Hostname: page-component-77c89778f8-7drxs Total loading time: 0 Render date: 2024-07-17T04:37:14.737Z Has data issue: false hasContentIssue false
  • English
  • Français

New Results on the Motions of Asteroids in Resonances

Published online by Cambridge University Press:  07 August 2017

R. Dvorak
R. Dvorak*
Affiliation:
Institute of Astronomy University of Vienna Türkenschanzstrasse 17 A-1180 Vienna e-mail: DVORAK@AVIA.UNA.AC.AT

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this article we present a numerical study of the motion of asteroids in the 2:1 and 3:1 resonance with Jupiter. We integrated the equations of motion of the elliptic restricted 3-body problem for a great number of initial conditions within this 2 resonances for a time interval of 104 periods and for special cases even longer (which corresponds in the the Sun-Jupiter system to time intervals up to 106 years). We present our results in the form of 3-dimensional diagrams (initial a versus initial e, and in the z-axes the highest value of the eccentricity during the whole integration time). In the 3:1 resonance an eccentricity higher than 0.3 can lead to a close approach to Mars and hence to an escape from the resonance. Asteroids in the 2:1 resonance with Jupiter with eccentricities higher than 0.5 suffer from possible close approaches to Jupiter itself and then again this leads in general to an escape from the resonance. In both resonances we found possible regions of escape (chaotic regions), but only for initial eccentricities e > 0.15. The comparison with recent results show quite a good agreement for the structure of the 3:1 resonance. For motions in the 2:1 resonance our numeric results are in contradiction to others: high eccentric orbits are also found which may lead to escapes and consequently to a depletion of this resonant regions.

Keywords

Kirkwood GapsChaotic MotionNumerical Experiments
Type
Part III - The Asteroidal Belt
Information
Symposium - International Astronomical Union , Volume 152: Chaos, Resonance and Collective Dynamical Phenomena in the Solar System , 1992 , pp. 145 - 152
Copyright
Copyright © Kluwer 1992 

References

Chirikov, B.V., and Vecheslavov, V.V.:1986, “Chaotic Dynamics of Comet Halley”, Novosibirsk, preprint Google Scholar
Froeschlé, C., and Scholl, H.: 1981, “The Stochasticity of Peculiar Orbits in the 2/1 Kirkwood Gap”, Astron. Astrophys., 93, p.62 Google Scholar
Froeschlé, C., and Scholl, H.: 1982, “A Systematic Exploration of Three-dimensional Asteroidal Motion at the 2/1 Resonance”, Astron. Astrophys. 111 p.346 Google Scholar
Froeschlé, C., and Gonczi, R.: 1988, “On the Stochasticity of Halley like comets”, Cel. Mech. 43, 325 CrossRefGoogle Scholar
Giffen, R.: 1973, “A Study of Commensurable Motion in the Asteroid Belt”, Astron. Astrophys. 23, p.387 Google Scholar
Hanslmeier, A., and Dvorak, R.:1984, “Numerical Integration with Lie-Series”, Astron. Astrophy. 132, 203 Google Scholar
Lemaitre, A., and Henrard, J.: “On the Origin of Chaotic Behaviour in the 2/1 Kirkwood Gap”, Icarus, 83, p.391.CrossRefGoogle Scholar
Henrard, J., and Caranicolas, N.D.: 1990, “Motion near the 3/1 Resonance of the planar elliptic restricted three body problem”, Cel. Mech. 47, p.99 Google Scholar
Laskar, J.: 1989, “A numerical experiment on the chaotic behaviour of the solar system”, Nature, 338, No.6212, p.237 Google Scholar
Morbidelli, A. and Giorgilli, A.:1990, “On the dynamics in the asteroids belt. Part II: Detailed study of the main resonances.” Cel. Mech., 47, p.173 Google Scholar
Murray, C.C., and Fox, K.: 1984, “Structure of the 3: 1 Jovian Resonance: A Comparison on Numerical Methods”, Icarus, 59, p.221 CrossRefGoogle Scholar
Murray, C.D.: 1986, “Structure of the 2:1 and 3:2 Jovian resonances”, Icarus, 65, p.70 CrossRefGoogle Scholar
Poincaré, H.:1902, “Sur les planètes du type d'Hécube”, Bull. Astron. 19, p.289 Google Scholar
Scholl, H., and Froeschlé, C.: 1975, “Asteroidal motion at the 5/2, 7/3 and 2/1 resonances”’ Astron. Astrophys. 42, p. 457 Google Scholar
Sessin, W., and Ferraz-Mello, S.: 1984; “Motion of two Planets with periods commensurable in the ratio 2/1”, Cel. Mech. 32, 307 Google Scholar
Wisdom, J.: 1982, “The origin of the Kirkwood gaps: A mapping for Asteroidal motion near the 3/1 commensurability”, Astron. J. 87, p.577 CrossRefGoogle Scholar
Wisdom, J.: 1983, “Chaotic behaviour and the origin of the 3/1 Kirkwood gap”, Icarus, 56, p.51 CrossRefGoogle Scholar
Wisdom, J.: 1987, “Urey Prize Lecture: Chaotic Dynamics in the Solar System”, Icarus, 72, p.241 CrossRefGoogle Scholar
Yoshikawa, M.: 1989, “A Survey of the Motions of Asteroids in the Commensurabilities with Jupiter”, Astron. Astrophys. 213, p.436 Google Scholar
Yoshikawa, M.: 1990, “Motions of Asteroids at the Kirkwood Gaps I. On the 3:1 Resonance with Jupiter, Icarus, 87, p.78 CrossRefGoogle Scholar
Yoshikawa, M.: 1991, “Motions of Asteroids at the Kirkwood Gaps I. On the 5:2, 7:3, and 2:1 Resonances with Jupiter”, Icarus 92, p.94 CrossRefGoogle Scholar