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W.F. Bottke (Cornell U.), R Jedicke (U. Arizona), A. Morbidelli, B. Gladman, J.-M. Petit (Obs. de la Cote d'Azur)
No accurate estimate of the orbital and absolute magnitude distribution of the Near-Earth Objects (NEOs) currently exists, largely because: (i) the known NEOs are biased by complicated observational selection effects which favor the discovery of bright or large objects that come close to Earth; (ii) relatively few NEOs have been discovered, making debiasing efforts difficult; (iii) NEO orbits are chaotic on short timescales (< 1000 years); and (iv) the source regions and replenishment mechanisms for the NEOs are not well understood. For these reasons, observers are still struggling to increase NEO detection rates, while the interpretation of existing data continues to be problematic.
We propose a new method to attack this problem, one which takes advantage of theoretical advances and new numerical tools. To treat observational biases, we have applied a model-independent, semi-analytical method for calculating the probability that an asteroid observation program will find a given asteroid in a (a, e, i, and H; semimajor axis, eccentricity, inclination, and absolute magnitude, respectively) bin per square degree at opposition at the Vernal Equinox (Jedicke and Metcalfe 1998). To discover how NEOs are replenished, we have used symplectic numerical integration techniques which can track the orbital paths of test bodies started in several potential NEO source regions (e.g., 3:1 resonance, v6 resonance, multiple weak mean-motion resonances). By merging the observational biases with these NEO dynamical ``roadmaps" (and an NEO absolute magnitude distribution), we get a probability distribution which, if the sources have been weighted correctly, can be directly compared to the known NEOs. By testing a range of possible source combinations, we have produced a ``best-fit'' distribution which not only yields the normalized and debiased NEO orbital and absolute magnitude distribution (over various NEO sizes) but also the relative importance of each NEO replenishment source.
These results have several important applications for NEO observers and for studies of the impact rates of asteroids onto the terrestrial planets. These issues are discussed in an abstract by Morbidelli et al. (this issue).