James, That paper was well written with lots of history , thanks for posting . Looks like much of that research was done during Apollo. I have a attached a new paper just released on Arxiv. It discusses the paradigm of trying to explain how some of the "craters" have raised center cones with boulders perched atop of them. Their theory is "granular impactors" which sounds pretty funky to me. Sounds like it is still up for interpretation.
http://arxiv.org/pdf/1302.0259v2.pdf Succinctly, the paradigm of crater formation, which fails to explain certain features like the existence of boulders perched on central peaks, says that craters and central peaks were created by the target fluidization produced by solid meteorite impacts, followed by collapse of the transient crater where final shapes of craters emerge [4-6]. Many of the craters also have what appear to be raised scarring or tracks around the craters, similar to electrical scarring. I think it is beta decay. Stewart On Thu, Feb 28, 2013 at 8:07 PM, James Bowery <[email protected]> wrote: > To rephrase your objection to my more rigorous Poisson process treatment: > > "The assumption 'The Chelyabinsk meteor and the 2012 DA events are > statistically similar events.' is questionable." > > Your argument would clearly be reasonable if the size of theChelyabinsk meteor > and the size of the 2012 DA asteroid were around the same. They weren't. > The 2012 DA asteroid hit a much larger radius target but it was, itself, > a much larger and therefore rarer size celestial object than was the > Chelyabinsk > meteor. > > It is not so easy to brush off my assumption as unreasonable. > > On Thu, Feb 28, 2013 at 6:58 PM, Daniel Rocha <[email protected]>wrote: > >> I don't think the coincidence that remote. You have to calculate the >> probabilities as the asteroids were crossing spheres the size of of their >> distance to earth. While the one that hit Russia hit Earth within its usual >> radius, the more distant asteroid "hit Earth" with a radius as big as >> Jupiter. That increases A LOT the probability of these kind of coincidences >> since the total cross section is much higher for these kinds of events. >> >> >> -- >> Daniel Rocha - RJ >> [email protected] >> > > > I've copied that more rigorous Poisson process treatment below: > > OK, since Paulson has pulled a hit and run (the "hit" occuring when he > implied he had done a rigorous calculation of the odds and the "run" when I > asked him to show his work), I'll show the work of an actual rigorous > calculation: > > First of all, the correct treatment is as a Poisson > process<http://www.math.ucla.edu/~hbe/resource/general/3c.2.05f/sec12-4-6.pdf> > : > > P(k)=e^(-Λ)*Λ^k/k! > > Where > > P is the probability > k = the number of times the rare event occurs > Λ=λt > λ= the rate per unit time > t= the time interval over which the k rare events occur > > > Assuming: > > The Chelyabinsk meteor and the 2012 DA events are statistically similar > events. > These events occur roughly every 100 years. > Our unit of time is 1 hour. > A human lifetime is 80 years. > > > λ=1/(100year/1hour) > 1/(100year/1hour) > 1 / ([100 * year] / [1 * hour]) > = 0.0000011415525 > > t=16 > > Λ=λt > 0.0000011415525*16 > = 0.00001826484 > > P(X=2)=e^(-Λ)*Λ^2/2! > e^(-0.00001826484)*0.00001826484^2/2 > ([e^-0.00001826484] * [0.00001826484^2]) / 2 > = 1.6679914E-10 > > So, the odds of any particular 16 hour interval experiencing 2 of these > rare events is about: > > 1/1.6679914E-10 > 1 / 1.6679914E-10 > = 5.9952347E9 > > > 1 in 6 billion > > > So in an 80 year lifespan the odds of experiencing such a coincidence is: > > > 1-(1-1.6679914E-10)^(80years/16hours) > 1 - ([1 - 1.6679914E-10]^[{80 * year} / {16 * hour}]) > = 0.0000073057752 > > 1/0.0000073057752 > 1 / 0.0000073057752 > = 136878.01 > > about 1 in a hundred thousand. >
