On Mon, Jan 07, 2002 at 07:51:06AM -0600, Dan Minette wrote: > I did a small back of the envelope calculation on this. There should be, > roughly, 1 asteroid that hits the earth for every 10,000 that passes within > 400,000 miles.
This seemed like a fun calculation, so I tried it, assuming a 4000 mile earth radius. I got 20,000:1 odds. Did I make it an error? For every asteroid that passes within R miles of the earth, consider the instant when the asteroid first intersects the sphere, centered at the earth, with radius R. Assume the radius of the earth is r. Then the earth subtends a solid angle of Pi*r^2/R^2 for the asteroid at that instant. The asteroid is equally likely to be heading in any solid angle of 2*Pi steradians (since it is going into the sphere, not out, it is half of 4*Pi). 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? -- "Erik Reuter" <[EMAIL PROTECTED]> http://www.erikreuter.com/
