On Tue, Jan 08, 2002 at 10:09:20AM -0600, Dan Minette wrote: > ----- Original Message ----- From: "Erik Reuter" > <[EMAIL PROTECTED]> > > > > > Therefore, the probability P that the asteroid hits the earth is > > > > 2*Pi / (Pi*r^2/R^2) > > > > 1/P = 2 ( R / r ) ^2 or 20,000:1 (actually, 19,999:1 if we are > > picky). > > > > Is there an error in my thinking? > > > Let me use that same calculation twice to show that, together with > the assumption made above, it comprises a system with internal > inconsistency. Let us assume that R is 40,000,000 miles. Let us > assume that there is indeed an isotropic source of asteroids in a thin > spherical belt at that distance. Let us also neglect the effects of > gravity (at 40 million miles this is certainly invalid, but it does > help illustrate the difficulty in the technique). > > Let us look at two cases, where r1=400,000 miles, and where r2=4,000 > miles. For r1, we have 1/P =2*100^2=20,000, for r2, we have > 1/P=2*10000^2=200,000,000. The ratio of these two numbers is 10,000, > not 20,000.
Maybe I am just dense, but I don't see how this is inconsistent. You've shown that if 1/P = a * ( R / r ) ^2 , then the ratio of P's for different r's cancels out the constant 'a'. Please fill in the missing steps from here to inconsistency. > Since you did the math OK, I think the problem is assuming a half > isotropic source. Unfortunately, if I assume a full isotropic source, then I get 1/P = 4 ( R / r ) ^2 which is even further from your answer. I suspect your answer is correct, but I'd like to know exactly why my thinking is wrong here. -- "Erik Reuter" <[EMAIL PROTECTED]> http://www.erikreuter.com/
