[meteorite-list] Two clarifications on prior post

From: Sterling K. Webb <kelly_at_meteoritecentral.com>
Date: Thu Apr 22 09:55:42 2004
Message-ID: <3C393EAA.F0AFB897_at_bhil.com>

Hi,

    I posted a longish piece to The Meteorite List on Dec. 9, 2000, subject: "How Many Meteorites Fall?"
that spent a lot of time on this question, if anybody wants to check the archives. A couple of quotes:

         "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 argued that data indicated a fall rate three to five times greater than the MORP estimate. How you
relate the world-wide fall to an individual patch is as follows:

         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.)

    Of course, if the fall rate was five times greater, a meteorite would land on one square kilometer
every 4340 years! Here, "meteorite" means one incoming object which may fragment into many, many objects
in the real world.

    Robert also touched on scaling "laws":

     Here, there are some theoretical, exponential scaling laws you
     can use to estimate comparative fall rates between stones above
     10 grams and stones above 1000 grams. I'm sure it's at least
     a 20:1 ratio (i.e. at least 100,000 square miles). Hopefully
     someone on the list can provide more definitive data.

    These are called the "power laws," because the mathematical expression has a "power" in it (usually 2)
and is derived from the (reasonable) assumption that objects that are derived from the chaotic breaking up
of larger objects -- which is all meteorites -- end up with the same total weight in each weight class.
That is, for every 100 gram stone, there are ten 10 gram stones and 100 one gram stones, etc.
    So that figure of one 100 gram meteorite per square kilometer every 4340 years, is also one 10 gram
stone every 434 years and 1 one gram stone every 43.4 years and one 100 milligram stone every 4.34 years,
and so on, down to cosmic dust drifting down all the time and filling the ocean sediments with meteoritic
sludge!

    Hope that makes it better instead of fuzzier!

Sterling
------------------------------------------------------
"Matson, Robert" wrote:

> Hi again,
>
> Dave Freeman was kind enough to e-mail me about a point
> of confusion in my prior post. I didn't pay close enough
> attention to Robert Beauford's last question:
>
> > An object over 1 kilo (2.2 lbs) might fall in a given 1 square
> > mile piece of land only once in every (how many) years?
>
> I mistakenly answered the related question "An object over 1 kilo
> might fall on a ? square mile piece of land once per year"
> (following the example of the prior question). I based my
> answer on a WAG (wild ass guess) at the ratio of falls producing
> 10-gram meteorites to falls producing 1-kilogram meteorites
> (20 to 1). So, given my earlier answer that one 10-gram
> meteorite per year falls on a 5000-square-mile plot of land,
> this is equivalent to saying on average that one 10-gram
> meteorite falls every 5000 years on a 1-square-mile plot of
> land. Assuming that 20:1 ratio kilo-to-10-gram ratio was
> correct, that would mean you'd need to wait 100,000 years
> on average for a 1 kilo meteorite to land in a given 1 square
> mile area.
>
> However, these numbers are all based on *falls* per unit time,
> not meteorites per unit time. Since each fall usually produces
> a number of meteorites (sometimes thousands or even tens of
> thousands!), this changes the statistics on numbers of non-
> unique 10-gram or 1-kilo meteorites per given area. To really
> solve the problem, you'd need to know more about the statistics
> of strewnfield areas, and average numbers of 10+ gram and 1+ kilo
> meteorites dropped per fall.
>
> Best,
> Rob
>
Received on Mon 07 Jan 2002 01:22:35 AM PST