the Steiner Singers from Ramsau, and also part of
"Das Lichte Land" ("The Heavenly Country") by the Stvrian poet Peter
Rosegger, read by Professor J. F. G. Grosser.
First of all we have to thank the Oesterreichischen Bundes
ministerium fuer Wissenschaft und Forschung for financial support.
We also have to thank the Oesterreichischen Forschungsgemeinschaft and
Celestial Mechanics 34 (1984) 5.
6 PREFACE
the Steiermaerkischen Wissenschafts- und Forschungslandesfond. We
believe that, due to the co-operative effort of all concerned, everyone
present had an enjoyable, as well as a useful and instructive, time at
Ramsau. Many thanks are due to the Chairmen of the various sessions,
each of whom acted as Editor for the proceedings of his session.
Thanks are also due to those colleagues who refereed the reviews and
papers presented at the seSS1ons. Last, but by no means least, we are
very glad to record our thanks to our hosts at the Alpengasthof Peter
Rosegger, Fritz and Barbara Walcher, for their hospitality and kindness
to us, making our stay in Ramsau such a pleasant one.
R.L.D.
R.D.
P.J.M.
THE MEANING OF CELESTIAL MECHANICS IN THE
KOSMOS OF ALEXANDER VON HUMBOLDT
F. Schmeidler
Universitats-Sternwarte Munchen
D-8000 Munchen
Germany, F.R.
The generous assistance 1n problems of organization which was
given to our colloquium by the Interalp-Institut is justification to say
some words about the Academia Cosmologica Nova, since the Interalp
Institut is strongly connected with this academy. One more reason to
mention the Academia Cosmologica Nova is its work on Alexander von
Humboldt whose name occurs in the title of the colloquium which begins
today. The general attitude taken by Alexander von Humboldt in all of
his works is characterized by many ideas which, according to the opinion
of the Academia Cosmologica Nova, are still important in our time.
The Academia Cosmologica Nova was founded in 1976. Its aim is to
promote understanding for scientific questions in the general public.
It intends also to create harmonic relations between humanities and
natural sciences, which can only by achieved if narrow-minded limitation
to special problems is strictly avoided. Interdisciplinary work is the
only way which produced a chance to find a general understanding for all
branches of science.
It was for these reasons that the Academia Cosmologica Nova was
prepared to follow a suggestion which carne from the "Sammelstiftung der
Preussischen Akademie der Wissenschaften" to work out a modern edition
of the "Kosmos" of Alexander von Humboldt: the idea of this suggestion
was that the work of Humboldt should be brought to a level corresponding
to the scientific standard of our time.
Celestial Mechanics 34 (1984) 7-10. 0008-8714/84.15
© 1984 by D. Reidel Publishing Company.
F. SCHMEIDLER
Alexander von Humboldt was born in 1776 and lived until 1859; he
and his brother Wilhelm, who was two years older, were famous men in
German cultural life in the 19th century. Alexander started in 1799 a
long journey through the continent of South America about which little
was known in that time. Five years later he returned to Europe. After
wards he lived about twenty years in Paris, where he worked out the
scientific results of his long journey. In 1827 he came back to Berlin.
Now he undertook the compilation of a comprehensive book which was
intended to become a general description of the physical world. The idea
to write such a book had come to him long years before. At last, the
book became the famous work entitled "Kosmos" which was, according to
reports given by experts of this time, the most widely known book next
to the Bible in 19th century Germany.
The first volume of the modern edition of the "Kosmos" to be pub
lished by the Academia Cosmologica Nova, is ready to be printed; it
contains astronomy or, according to the expression used by Humboldt, the
uranological part of the "Kosmos". We have cancelled all those passages
in Humboldt's work which are today either wrong or irrelevant. We have
added footnotes or commentaries, wherever new scientific findings exist
which Humboldt could not yet know. Our colleague and member of the
Academia Cosmologica Nova, Dr. Dvorak, has done most of this work as
main contributor. The two other volumes of the new edition have been
treated in the same way and are nearing completion; we hope that all
volumes will be published in 1984 or 1985.
It is clear that in a book like the "Kosmos" many questions of
celestial mechanics are discussed, because celestial mechanics was one
of the most important parts of astronomy in the time of Alexander von
Humboldt. Furthermore, Humboldt had friendly relations with many French
mathematicians and astronomers who worked on celestial mechanics during
the long years of his stay at Paris. So it is not surprising that the
following sentences can be found in the introductory chapter of the
first volume of the "Kosmos":