David, please correct me if I'm wrong (not that anybody here is bashful
about doing that).
From your message, I take it that you have looked at assembling an annulus
of junk into a planet. If you assume that the planet has no spin, then its
orbital angular momentum must equal that of all of the junk beforehand.
This requirement gives you one criterion for the orbital radius of the
planet. If you assume no dissipation of energy during the coagulation
process (the junk just quietly assembles itself, and you ignore the binding
energy of the planet), then energy conservation gives a different criterion
for the orbital radius of the planet, which ends up being smaller than the
angular momentum criterion. I confirmed this myself, using a uniform
surface density of material in the annulus (I guess you said that you did
it for several distributions).
So, to get the two derivations of the orbital radii to agree, some of the
angular momentum must be taken up by the spin of the planet. Or, the orbit
of the planet has to be "pumped up," ie. energy has to be inserted,
allowing it to go into a larger orbit than the energy criterion would
indicate. You argue that this might come from the collisions involved in
the coagulation of the junk to form the planet.
But, how would the increase in the binding energy of the planet become
available to alter the planet's orbit? Collisions "from behind" would tend
to accelerate the planet, but there should be about as many collisions from
ahead, which would slow it down. Near misses can accelerate small objects
to high speeds, but on average they slow more massive objects down (they
seek equipartition). About the only mechanism that I've heard invoked to
alter a planet's orbit is the tidal transfer of angular momentum through
the disk of material.
I gotta dig up some references.
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Stephen D. Murray
Physicist, A Division
Lawrence Livermore National Laboratory
phone: (925) 423-9382 FAX: (925) 423-0925
email: sdmurray@llnl.gov
web page: http://members.home.com/murraysj/
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