Statistics – Computation
Scientific paper
May 2000
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2000dda....31.0603c&link_type=abstract
American Astronomical Society, DDA Meeting #31, #06.03; Bulletin of the American Astronomical Society, Vol. 32, p.862
Statistics
Computation
2
Scientific paper
The probability that an asteroid or comet will collide with the Earth during a future close passage depends on its orbit uncertainties during that encounter. These uncertainties in turn depend on the duration over which the object has been observed, and the time interval from the last observation to the encounter. Linear techniques for analyzing encounter uncertainties are elegant and fast, and can be used to obtain a quick estimate of impact probability. But if orbit uncertainties during the encounter are large, due to a short data arc, or a long prediction interval, or intervening close approaches, the linear method breaks down. Monte Carlo techniques can be used to overcome these obstacles, enabling analysis of encounters farther in the future than would otherwise be possible. Although these methods require considerably more computation than linear techniques, the computational load is not prohibitive. Our Monte Carlo method begins by populating the uncertainty region in epoch orbital element space with thousands of random points. Each of these is numerically integrated to the encounter of interest, and the target-plane asymptote intercept coordinates are computed. A straight-forward estimate of collision probability is just the ratio of impacting points to the total population. If the points are too sparse, however, a collision probability can be obtained by splitting the points into linearly related streams, deriving a local point density both along the line of variation and perpendicular to it, and integrating this 2D density over the Earth disk. Use of this technique for estimating impact probabilities of asteroids 1999 AN10, 1998 OX4, and 2000 BF19 will be discussed.
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