In infinite wisdom Joseph Lazio answered:

[I thought this exchange on the number of terrestrial mass planets
to be getting to the point where a followup was not necessary.
However, I've since realized that there is an important point.]

R> In infinite wisdom Joseph Lazio answered:

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

R> Almost exclusively gas giants, only a few oddball terrestrial
R> planets.  I don't see how you can derive that there are "more
R> lower-mass planets than Jupiter-mass planets" from the data at
R> hand.

From Marcy et al. (2003, "Properties of Extrasolar Planets," ...)

  The distribution of masses rises rapidly toward the lower masses,
  dN/dM ~ M^{-0.7} ....

R> Where M is 1 jupiter mass.

This is both incorrect and highlights an important point.  The mass
distribution I write above is a function.

It's not a function as such, it's more of a relationship. A function
takes one input and produces one output. Even if M is defined, and
it does not appear to be, you relate any N to any M, or vice verse.

It is valid over a range of
masses, not just at 1 Jupiter mass as Rich seems to believe.

Then name the range.

And what do you mean by valid? You mean this is observed in the
solar system? Or do you mean this applies to every star?

It might
have helped had I have written this as dN/dM = A*M^{-0.7}, where A is
a constant that is determined from the data. 

I'm not sure this would establish it's validity everywhere.

To make this point more explicit, we can use this mass distribution to
compare the number of planets of different masses.  Suppose we want to
know how many more 0.5 Jupiter mass planets there are compared to the
number of 2 Jupiter mass planets.  Then dN/dM(2M_J) ~ (2M_J)^{-0.7}
and dN/dM(0.5M_J) ~ (0.5M_J)^{-0.7}, and their ratio is
(0.5M_J/2M_J)^{-0.7} = 2.6.  That is, there are about 3 times as many
0.5 Jupiter mass planets as there are 2 Jupiter mass planets.

Are there? I don't see any planets with 2 jupiter masses hereabouts.

If you claim the relationship has universal validity, perhaps you can
show me the observational basis.

This brings me to the important point.  How low in mass does this
function apply.  Planets with masses of 0.1M_J have been discovered,

Lower bound. They are almost certainly more massive, how massive is
not know.

and the function seems to apply at least this low.  Earth is about
0.003M_J.  One might worry that there could be some difference in the
way that gas giants and terrestrial planets form.

One might.

If that is the
case, extrapolating this mass distribution to terrestrial planet
masses may not be valid.

When you posted the relationship, with no conditions, you seem to have
been asserting it's validity down to comets and dust.

So what is the evidence for terrestrial mass planets?  I'd now have to
say, not much. 

Odd, when I made that claim it was considered an attack on SETI.

If I were a gambling man, though, I'd be willing to bet that
terrestrial planets are numerous, for the following reasons.  First,
if Jupiter mass planets can form, it seems like forming something only
0.3% of their mass should be much easier.

Should be? Seems to me that they require different materials. As to
the dynamics of planetary formation, some of the planets exist where
our current models say they cannot exist. I don't think we have any
solid basis for making predictions.

Indeed, at a party last
night, somebody pointed out that we actually know of three extrasolar
*cometary* systems.  Second, we know of three terrestrial mass planets
orbiting PSR B1257+12,

Lower bounds again, they may well be of the 0.1 jupiter mass class.

and there were not supposed to be any planets orbiting pulsars.

Rather than creating confidence in our knowledge of planetary formation,
this shows that what we think we know is wrong, or at least woefully
incomplete. It does nothing to validate extrapolations beyond the
data we have.

Rich