wats@scicom.AlphaCDC.COM (Bruce Watson) (11/08/90)
Deja vu all over again. I vaguely remember a similar discussion about Skylab's demise in 1979. Salyut 7 has an equatorial inclination of 51.6 degrees so that it overflies the world from 51.6 south lat and 51.6 north lat. Let's assume that it equally probable that it could come down anywhere within these limits (although there appears to be some effort afoot to dump it in an ocean). The area of the earth between these latitude limits is given by: A = 2.pi.R.h = 2.pi.(6378km).2.(6378).cos(51.6) = 317e6 sq km. The population of the earth passed 5 billion (5000 million) recently. Let's assume that it is now 5.1e9. There are a number of relatively densely populated countries north of 51.6 north, but little population south of 51.6 south. Lets subtract 100 million and use 5e9 for the number of persons living within the latitude limits. So there are 16 people per square kilometer. Or one person for each .06 sq km = 63500 sq m. This is a square 250 meters on a side. If each person measures 1 by 2 meters (I'm being generous), then there are 32000 ways the person can occupy this area. Salyut 7 measures 17 by 4.2 meters. If Salyut 7 remains whole as it crashes to the earth ( again I'm being generous), there are 560 ways it can occupy the area. There are 57 ways the satellite and the person can intersect. The prob`ability of a person being struck is the ratio of the possibilties of success to the possibilities of arrangement: p(someone) = 57/(32000).(560) = 1/300000 (small) The probability that YOU will be hit by Salyut 7 is: p(you) = 2/317e6 = 1/160000000 (real small) Please check my arithmetic and my reasoing. If correct this implies that a Salyut 7 insurance policy for 160000000 dollars could be purchased for one dollar (excepting profit and overhead for the insurance company). A fair wager that someone in the world would be hit would be one dollar that someone would be hit and 300000 dollars that no one would be hit. This is contrary to our intuition. The reason, I think, is that it is hard to appreciate how large the earth is.