"R" == Rich  <someone@somewhere.com> writes:

R> Another thing that occurs to me is that most real-world
R> distributions tend to ba gaussian. One might reasonably expect
R> planetary mass distributions to be gaussian as well, rather than
R> linear.

R> In fact, I see no reason to expect a linear distribution at all.
R> Perhaps you guys know more than I, if so please explain why you
R> would expect a linear distribution than a guassian.

This is not correct on two counts.  First, there are many real-world
distributions that are not gaussian, and, second, the planetary mass
distribution is neither gaussian nor linear.  It's a power law, which
also occurs frequently in nature.

Most relevant might be a study of the asteroid diameter distribution,
<URL:http://www.sdss.org/news/releases/20010605.edr.img9.html>, which
shows that the asteroid diameter distribution is something like dN/dD
~ D^{-3}.  (It may be dN/dD ~ D^{-2.3} to dN/dD ~ D^{-4}.)

Interestingly enough, suppose one assumes that asteroids have a
constant density.  Then one can relate their diameter distribution to
their mass distribution, because mass and diameter would then be
related as M ~ D^3 or D ~ M^{1/3}.  Then the size distribution implies
a mass distribution of dN/dM ~ M^{-5/3} or M^{-1.6}.  One might recall
that I've posted the mass distribution of extrasolar planets.  It is
at least as steep as dN/dM ~ M^{-0.7}.  Stated another way, if dN/dM ~
M^{-x}, for extrasolar planets x > 0.7. 

The interested reader may wish to do a Web search on Zipf's law, Web
connectivity, or power law distributions in general.

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