By William H. Jefferys (auth.), Rudolf Dvorak, Jacques Henrard (eds.)

ISBN-10: 9048157021

ISBN-13: 9789048157020

ISBN-10: 9401724148

ISBN-13: 9789401724142

It is now a well-established culture that each 4 years, on the finish of iciness, a bunch of 'celestial mechanicians' from worldwide assemble within the Austrian Alps on the invitation of R. Dvorak. This time the colloquium was once held at Badhofgastein from March 19 to March 25, 2000 and used to be dedicated to the 'New advancements within the Dynamics of Planetary Systems'. The papers lined a wide variety of questions of present curiosity: t- oretical questions (resonances, KAM idea, delivery, ... ) and questions on numerical instruments (synthetic components, symptoms of chaos, ... ) have been relatively good represented; after all planetary theories and close to Earth items have been additionally rather well known. 3 detailed lectures have been introduced in honor of deceased colleagues whom, to our dismay, we'll not meet on the 'Austrian Colloquia'. W. Jefferys brought the Heinrich Eichhorn lecture on 'Statistics for the Twenty-first Century Astrometry', a subject matter on which Heinrich Eichhorn was once a expert. A. Roy brought a lecture honoring Victor Szehebely on 'Lifting the Darkness: technology within the 3rd Millenium', during which in wove anecdotes and remembrances of Victor which moved the viewers a great deal. A. Lemaitre spoke in honor of Michele Moons on 'Mech anism of trap in exterior Resonance'. the top of her speak was once dedicated to a brief and relocating biography of Michele illustrated by way of many slides.

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**Additional resources for New Developments in the Dynamics of Planetary Systems: Proceedings of the Fifth Alexander von Humboldt Colloquium on Celestial Mechanics held in Badhofgastein (Austria), 19–25 March 2000**

**Sample text**

1986, 'The outer solar system for 200 million years', Astr. J. 92, 176-194. Arnold, V. : 1963, 'Small denominators and problems of stability of motion in classical and celestial mechanics', Russ. Math. Sur. 18, 85-191. , Milani, A. : 1987, 'Long-term numerical integrations and synthetic theories for the motion of the outer planets', Astr. Astrophys. 181, 182-194. Cohen, C. J. and Hubbard, E. : 1965, 'Libration of the close approaches of Pluto to Neptune', Astr. J. 70, 10-13. Cohen, C. , Hubbard, E.

28 Z. KNEZEVIC AND A. MILANI TABLE I (A) Asteroids that became hyperbolic in the 2Myr integration. 14 2/l 2/l ? 17 7/3 h 2/l ? = 6060 year = 6200 year secular res. 9/4 2: 1 h = 6200 year Columns contain asteroid identifier, semimajor axis, eccentricity and inclination at the beginning of the integration, and comment on the relevant dynamical features that might give rise to chaotic diffusion. h denotes the Lyapunov time in years. phenomenon, and that the original number of asteroids must have been significantly larger than the present one.

For example, in the paper Milani and Kndevic ( 1994) we tested only 35 asteroids. In the computation of synthetic proper elements, a numerical integration over a long enough time interval [0, T] has to be performed. Given the output of the same integration, the same algorithm described in this section can be applied to shorter time intervals [tj, tj + 6. T], beginning at initial times tj, j = 1, .. T. For each of these 'running boxes' a value of the proper elements eP, sin IP and of the proper frequencies is obtained, and the dispersion of these N values can be used to estimate the stability in time of the results.

### New Developments in the Dynamics of Planetary Systems: Proceedings of the Fifth Alexander von Humboldt Colloquium on Celestial Mechanics held in Badhofgastein (Austria), 19–25 March 2000 by William H. Jefferys (auth.), Rudolf Dvorak, Jacques Henrard (eds.)

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