Statistics – Computation
Scientific paper
Sep 1995
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995metic..30..563r&link_type=abstract
Meteoritics, vol. 30, no. 5, page 563
Statistics
Computation
Asteroids, Earth-Approaching, Ejecta, Lunar, Martian, Meteoroids, Parent Bodies, Sources, Mail-Belt
Scientific paper
Until recently, only the orbit distribution of large Earth-approaching asteroids (diameter, d~1km) was known. Meteor orbits were known only from their atmospheric trajectories, and only for objects with d<1m. These were explained by previous theoretical models [1, 2] as the fragments of main-belt asteroids, perturbed by orbital resonances and planetary encounters to Earth-crossing orbits. Another calculation [3] showed that short-period comets, perturbed by encounters with Jupiter and the terrestrial planets, could supply a significant fraction of the Earth-crossing population. Now the Spacewatch Telescope at the University of Arizona has extended the observed sizes of the Earth approachers down to d~5m. The data reveal a size distribution that increases in slope with decreasing size, coincident with an increased fraction of low-eccentricity orbits [4]. The colors of the small Earth approachers also show significant deviations compared with the colors of larger Earth approachers and main-belt asteroids [5]. These observations are not predicted by previous models that assume a source in the main belt, and they may indicate the admixture of inactive, cometary fragments, and/or impact ejecta from a local source, such as the Moon, Mars, or Earth. Before looking to comets and impact ejecta, however, more work is required to rule out the main belt as a viable source. We have developed a new Monte Carlo program based on Opik theory to model both the size and orbit distributions of the Earth approachers, assuming they originate as collisional fragments of main-belt asteroids and continue to fragment by colliding with other main-belt asteroids, as they evolve to Earth-crossing. Using computational methods developed for earlier calculations [1, 2, 6], this model accounts for the dynamical effects of both the nu6 secular resonance and the 3:1 mean motion resonance with Jupiter. This model also takes into account a map of collision probability as a function of orbital elements calculated by Bottke et al. [7]. Given (1) the steady-state size distribution in the main-belt, Nmb(d); (2) the production rate of collisional fragments as function of size; (3) the distribution of main-belt source orbits; and (4) the ejection velocities for collisional fragments, this model predicts the frequency and orbit distribution of Earth approachers in the 1m-to-10km size range. Artificially biasing these predictions to account for the selection effects of the Spacewatch search, and then comparing these observations to the most recent Spacewatch observations, leads to the following conclusions: (1) The observed orbits for km-sized Earth approachers are well predicted by the model assuming only main-belt sources near the 3:1 mean motion resonance with Jupiter (a~2.5 AU) and sources near the nu6 secular resonance (a~2.08 AU). Additional sources, such as short-period comets, are not required; (2) The observed orbits for Earth approachers in the 10-50m size range are not predicted by the model. Too many of the smaller Earth approachers have low-eccentricity orbits with perihelia near 1.0 AU and aphelia less than 2.0 AU. Impact ejecta from Mars, the Moon, or Earth may be required to explain these observations. This result is in agreement with Bottke et al. [7]; (3) The observed size distribution for the Earth approachers is not consistent with the model if Nmb(d) is a uniform power-law. Nmb(d) must be flatter than the observed size frequency of the Earth approachers for d>100m, and then steepen to the observed frequency for d<100m. This slope change is consistent with IRAS albedo measurements of main-belt asteroids [8], and the size frequency of impact craters on (951) Gaspra [9]. Acknowledgements: This work was funded by grants from NASA. References: [1] Wetherill G. W. (1985) Meteoritics, 20, 1-22. [2] Wetherill G. W. (1988) Icarus, 76, 1-18. [3] Wetherill G. W. (1991) Comets in the Post-Halley Era, Vol. 1, 537-556. [4] Rabinowitz D. L. (1994) Icarus, 111, 364-377. [5] Rabinowitz D. L. (1994) Completing the Inventory of the Solar System, submitted. [6] Wetherill G. W. (1979) Icarus, 37, 96-112. [7] Bottke W. F. et al. (1994) Completing the Inventory of the Solar System, submitted. [8] Cellino A. et al. (1991) Mon. Not. R. Astron. Soc., 253, 561-574. [9] Belton M. J. S. et al. (1992) Science, 257,1647-1652.
Rabinowitz David L.
Wetherill George W.
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