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and references therein
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An acronym for Give A Parent To Every Child. Spectral methods to establish such connections are discussed by L. A. McFadden, M. J. Gaffey, and T. B. McCord [Science 229, 160 (1985)].
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Resonance borders are the borders of the main chaotic region accounting for secular oscillations. Use of resonant proper elements allows direct determination of whether a particle is "in" the resonance or not [A. Morbidelli et al., Icarus 118, 132 (1995)].
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We have used the techniques of V. Zappalà et al. [ibid. 124, 156 (1996)].
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End states, the decay of the number of particles, and the distribution of orbital elements are statistically identical over the time scale of ≃3 My, which is numerically feasible with conventional Bulirsch-Stoer and RADAU algorithms. See also (9). The symplectic algorithm is that of J. Wisdom and M. Holman [Astron. J. 102, 1528 (1991)], as modified by H. Levison and M. Duncan [Icarus 108, 18 (1994)]. The output (only) was numerically averaged to produce proper elements free of short-period oscillations.
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43949148386
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End states, the decay of the number of particles, and the distribution of orbital elements are statistically identical over the time scale of ≃3 My, which is numerically feasible with conventional Bulirsch-Stoer and RADAU algorithms. See also (9). The symplectic algorithm is that of J. Wisdom and M. Holman [Astron. J. 102, 1528 (1991)], as modified by H. Levison and M. Duncan [Icarus 108, 18 (1994)]. The output (only) was numerically averaged to produce proper elements free of short-period oscillations.
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1842356343
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note
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6 (all 110 particles were active), Vesta 3:1 (resonance boundaries were not used in calculating the initial conditions), and Koronis (small proper e's caused poor theoretical prediction of the resonance borders).
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R. Greenberg and M. Nolan, in Asteroids II, R. Binzel, T. Gehrels, M. S. Matthews, Eds. (Univ. of Arizona Press, Tucson, 1989), pp. 778-804; R. Greenberg and M. Nolan, in Resources of Near-Earth Space, J. Lewis et al., Eds. (Univ. of Arizona Press, Tucson, 1993), pp. 473-492; W. F. Bottke et al., Icarus 122, 406 (1996), especially figure A2.
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especially figure A2
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R. Greenberg and M. Nolan, in Asteroids II, R. Binzel, T. Gehrels, M. S. Matthews, Eds. (Univ. of Arizona Press, Tucson, 1989), pp. 778-804; R. Greenberg and M. Nolan, in Resources of Near-Earth Space, J. Lewis et al., Eds. (Univ. of Arizona Press, Tucson, 1993), pp. 473-492; W. F. Bottke et al., Icarus 122, 406 (1996), especially figure A2.
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1842360194
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When objects in mean-motion resonances arrive at conjunction with that planet, they are far from the planet and thus protected from close encounters
-
When objects in mean-motion resonances arrive at conjunction with that planet, they are far from the planet and thus protected from close encounters.
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24
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T. Gehrels, Ed. Univ. of Arizona Press, Tucson
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By definition, Apollo asteroids have pericenters q < 1.017 AU and a > 1, Amors satisfy q < 1.3 AU, and Atens a < 1 with Q > 0.983 [G. Shoemaker et al., in Asteroids, T. Gehrels, Ed. (Univ. of Arizona Press, Tucson, 1979), pp. 253-282].
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1842266715
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SEAs are small Earth-approaching asteroids with orbits similar to that of Earth. See (15)
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SEAs are small Earth-approaching asteroids with orbits similar to that of Earth. See (15).
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5 resonance (10 die), and 9 begin outside both (1 dies) over the 43-My integration.
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1842340742
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note
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The Jacobi constant is a conserved quantity for the massless particle in the circular restricted three-body problem. Particles dominated by close encounters with a single planet on a circular orbit conserve their encounter velocity with respect to that planet, which results in motion in a-e space roughly parallel to lines of constant q (14). On million-year time scales, the noncircularity of planetary orbits and distant perturbations induce considerable drift in the values of the Jacobi "constants."
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1842345506
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For stony objects, Wetherill (24) proposes a collisional half-life of order √r My while in the main belt, where r is the meteoroid radius in centimeters
-
For stony objects, Wetherill (24) proposes a collisional half-life of order √r My while in the main belt, where r is the meteoroid radius in centimeters.
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38
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0001798194
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These constraints are established by the a.m./p.m. asymmetry in fall times and from orbits determined by fireball observations [see (14) and G. Wetherill, Meteoritics 20, 1 (1985)]. These constraints also rule out deriving the bulk of the chondrites by breaking up asteroids already on NEA orbits.
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1842312925
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6, or due to the recently reconsidered Yarkovsky effect [J. A. Bums et al., Icarus 40, 1 (1979); D. Rubincam, J. Geophys. Res. 100, 1585 (1995)].
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6, or due to the recently reconsidered Yarkovsky effect [J. A. Bums et al., Icarus 40, 1 (1979); D. Rubincam, J. Geophys. Res. 100, 1585 (1995)].
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S. K. Vogt et al., Meteoritics 28, 71 (1993); G. Heusser et al., Meteoritics Planet. Sci. 31, 657 (1996); R. Wieler et al., ibid., p. 265.
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Wieler, R.1
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44
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36849158776
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The distribution of asteroids relative to the gaps is pictured in S. Dermott and C. Murray, Nature 301, 201 (1983).
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Dermott, S.1
Murray, C.2
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45
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1842402065
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We thank B. Bottke, C. Chapman, O. Eugster, P. Farinella, K. Marti, and G. Wetherill for constructive input to this study. T. Bowell provided the initial conditions for the NEA sample
-
We thank B. Bottke, C. Chapman, O. Eugster, P. Farinella, K. Marti, and G. Wetherill for constructive input to this study. T. Bowell provided the initial conditions for the NEA sample.
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