Here's a sanity check:
Let's say that the Chelyabinsk meteor and the 2012 DA14 asteroid were about
the same size. Using atmospheric entry frequency of about every century as
a wide-agreed observable we should expect to see something the size of the
2012 DA14 asteroid coming within the diameter of Jupiter about once every 3
years:
100*pi*(4000mi)^2/(pi*(22000mi)^2)
([100 * pi] * [{4000 * mile}^2]) / (pi * [{22000 * mile}^2])
= 3.3057851
Do we have any reason to believe this is a reasonable conjecture?
On Thu, Feb 28, 2013 at 7:07 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.
>
