lal_truckee wrote:
I believe the proper way to calculate impact odds is cross-sectional
area of the earth divided by the cross-sectional area of the
error-bounded predicted location of the asteroid at closest approach,
adjusted for statistical density distribution within the error-bounded
predicted location.

That's true, but a separate question. The original poster seemed to
be asking not how is the probability calculated, but why that probability
is "likely" to drop once better elements are obtained for the asteroid.
In particular, if it always drops, why isn't the initial probability
lower than it might be?

The answer is that it only drops *most* of the time. A tiny fraction of
the time, the Earth is still within an error's breadth of the recomputed
path, and since the error is smaller, the probability of impact is
correspondingly larger.

As an analogy, consider the rock thrown at my head. Initially, I only
know the point of impact to within, say, 10 m, and if I'm within that
10 m radius circle, there is a probability of impact with my head,
although that probability is small. Once the point of impact is known
to an accuracy of 1 m, the chances that my head is still in the circle
is small, so the probability of impact drops to near zero in 99 percent
of the cases. One percent of the time, though, my head is still within
the circle, and since the circle is smaller, the probability of impact
is larger.

Brian Tung
The Astronomy Corner at http://astro.isi.edu/
Unofficial C5+ Home Page at http://astro.isi.edu/c5plus/
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My Own Personal FAQ (SAA) at http://astro.isi.edu/reference/faq.txt