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Asteroid Proper Elements: The Big Picture

Published online by Cambridge University Press:  19 July 2016

Zoran Knežević  and
Andrea Milani
Zoran Knežević
Affiliation:
Astronomska opservatorija, Volgina 7, 11050 Beograd, Yugoslavia
Andrea Milani
Affiliation:
Dipartimento di Matematica, Via Buonarroti 2, 56127 Pisa, Italy E-mail milani@dm.unipi.it

Abstract

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Four perturbation theories presently used to compute asteroid proper elements are reviewed, and their results are briefly discussed (Milani and Knežević, 1990, 1992, 1994, for low to moderate eccentricity/inclination main belt objects; Lemaitre and Morbidelli, 1994, for high e, I objects; Milani, 1993, for Trojans; Schubart, 1982, 1991 for Hildas). The most important recent improvements are described, in particular those pertaining to the upgrades of the previous analytic and semianalytic solutions. The dynamical structure of the asteroid main belt, as defined by the low order mean motion resonances and by linear and nonlinear secular resonances, is considered from the point of view of the effects of these resonances on the accuracy and/or reliability of the computation of proper elements and on the reliability of the identification of asteroid families.

Type
Dynamics
Information
Symposium - International Astronomical Union , Volume 160: Asteroids, Comets, Meteors 1993 , 1994 , pp. 143 - 158
Copyright
Copyright © Kluwer 1994 

References

Anders, E.: 1965, “Fragmentation history of asteroids.” Icarus 5, 399–408.CrossRefGoogle Scholar
Arnold, J.R.: 1969, “Asteroid families and jet streams”. Astron. J. 74, 1235–1242.CrossRefGoogle Scholar
Bien, R. and Schubart, J.: 1987, “Three characteristic parameters for the Trojan group of asteroids”, Astron. Astrophys. 175, 292–298.Google Scholar
Brouwer, D.: 1951, “Secular variations of the orbital elements of the principal planets.” Astron. J. 56, 9–32.CrossRefGoogle Scholar
Brouwer, D. and Van Woerkom, A.J.J.: 1950, “The secular variations of the orbital elements of the principal planets.” Astron. Papers Amer. Ephem. Naut. Almanac 13, 81–107.Google Scholar
Henrard, J.: 1990, “A semi-numerical perturbation method for separable hamiltonian systems.” Celest. Mech. 49, 43–67.CrossRefGoogle Scholar
Hirayama, K: 1918, “Groups of asteroids probably of common origin.” Astron. J. 31, 185–188.CrossRefGoogle Scholar
Hirayama, K: 1923, “Families of asteroids.” Japan. J. Astron. Geophys. 1, 55–93.Google Scholar
Hirayama, K: 1928, “Families of asteroids, second paper.” Japan J. Astron. Geophys. 5, 137–162.Google Scholar
Hori, G.: 1966, “Theory of general perturbations with unspecified canonical variables.” Publ. Astron. Soc. Japan 18, 287–296.Google Scholar
Knežević, Z.: 1992a, “An efficient algorithm for the analytic computation of planetary short-periodic perturbations.” Bull. Acad. Serbe Sci. Arts (Sci. math.), 104(18), 39–46.Google Scholar
Knežević, Z.: 1992b, “Minor planet short-periodic perturbations: the indirect part of the disturbing function.” Celestial Mechanics, 55, 387–404.CrossRefGoogle Scholar
Knežević, Z.: 1994, “Generic term representation of the long periodic determining function.” Planet. Space Sci., in press.Google Scholar
Knežević, Z., Froeschlé, Ch., Lemaître, A., Milani, A., and Morbidelli, A.: 1994, “Comparison of two theories for calculation of asteroid proper elements.”, in preparation.Google Scholar
Kozai, Y.: 1962, “Secular perturbations of asteroids with high inclination and eccentricity.” Astron. J. 67, 591–598.CrossRefGoogle Scholar
Lemaitre, A., and Morbidelli, A.: 1994, “Calculation of proper elements for high inclined asteroidal orbits.” Celestial Mechanics, in press.CrossRefGoogle Scholar
Lindblad, B.A., and Southworth, R.B.: 1971, “A study of asteroid families and streams by computer technique.” In: Physical Studies of Minor Planets (Gehrels, T., Ed.), NASA SP-267, U. S. Govt. Print. Off., pp. 337–352.Google Scholar
Milani, A.: 1993, “The Trojan asteroid belt: Proper elements, stability, chaos and families.” Celest. Mech. 57, 59–94.CrossRefGoogle Scholar
Milani, A.: 1994, “Proper elements and stable chaos.” In: From newton to chaos: modern techniques for understanding and coping with chaos in N-body dynamical systems (Roy, A. E., Stevesi, B.A., Eds.), Plenum, New York, in press.Google Scholar
Milani, A., and Knežević, Z.: 1990, “Secular perturbation theory and computation of asteroid proper elements.” Celestial Mechanics 49, 347–411.CrossRefGoogle Scholar
Milani, A., and Knežević, Z.: 1992, “Asteroid proper elements and secular resonances.” Icarus 98, 211–232.CrossRefGoogle Scholar
Milani, A., and Knežević, Z.: 1994, “Asteroid proper elements and the dynamical structure of the asteroid belt.” Icarus, in press.CrossRefGoogle Scholar
Milani, A., and Nobili, A.M.: 1992, “An example of stable chaos in the Solar System.” Nature 357, 569–571.CrossRefGoogle Scholar
Morbidelli, A.: 1993, “Asteroid secular resonant proper elements.” Icarus 105, 48–66.CrossRefGoogle Scholar
Morbidelli, A. and Henrard, J. 1991a. Secular resonances in the asteroid belt: Theoretical perturbation approach and the problem of their location. Celest. Mech. 51, 131–168.CrossRefGoogle Scholar
Morbidelli, A. and Henrard, J. 1991b. The main secular resonances ν5, ν6 and ν16 in the asteroid belt. Celest. Mech. 51, 169–198.CrossRefGoogle Scholar
Nobili, A.M., Milani, A. and Carpino, M.: 1989, “Fundamental frequencies and small divisors in the orbits of the outer planets.” Astron. Astrophys. 210, 313–336.Google Scholar
Schubart, J.: 1982, “Three characteristic parameters of orbits of Hilda-type asteroids Astron. Astrophys. 114, 200–204.Google Scholar
Schubart, J.: 1991, “Additional results on orbits of Hilda-type asteroids.” Astron. Astrophys. 241, 297–302.Google Scholar
Van Houten, C.J., Van Houten-Groeneveld, I., Herget, P., and Gehrels, T.: 1970, “The Palomar-Leiden Survey of faint minor planets.” Astron. Astrophys. Suppl. 2, 339–448.Google Scholar
Williams, J.G.: 1969, “Secular perturbations in the Solar System.” Ph.D. Thesis, Univ. California, Los Angeles.Google Scholar
Williams, J.G.: 1979, “Proper orbital elements and family memberships of the asteroids.” In: Asteroids (Gehrels, T., Ed.), pp.1040–1063, Univ. Arizona Press.Google Scholar
Williams, J.G.: 1989, “Asteroid family identifications and proper elements.” In: Asteroids II (Binzel, R. P., Gehrels, T., Matthews, M. S., Eds.), pp. 1034–1072, Univ. Arizona Press, Tucson.Google Scholar
Williams, J.G., and Faulkner, J.: 1981, “The position of secular resonance surfaces.” Icarus 46, 390–399.CrossRefGoogle Scholar
Williams, J.G., and Hierath, J.E.: 1987, “Palomar–Leiden minor planets: Proper elements, frequency distribution, belt boundaries, and family membership.” Icarus 72, 276–303.CrossRefGoogle Scholar
Yuasa, M.: 1973, “Theory of secular perturbations of asteroids including terms of higher order and higher degree.” Publ. Astron. Soc. Japan 25, 399–445.Google Scholar
Zappalà, V., Cellino, A., Farinella, P., and Knežević, Z.: 1990, “Asteroid families I: identification by hierarchical clustering and reliability assessment.” Astron. J. 100, 2030–2046.CrossRefGoogle Scholar
Zappalà, V., Cellino, A., Farinella, P., and Milani, A.: 1994, “Asteroid families: II. Extension to unnumbered multi-opposition asteroids.” Astron. J. 107, 772–801.CrossRefGoogle Scholar