A Comparison of the Dynamical Evolution of Planetary Systems

Transcription

1 A Comparison of the Dynamical Evolution of Planetary Systems

2 A Comparison of the Dynamical Evolution of Planetary Systems Proceedings of the Sixth Alexander von Humboldt Colloquium on Celestial Mechanics Bad Hofgastein (Austria), March 2004 Edited by Rudolf Dvorak and Sylvio Ferraz-Mello Reprinted from Celestial Mechanics and Dynamical Astronomy, Volume 92(1 3),

3 A C.I.P. catalogue record for this book is available from the Library of Congress ISBN Published by Springer, P.O. Box 17, 3300 AA Dordrecht, The Netherlands Sold and distributed in North, Central and South America By Springer, 101 Philip Drive, Norwell, MA 02061, USA In all other countries, sold and distributed By Springer, P.O. Box 322, 3300 AH Dordrecht, The Netherlands Printed on acid-free paper All Rights Reserved Ó 2005 Springer No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electric or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner. Printed in the Netherlands

4 Cover photograph: Alexander von Humboldt und Aime Bonpland in der Urwaldhu tte (Alexander von Humboldt and Aime Bonpland in the Forest Cottage). Picture by: Eduard Ender, ca Supplied courtesy: Berlin-Brandenburgische Akademie der Wissenschaften, Berlin, Germany.

5 TABLE OF CONTENTS ANDREA MILANI and ZORAN KNEŽEVIC / From Astrometry to Celestial Mechanics: Orbit Determination with Very Short Arcs 1 18 RUDOLF DVORAK and RICHARD SCHWARZ / On the stability regions of the Trojan asteroids CHRISTOS EFTHYMIOPOULOS / Formal Integrals and Nekhoroshev Stability in a Mapping Model for the Trojan Asteroids P. ROBUTEL, F. GABERN and A. JORBA / The Observed Trojans and the Global Dynamics Around the Lagrangian Points of the Sun Jupiter System KLEOMENIS TSIGANIS, HARRY VARVOGLIS and RUDOLF DVORAK / Chaotic Diffusion and Effective Stability of Jupiter Trojans O. MILONI, S. FERRAZ-MELLO and C. BEAUGE / Analytical Proper Elements for the Hilda Asteroids I: Construction of a Formal Solutions BA LINT E RDI and ZSOLT SA NDOR / Stability of Co-orbital Motion in Exoplanetary Systems C. MARCHAL / The General Solution of the Planar Laplace Problem DIONYSSIA PSYCHOYOS and JOHN D. HADJIDEMETRIOU / Dynamics of 2/1 Resonant Extrasolar Systems Application to HD82943 and GLIESE C. KALAPOTHARAKOS and N. VOGLIS / Global Dynamics in Self- Consistent Models of Elliptical Galaxies G. CONTOPOULOS and M. HARSOULA / Chaotic Motions in the Field of Two Fixed Black Holes J. E. HOWARD / Discrete Virial Theorem CLAUDE FROESCHLE, MASSIMILIANO GUZZO and ELENA LEGA / Local and Global Diffusion Along Resonant Lines in Discrete Quasi-Integrable Dynamical Systems YI-SUI SUN, LI-YONG ZHOU and JI-LIN ZHOU / The Role of Hyperbolic Invariant Sets in Stickiness Effects

6 H. LAMMER, YU. N. KULIKOV, T. PENZ, M. LEITNER, H. K. BIERNAT and N. V. ERKAEV / Stellar-Planetary Relations: Atmospheric Stability as a Prerequisite for Planetary Habitability W. VON BLOH, C. BOUNAMA and S. FRANCK / Dynamic Habitability of Extrasolar Planetary Systems

7 Celestial Mechanics and Dynamical Astronomy (2005) 92:vii viii DOI /s Springer 2005 PREFACE The traditional Alexander von Humboldt Colloquium on Celestial Mechanics, the sixth in the series after the first one 20 years ago, was held in Bad Hofgastein, in the Hotel Winkler, on March, Like in the former colloquia, some 45 scientists from all over the world gathered in the Austrian Alps to present and discuss their newest results in different fields of our science. We had a wide spectrum of talks covering the most recent developments in our area from the theoretical point of nonlinear dynamical systems to the application to real astrodynamical problems. We had interesting talks and discussions on the formation of planetary systems, their stability and also the problem of habitable zones in extrasolar planetary systems. A special topic was the stability of Trojans in our planetary system, where more and more realistic dynamical models are used to explain their complex motions: besides the important contribution from the theoretical point of view, the results of several numerical experiments revealed the structure of the stable zone around the libration points. Even in extrasolar planetary systems, such stable orbits for terrestrial like planets may exist and be stable. The Heinrich Eichhorn lecture, given by Zoran Knežević, from Beograd, in honor of this Austrian astronomer, was devoted to another very important topic in Celestial Mechanics: the determination of orbits of Near Earth Asteroids. All authors were encouraged to write papers of a length that they considered suitable for the presentation of their results. The editorial board of Celestial Mechanics and Dynamical Astronomy arranged for competent and fast refereeing so that all papers could be reviewed and, when necessary, revised before publication. Each preface in the five preceding colloquia showed that as time is going on it is more and more difficult to find sponsors for our scientific meetings, a fact from which many of us are suffering. Nevertheless we managed to find the necessary funds also for the 2004 meeting. Special thanks have to go to the director of the IAP in Potsdam, Prof. Klaus Strassmeier, without whom, our efforts would have been unsuccessfully. His interest on the subject of extrasolar planetary systems, a hot topic in Astronomy, and his financial support saved our meeting. We also have to thank the Austrian government, which supported us with a notable amount of money, furthermore the Salzburger Landesregierung, the Österreichische Forschungsgemeinschaft and the Austrian Space Agency. Thanks are also due to the Marktgemeinde

8 viii PREFACE Bad Hofgastein who made the very successful Salzburger Abend with indigenous music from Salzburg possible. Special thanks also to the former director of the Institute of Astronomy in Vienna, Prof. Paul Jackson for his generous private donation. We should not forget our hosts Mr. and Mrs. Winkler and their employees from the hotel who made the stay quite enjoyable. None of us will forget the very last evening, when the staff of kitchen under the leadership of the cook himself came to offer us as farewell the famous Salzburger Nockerln, a traditional Austrian dessert. Everyone got a lot of scientific input during the lectures and the discussions and, to summarize, we all had a splendid week in Salzburg in the Hotel Winkler. We all hope to come again in 2008 to discuss new results and new perspectives on a high level scientific standard in the Gasteinertal. Rudolf Dvorak and Sylvio Ferraz-Mello