[meteorite-list] How Many Meteorites Fall?

From: Sterling K. Webb <kelly_at_meteoritecentral.com>
Date: Thu Apr 22 10:22:38 2004
Message-ID: <3EEA6E35.E2F02498_at_bhil.com>

Dear List,

    This is that post on fall rates that Rob Matson referred to.
I was thinking about it again, because of Park Forest and the
hits
on houses and cars. I had predicted that we would have at least
one
more meteorite hit on a car in the two decades since the last one
(1992), and now in just 11 years we have a fabulous cluster of
hits
in Park Forest, which just re-inforces the suggestion that the
fall
rate is higher than is usually thought (more like 80,000 + per
year).


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.


Copyright 2000
Sterling K. Webb
(kelly_at_bhil.com)
November 30, 2000
Received on Fri 13 Jun 2003 08:37:09 PM PDT