On Feb 24, 8:40*am, jacob navia wrote:
[Mod. note: quoted text trimmed -- mjh]
Sedna is at 1000 AU, what squared gives a factor of 1 million in your
formula:

pi*(AU)^2

That makes 1.9*10^8 years, i.e. 190 million years, nothing at
astronomical scales.

I wonder then if Sedna is not a captured free floating planet that
happened to pass nearby.

Interesting...

At 1000 AU, the orbital speed is of the order of 1 km/sec, and this is
about the speed an object must have for there to be any chance of
being captured. So 30 km/sec (which is what I assumed above for the
average peculiar speed of interstellar objects) is much too high for a
capture. And the density of objects with a speed of just 1 km (or
less) would be much smaller. If you assume a Maxwell-Boltzmann
distribution, then the density of particles is proportional to v^2 for
speeds small compared to the average speed, so in this case only
(1/30)^2 = 1/900 of the total density N. And because v would be
smaller by factor 1/30 as well, you would then still be at a time of
5*10^12 years, i.e. there would be just a 1/1000 chance that it has
occurred during the lifetime of the sun. And this is only the
probability for an object to get sufficiently close to the sun in the
first place. You then have to multiply this with the (conceivably even
much smaller) probability that it has a very close encounter with an
object of a comparable size in the solar system (because that is the
only way for it to lose kinetic energy and thus become captured by the
solar system).

But anyway, as we know from previous discussions, Robert suggests the
capture theory as a general alternative to explain the formation of
planetary systems, so also at 1AU or even closer (because that is what
his principle of a fundamental similarity between planetary systems
and atomic systems would demand).

Thomas