Abstract
For both asteroids and meteor streams, and also for comets, resonances playa major role for their orbital evolutions but on different time scales. For asteroids both mean motion resonances and secular resonances not only structure the phase space of regular orbits but are mainly at the origin for the inherent chaos of planet crosser objects.
For comets and their chaotic routes temporary trapping into orbital resonances is a well known phenomenon. In addition for slow diffusion through the Kuiper belt resonances are the only candidates for originating a slow chaos.
Like for asteroids, resonances with Jupiter playa major role for the orbital evolution of meteor streams. Crossing of separatrix like zones appears to be crucial for the formation of arcs and for the dissolution of streams. In particular the orbital inclination of a meteor stream appears to be a critical parameter for arc formation. Numerical results obtained in an other context show that the competition between the Poynting-Robertson drag and the gravitational interaction of grains near the 2/1 resonance might be very important in the long run for the structure of meteor streams.
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References
Arnold, V.: 1978, Mathematical Methods of Classical Mechanics, Springer Verlag, New York
Babadzhanov, P.B. and Obrubov, Yu.V.: 1987, ‘Evolution of Meteor Streams’, in Z. Ceplecha and P. Pecina (eds.) Interplanetary Matter, Publ. Astron. Inst. Czechosl. Acad. Sci. No. 67, 141–150
Babadzhanov, P.B. and Obrubov, Yu.V.: 1989, ‘Dynamics and Spatial Shape of Short-Period Meteoroid Streams’, in D. McNally (ed.), Highlights of Astronomy, Kluwer Acad. Publ., vol. 8, 287–293.
Babadzhanov, P.B. and Obrubov, Yu.V.: 1991, ‘P/Machholz 1986 VIII and Quadrantid Meteorid Stream. Orbital Evolution and Interrelation’, to appear in Asteroids, Comets, Meteors 1991, Flagstaff, USA
Brouwer, D., van Woerkom, A.J.J.: 1950, ‘The secular variation of the orbital elements of the principal planets’, Astron. Papers U.S. Naval Obs., 13, 85–107.
Farinella, P., Gonczi, R., Froeschlté Ch., Froeschle, C.: 1991, ‘Injecting asteroids fragments into resonances’, submitted for Asteroids, Comets, Meteors 1991, Flagstaff, USA
Franklin, F., Lecar, M. and Soper, P.: 1989, ‘On the original distribution of the asteroids. Do stable orbits exist between Jupiter and Saturn ?’, Icarus 79, 223–227
Froeschlé, C., and Scholl, H.: 1977, ‘A qualitative comparison between the circular and elliptic model for resonant asteroidal orbits’, Astron. astrophys. 57, 33–39
Froeschlé, C. and Scholl, H.: 1982, ‘A systematic exploration of three-dimensional asteroidal motion at the 2/1 resonance’, Astron. Astrophys 111, 346–356
Froeschlé, C., and Scholl, H.: 1983, ‘The dynamical structure of the Asteroidal Belt’, in C.I. Lagerkvist and H. Rickman (eds.) Asteroids, Comets, Meteors, Uppsala Univ., pp. 115–125.
Froeschlé, C. and Scholl, H.: 1986, ‘Gravitational splitting of quadrantid-like Meteor Streams in resonance with Jupiter’, Astron. Astrophys. 158, 259–265
Froeschlé, C., Scholl, H.: 1987, ‘Resonance Intermittence causes the Gravitational Splitting of Meteor Streams’, Proceedings of the tenth European Regional Astronomical meeting of the IAU, Prague, 151–155
Froeschlé, C., and Greenberg, R.: 1989, ‘Mean Motion Resonances’, in Binzel R.P. Gehrels and Mattews M.S. (eds.) Asteroids, Tucson Univ. of Arizona Press, 827–844
Froeschlé, Ch., Scholl, H.: 1991, ‘The Effect of Secular Resonances in the Asteroid Region between 2.1 and 2.4 AU’, submitted for Asteroids, Comets, Meteors 1991, Flagstaff, USA
Gladman, B., and Duncan, M: 1990, ‘On the fates of minor bodies in the outer Solar System’, Astron. J. 100, 1680–1693
Gonczi, R., Froeschlé, Ch., Froeschlé, C.: 1982, ‘Poynting-Robertson Drag and Orbital Resonance’, Icarus 51, 633–654.
Gonczi, R., Froeschlé, Ch., Froeschlé, C.: 1983, ‘Evolution of Three Dimensional Resonant Orbits in Presence of Poynting-Robertson Drag’, in C.I. Lagerkvist and H. Rickman (eds.) Asteroids, Comets, Meteors, Uppsala Univ., 137–143
Gonczi, R., Rickman, H. and Froeschlté C.: 1991, ‘The Connection between comet P/Machholz and the Quadrantid meteor streams’, M. N. R. A. S, in press
Greenberg, R.: 1977, ‘Orbit-orbit resonances in the Solar System: Varieties and similarities’, Vistas in Astron. 21, 209–239
Greenberg, R. and Scholl, H.: 1979, ‘Resonances in the asteroidal belt’, in T. Gehrels (ed.) Asteroids, Univ. of Arizona Press, 310–333
Green, D.W.E., Rickman, H., Porter, A.C. and Meech, K.J.: 1990, ‘The Strange Periodic Comet Machholz’, Science 247, 1063–1067
Hamid, S.E. and Youssef, M.N.: 1963. ‘A short Note on the Origin and Age of the Quadrantids’, Smithsonian Contr. Astrophys. 7, 309–311
Heppenheimer, T.A.: 1980, ’secular resonances and the origin of eccentricities of Mars and the Asteroids’, Icarus 41, 76–88
Hugues, D.W., Williams, L.P., Murray, C.D.: 1979. ‘The orbital evolution of the Quadrantid Meteor Stream between AD 1830 and 2030’, M.N.R.A.S. 189,493–500
Knezevic, Z., Milani, A., Farinella, P., Froeschle, Ch. and Froeschle, C.: 1991, ’secular resonances from 2 to 50 AU’, Icarus 93, 316–330
Levinson, H.F.: 1991, ‘The long-term dynamical behaviour of small bodies in the Kuiper belt’, Astron. J. 102, 787–794
Lindblad, B.A.: 1973, ‘The distribution of 1/a in photographic meteor orbits.’, in Hemenway, C.L., Millman, P.M. and Cook, A.F. (eds.) Evolutionary and physical properties of meteoroids, NASA Special Publication, Washington, D.C., 319, 175–181
McIntosh, B.A.: 1990, ‘Comet P/Machholz and the Quadrantid Meteor Stream’, Icarus 86,299–304
Milani, A. and Knežtevic, Z.: 1990, ’secular perturbation theory and computation of asteroid proper elements’, Celest. Mech. 49, 347–411
Morbidelli, A. and Henrard, J.: 1991a, ’secular resonances in the asteroidal belt. Theoritical perturbation approach and the problem of their location’, Celest. Mech. 51,131–168
Morbidelli. A., and Henrard, J.: 1991b, ‘The main secular resonances Vs V6 and V16 in the asteroidal belt’, Celest. Mech. 51,169–198
Peale, S.J.: 1976, ‘Orbital resonances in the Solar System’, Astron. Astrophys. 14, 215–215.
Poincaré, H.: 1902, ’sur les planetes du type d’Hécube’, Bull. Astron. 19, 289–315
Rickman, H. and Froeschlé, C.: 1979, ‘Orbital evolution of short period comet treated as a Markov process’, Astron. J. 84, 1910–1917
Rickman, H. and Froeschlé, C.: 1988, ‘Cometary dynamics’, Celest. Mech. 43, 243–263
Scholl, H., and Froeschlé, C.: 1988, ‘Gravitational breaking of meteor streams in resonance with Jupiter’, Astron. Astrophys. 195,345–349
Scholl, H., Froeschlé, Ch., Kinoshita, H., Yoshikawa, M. and Williams, J.G.: 1989, ’secular resonances’, in Binzel R.P. Gehrels and Mattews M.S. (eds.) Asteroids, Tucson Univ. of Arizona Press, 845–861.
Scholl, H. and Froeschlé, Ch.: 1991, ‘The V6 Secular Resonance Region near 2.AU: a Possible Source of Meteorites’, Astron. Astrophys. 245, 316–321
Schubart, J.: 1968, ‘Long-period effects in the motion of Hilda-type planets’, Astron. J. 73, 99–103
Schubart, J.: 1978, ‘New results on the commensurability cases of the problem Sun-Jupiter-Asteroids, in V. Szebehely (ed.) Dynamics of Planets of Satellites and Theories of Their Motion, IAU Coli N° 48, D. Reidel: Dordrecht, 137–143
Schubart, J: 1979, ‘Asteroidal motion at commensurabilities treated in three dimensions’, in R.L. Duncombe (ed.) Dynamics of the Solar System, D. Reidel: Dordrecht, 205–215
Torbett, M.V., and Smoluchowski, R.: 1990, ‘Chaotic motion in a primordial comet disk beyond Neptune and comet influx to the Solar System’, Nature 345, 49–51
Weibel, N.M., Kaula, W.M. and Newmann, W.I.: 1990, ‘A computer search for stable orbits between Jupiter and Saturn’, Icarus 83, 382–392
Wetherill, G.W.: 1988, ‘Where do the Apollo objects come from 7’, Icarus 76, 1–18
Williams, J.G.: 1969, ’secular Perturbations in the Solar System’, Ph. D. Thesis, Univ. of California, Los Angeles.
Williams, I.P., Murray, C.D. and Hughes, D.W.: 1979, ‘The Long-Term Orbital Evolution of the Quadrantid Meteor Stream’, M. N. R. A. S. 189,483–492
Williams, J.G., and Faulker, J.: 1981, ‘The positions of secular resonance surfaces’, Icarus 46, 390–399
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Froeschlé, C., Froeschlé, C. (1992). Collective Resonant Phenomena On Small Bodies In The Solar System. In: Clube, S.V.M., Yabushita, S., Henrard, J. (eds) Dynamics and Evolution of Minor Bodies with Galactic and Geological Implications. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2743-1_6
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DOI: https://doi.org/10.1007/978-94-011-2743-1_6
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