[meteorite-list] How Many Meteorites Fall?
From: Kelly Webb <kelly_at_meteoritecentral.com>
Date: Thu Apr 22 09:37:33 2004 Message-ID: <3A32B11C.2ED40886_at_bhil.com> Dear List, Thought this would be of some interest to Listees. The news is good, I think. More meteorites may fall to earth than is generally assumed, always good news for hunters. I know I can always count on critiques, corrections if needed, additions, amendments, and quibbles. All are welcome. Sterling K. Webb -------------------------------------------------------------------- A NOVEL MEASURE OF METEORITIC FLUX By Sterling K. Webb METHODOLOGY: Beyond general interest in the particulars of meteoritic impact, there is good reason to catalog cases in which meteorites have struck such things as people, cars, buildings or ships. Such cases provide an opportunity to directly measure the total number of meteorites that fall to earth every year by the method of collisional cross sections. It works like this: if we know that some specific area amounts to one-millionth of the earth's total area, and that target area gets hit by a meteorite once a decade on average, then it is easy to calculate that the earth must be hit by a million meteorites per decade, or 100,000 meteorites per year. The most important aspect of the cross section method is that it does not matter whether the target area is a single contiguous block or consists of billions of patches randomly scattered over the planet. In fact, using a number of widely distributed targets is likely to produce more accurate results, because it provides a better sampling procedure. Take as an example the cases of meteorites striking human beings. We know the size of a single potential target, the average human being. We know the total number of humans on the planet for most historic eras. The product of the population number times the size of an individual human being constitutes the collisional cross section of humanity. Comparing the cross section (target size) of humanity to the area of the entire planetary surface and the rate of how often people are struck provides a method for deriving a number for how many meteorites per year fall over the planet as a whole. This method can be applied to meteorite hits on any class of objects for which we can calculate a total cross section and for which we have data. Another advantage of this method is that each calculation on a class of targets is independent of the calculations involving any other class of targets, allowing us to compare a number of independent measures of meteorite flux. HOW MANY METEORITES FALL EACH YEAR? Many years ago, Nininger estimated that 500 meteorites ranging from 100 grams to 10 kilograms in mass fell on land each year (approximately 2000 for the entire Earth). More recently, Canada's Meteor Observation and Recovery Project estimated 23,930 meteorites per year as the worldwide fall rate. I shall use this rate as a basis for comparison to establish an expected frequency for impacts on people, dogs, cars, buildings, and ships. DATA USED: A table of 141 reported cases of meteorite impacts on people, dogs, cars, buildings and ships can be found at the end of the thirteenth chapter of John S. Lewis, Rain of Iron and Ice, Addison-Wesley, 1996. I have taken that table as an initial trial database for just such an analysis. Some of the cases cited are familiar and widely quoted and others are much more poorly known. Usually these cases are treated only in an anecdotal manner or as vaguely indicative (as if to say, enough meteorites fall that once upon a time a dog was killed, or a car struck, by a meteorite, for example). They are not treated by Lewis as quantitative data, but they have that potential use. To analyze this list of events in a quantitative manner is a procedure that depends on the completeness of the data for the accuracy of its results. It should be understood that in this situation any incompleteness in the data (omissions of events) makes the calculated flux lower than it really is, so any additions to the data would raise the value of the meteoritic flux. There is no evidence that Lewis intended his list to be either complete or all-inclusive. In addition, there are probably accounts that have yet to be discovered, events that went unreported or whose reporting was discouraged, and events in which the meteoritic explanation was never considered. Thus, it is important to stress that this analytical technique establishes only a minimum value and does not constrain the maximum value of the variable in question, how many meteorites fall to earth per year. CROSS SECTIONS AND MEAN-TIME-TO-IMPACT: Taking the area of the Earth to be 5.1 x 10^8 km^2 and the meteorite flux to be 23,930 yr^-1, this yields the assumed collisional cross section of the earth to be 21,360 km^2 yr^-1. This rate means that one meteorite per year falls on an area of 21,320 square kilometers. The inverse function of this value is how long we have to wait for a meteorite to fall on a standard area, or the mean time to impact: 21,360 yr km^-2. To put this flux into perspective, if you owned a house with a half-acre yard, you would have to wait 10,552,000 years for a meteorite to fall in your front or back yard or on your roof! (On average, that is; it could happen tomorrow.) TARGET CROSS SECTIONS: I have taken the collisional cross section of any target to be its profile when viewed from a 45-degree elevation and from a orientation of 45 degrees from its orthogonal axes, thus averaging all the possible directions a meteorite could come from. In the case of human beings, whether standing up or fully recumbent, this results in an individual cross section of 0.4 m^2. The cross section of an automobile is more than an order of magnitude greater: 6.25 m^2. (This value for cars is self-compensatory for changes in the proportions of U.S. autos from the 1920's to today by virtue of the fact that older vehicles are taller but narrower and newer ones are lower but wider.) IMPACTS ON HUMAN TARGETS: The total collisional cross section of humanity is: DATE CROSS SECTION MEAN TIME TO IMPACT (population) (_at_23,930 yr^-1) ==== ============= =================== ============ in 1630 A.D. 200.0 km^2 mean time 106.9 yr (half billion) in 1830 A.D. 400.0 km^2 mean time 53.4 yr (1 billion) in 1930 A.D. 800.0 km^2 mean time 26.6 yr (2 billion) in 1960 A.D. 1200.0 km^2 mean time 17.8 yr (3 billion) in 2000 A.D. 2400.0 km^2 mean time 8.9 yr (6 billion) The assumed flux of 23,930 meteorites per year would predict 1.1 human impacts for the fifty year span between 1825 to 1875, 1.25 impacts for the fifty years 1875-1925, and 2.25 impacts for the 1925 to 1975 period. The actual data for human impacts is as follows: PERIOD CASES DEATHS INJURIES TOTAL % EXPECTATION ====== ===== ====== ======== ===== ============= 1825-1875: 4 cases 2 deaths 3 injuries 5 total 364% by cases 1875-1925: 4 cases 9 deaths 1 injury 10 total 333% by cases 1925-1975: 5 cases 1 death 32 injuries 33 total* 1470% by persons (* 28 injuries, no deaths, in one shower - 1946) As you can see, the incidence suggests a meteoritic flux is at least three to four times greater than the assumed value, or 71,790 to 95,720 meteorites per year. That flux corresponds to a terrestrial cross section of 5340 km^2 yr^-1 to 7120 km^2 yr^-1. A RESERVATION: One problem of interpreting the human impact rate is the fact that all human populations create structures with which they are closely associated, spending 35% to 90% of their time under shelter. This causes an overlap of the human target population with the structure target population. This may confuse the results in this way. If a human being is inside a building which is struck by a meteorite and the collapse of the building causes the death of the person but the meteorite never actually touches the victim, is it fair to count that death as being directly caused by meteoritic impact? (The cross section method requires that each target population be considered separately.) One case in the 1825-1875 period and one case in the 1875-1925 period are just such cases. If they were to be eliminated from the analysis, the implied meteoritic flux drops to around 52,000 to 65,000 meteorites per year. However, in both these cases, we do not know from the source whether the victim was struck or not. There are many more cases of persons untouched in a room struck by meteorites, however. In the one case of a combined building and person hit in the 1925-1975 period, the meteorite multiply perforated the building but managed to strike (non fatally) the target human. So, it counts. In strictest terms, this method should be applied to the number of persons physically contacted by meteorites. This would yield results of 5, 8, and 15 times the expected rate, 100,000 to 300,000 meteorites per year. But, of course, we know that most of these cases of multiple injury are caused by multiple objects in the same shower, fragments of the same entering object, so it hardly seems "fair" to count each human struck, although that is what the method demands. IMPACTS ON BUILDINGS: Here is the raw data: DATES TOTAL HITS MULTIPLE HITS (Year) ===== ========== ==================== 1800-1849 9 2 (1803) 1850-1899 6 -- 1900-1909 3 -- 1910-1919 6 -- 1920-1929 1 -- 1930-1939 7 2,2 (1936, 1938) 1940-1949 3 2 (1949) 1950-1959 6 2 (1950) 1960-1969 10 2,4 (1961, 1969) 1970-1979 6 2,2 (1971, 1973) 1980-1989 11 2,2,3 (1988, 1989, 1984) I have found as yet no reliable way of estimating the structural cross section of the world's buildings. The U.S.A. contains about 38,000 km^2 of human structures, but this density cannot be extrapolated to the world as a whole. For that reason, I cannot apply the cross section method to this data. The data shows a constant and slowly rising, but highly variable, trend which suggests incomplete reporting and a lack of detection and attention. The cause of the dip in the rate for the 1940's is easily explained; at a time when Rotterdam was rendered to ashes and Dresden was turned into the backside of the Moon, who would notice a smallish meteorite impact? The population of meteorites is sorted according to a power law, meaning that there many more small objects than large ones. Nearly all of the building impact reports are fairly dramatic in nature, suggesting that only the most substantial impactors are detected. The actual impact rate for our population of meteorites may be 5 to 10 times greater than these data show, but without a good estimate of the total cross section of structures, it's impossible to say. IMPACTS ON CARS: Total collisional cross section of U.S. Automobiles (Vehicle data from The Statistical Abstract of the United States, various years) DATE CROSS SECTION Mean Time to Impact ==== ============= =================== 1940 260 km^2 82.2 yrs 1950 306 km^2 69.8 yrs 1960 386 km^2 55.3 yrs 1970 503 km^2 42.5 yrs 1980 654 km^2 32.7 yrs 1990 880 km^2 24.3 yrs 2000 1040 km^2 20.5 yrs The assumed flux of 23,930 meteorites per year would predict 1.65 to 1.75 impacts on U.S. automobiles in this past century. The actual rate is four impacts: in 1938, 1950, 1977, and 1992. The data is less contaminated by the association of the targets with human shelters (only one car was hit while in a garage). Further, since Americans are quite sensitive to and observant of damage to their cars, the chances of under-reporting is less than with buildings. I believe this to be the "cleanest" set of data. The data for U.S. automobiles is 250% of expectation, again suggesting a flux of 59,825 meteorites per year, or a terrestrial collisional cross section of 8528 km^2 yr^-1. In all these cases, the impactor was in excess of 1 kilogram. This suggests, again, that smaller impactors may have been unreported. A slow moving 100 gram stone that whanged into an eighteen wheeler barreling down the interstate might provoke no response greater than "dam kids!" (while a fast moving 10 kilogram stone would certainly produce more spectacular results). IMPACTS ON SHIPS: There are a fair number of reports of ships hit, sailors killed, and marine near misses. It is impossible to easily produce a cross section for a target population that ranges in size from modern super-tankers hundreds of meters long to dories and skiffs two meters long, particularly over historic periods. The fact that there are any marine reports is suggestive but not quantifiable without a reliable cross section measurement. One might consider the case of a medium sized modern ocean-going vessel of 100 meters in length with a 20 meter beam (and equal height), displacing about 15,000 tons. At a fall rate of 23,930 meteorites per year, a fleet of 7000 such vessels could expect to cruise the seas of the world nonstop from the time of the ancient Greeks until today before accumulating a 50-50 chance of a single meteorite impact! Contrast that rate with the occurrence of two impacts on ships within 18 months (in 1936-38) or the impact of two substantial fireballs in Fortune Bay, Newfoundland, within one month's time. I could calculate how far off expectation that is, but I don't think my calculator has that many zero's. IN-JOKE: I have not been able to calculate a collisional cross section for the dog population of the planet. CONCLUSIONS: This analysis suggests that the actual meteoritic flux is much greater than what is currently assumed (23,930 meteorites per year). The data implies a better fit with a meteoritic flux of 60,000 to 100,000 meteorites per year at a minimum. DATA RELIABILITY: There is, and always will be, reservations about the accuracy or authenticity of historical reporting of events attributed to meteoritic activity, but it worth noting that to reduce the flux implied by these reports to a value of 23,930 meteorites per year would require throwing out half to two thirds of the data, which I would regard as unreasonable. There is a rough similarity between the results of the analyses of the data for human impacts worldwide and the more restricted set of data on impacts on U.S. automobiles in that the estimated fall rates from the two sets of data overlap. Since the two calculations are not dependent, it would seem unlikely that this correlation is fortuitous. That the data is potentially incomplete implies that the true meteoritic flux may well be higher than the minimum that this analysis suggests. POSTSCRIPT: ADDITIONAL DATA? As always, more data is needed. Additional cases represent a more comprehensive data set, and each would substantially increase the calculated rate of fall. Obviously, every potential case for inclusion in the data could (and would) be disputed by some and accepted by others. What is required to reach a level of acceptable reliability? So, I have restricted my analysis here to a data set compiled by someone other than myself and previously published (i.e., Lewis), so as to avoid the possibility of biasing the results by adding to the data incidents not all vetted by the same source, but there are other reports. I have been able to find newspaper accounts of a car struck on May 10, 1961, in Minnesota, and a number of impact injury cases, none of which are included in Lewis' list. The best of these human impact cases took place on November 6, 1951, in Bremerton, Washington; a man's arm was seriously injured (burned) in his hotel room by an impacting object which set portions of the room afire. The incident was witnessed from across the street by a policeman (who was writing a parking ticket at the time); he saw a fiery streak cross the sky, streak into the hotel room window, and explode. You could hardly ask for a better documented case: a cop as a witness to the fall, a verified fire investigation report, and a medical treatment report from the hospital at the Navy shipyard where the victim was treated. Yet, in this case, a meteoritic explanation seems never to have been suggested at any time, presumably because the impactor was never found (or recognized). However, there are undoubtedly those for whom the absence of the rock would make the report unreliable (or at least, indeterminate). How many more cases are there? Copyright 2000 Sterling K. Webb (kelly_at_bhil.com) November 30, 2000 ------------------------------------------------------------------- NOTE: Thanks and kudos to E. L. Jones for a great piece of work investigating a recent purported meteorite strike on an automobile and saving me from re-calculating a whole section! Still, the odds favor another car hit in the next couple of decades. NOTE2: Uses of the technique. Example: Wyoming, with over 250,000 km^2, should get hit with between 12 and 40 meteorites per year, depending on the flux you assume. They're out there, Dave! If the fall rate was 30 per year for Wyoming, then since the ice went away 10,000 years ago, there would have been 300,000 falls, or about 1 per square km (247 acres). 247 acres is a front yard in Wyoming, isn't it? NOTE3: If you want to reply or respond to this post, save wear'n'tear on the servers. Don't append this entire text, just type in the subject line "Re: How Many Meteorites Fall?" to your message. Received on Sat 09 Dec 2000 05:24:28 PM PST |
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