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Trojans in Stable Chaotic Motion

Published online by Cambridge University Press:  12 April 2016

E. Pilat-Lohinger ,
R. Dvorak  and
Ch. Burger
E. Pilat-Lohinger
Affiliation:
Instituí für Astronomie, Universität Wien, Ttirkenschanzstraße 17, A-1180 Vienna, Austria
R. Dvorak
Affiliation:
Instituí für Astronomie, Universität Wien, Ttirkenschanzstraße 17, A-1180 Vienna, Austria
Ch. Burger
Affiliation:
Instituí für Astronomie, Universität Wien, Ttirkenschanzstraße 17, A-1180 Vienna, Austria

Abstract

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The orbits of 13 Trojan asteroids have been calculated numerically in the model of the outer solar system for a time interval of 100 million years. For these asteroids Milani et al. (1997) determined Lyapunov times less than 100 000 years and introduced the notion “asteroids in stable chaotic motion”. We studied the dynamical behavior of these Trojan asteroids (except the asteroid Thersites which escaped after 26 million years) within 11 time intervals - i.e. subintervals of the whole time - by means of: (1) a numerical frequency analysis (2) the root mean square (r.m.s.) of the orbital elements and (3) the proper elements. For each time interval we compared the root mean squares of the orbital elements (a, e and i) with the corresponding proper element. It turned out that the variations of the proper elements ep in the different time intervals are correlated with the corresponding r.m.s.(e); this is not the case for sin Ip with r.m.s.(i).

Keywords

: Trojan asteroidslong term evolutionproper elements
Type
Extended Abstracts
Information
International Astronomical Union Colloquium , Volume 172: Impact of Modern Dynamics in Astronomy , 1999 , pp. 117 - 126
Copyright
Copyright © Kluwer 1999

References

Barber, G.: 1986, “The Orbits of Trojan Asteroids”, in Lagerkvist, C.I., Lindblad, B.A., Lundstedt, H. and Rickman, H. (eds.), Asteroids, Comets, Meteors II, University of Uppsala, 161.Google Scholar
Bien, R., Schubart, J.: 1984, “Trojan orbits in secular resonances”, Cel.Mech & Dyn. Astro., 34, 425.Google Scholar
Bien, R., Schubart, J.: 1987, “Three characteristic parameters for the Trojan group of asteroids”, AstronAstrophys., 175, 292.Google Scholar
Burger, Ch.: 1998, “The Method of Labrouste with an Application in Celestial Mechanics”, Diploma thesis, University of Vienna, 75 p.Google Scholar
Chapront, J.: 1995, “Representation of planetary ephemerides by frequency analysis. Application to the five outer planets”, Astron. Astrophys., 109, 181.Google Scholar
Dvorak, R., Pilat-Lohmger, E.: 1998, “Les asteroides troyens: une nouvelle analyse” in Benest, D. & Froeschlé, C. (eds.) Aux Frontières de la Dynamique chaotique des systèmes gravitationelles O.C.A. Observatoire de Nice, 19.Google Scholar
Erdi, B.: 1984, “Critical inclination of Trojan asteroids”, Cel.Mech & Dyn. Astro., 34, 435.Google Scholar
Erdi, B.: 1988, “Long periodic perturbations of Trojan asteroids”, Cel.Mech. & Dyn. Astro., 43, 303.Google Scholar
Erdi, B.: 1996, “On the Dynamics of Trojan Asteroids”, in Ferraz-Mello, S., Morando, B., and Arlot, J.E.(eds.), IAU Symposium 172, Dynamics, Ephemerides and Astrometry in the Solar System, 171.Google Scholar
Erdi, B.: 1997, “The Trojan Problem”, Cel.Mech & Dyn. Astro., 65, 149.Google Scholar
Hanslmeier, A., Dvorak, R.: 1984, “Numerical Integration with Lie Series”, Astron. Astrophys., 132, 203.Google Scholar
Lemaitre, A.: 1993, “Proper Elements: What are they”, CeLMech. & Dyn. Astro., 56, 103.CrossRefGoogle Scholar
Levison, H.F., Shoemaker, E.M. and Shoemaker, C.S.: 1997, “Dynamical Evolution of Jupiter’s Trojan asteroids”Nature, 385, 42.Google Scholar
Lichtenegger, H.: 1984, “The Dynamics of Bodies with Variable Masses”, Cel.Mech. 34, p. 357.Google Scholar
Milani, A.: 1993, “The Trojan Asteroid Belt Proper Elements, Stability, Chaos and Families”, Cel.Mech & Dyn. Astro., 57, 59.Google Scholar
Milani, A.: 1994, “The Dynamics of the Trojan Asteroids”, in Milani, A. di Martino, M., Cellino, A. (eds.) IAU Symposium 160, ACM 1993, Kluwer Academie Publishers, The Netherlands. 159.Google Scholar
Milani, A., Nobili, A., Knežević, Z.: 1997, “Stable Chaos in the Asteroid Belt”, Icarus, 125, 13.Google Scholar
Pilat-Lohinger, E., Dvorak, R., Burger, Ch.: 1998, “Asteroids in stable chaotic motion” in Dvorak, R. Haupt, H. and Wodnar, K. (eds.): Modern Astrometry and Astrodynamics, Verlag der Österreich-Akad.d.Wiss., Wien, 29.Google Scholar
Rabe, J.: 1965, “Limiting Eccentricities for Stable Trojan Librations”, Astron. J., 70, 687.Google Scholar
Schubart, J., Bien, R.: 1984, “An application of Labrouste’s method to quasi-periodic asteroidal motion”, Cel.Mech & Dyn. Astro., 34, 443.Google Scholar
Schubart, J., Bien, R.: 1987, “Trojan asteroids - Relations between dynamical parameters”, Astron. Astrophys., 175, 200.Google Scholar
Shoemaker, E.M., Shoemaker, C.S., Wolfe, R.F.: 1989, “Trojan asteroids - Population, dynamical structure and origin of the L4 and L5 swarms.” in Asteroids II, Tucson, Univ. of Arizona Press, 487 Google Scholar