ebook img

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

450 Pages·1985·13.2 MB·English
Save to my drive
Quick download
Download
Most books are stored in the elastic cloud where traffic is expensive. For this reason, we have a limit on daily download.

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

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":

Description:
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 challen
See more

The list of books you might like

Most books are stored in the elastic cloud where traffic is expensive. For this reason, we have a limit on daily download.