Re: How does planetismal theory of earth explain molten core?

The classical explanation is that the heat for melting comes from several
sources.  The first is the release of gravitational potential energy.  As
those planetismals are slowly attracted toward the accreting planet, they
accelerate and that potential is converted to kinetic energy.  When the
accelerating planetismal finally collides with the growing proto-planet,
that energy is converted again, largely to heat.  This is true, even today,
of meteorite collisions with Earth.  

In addition, the early earth had a much higher concentration of radioactive
elements than the present day Earth, many with short half-lives. As these
elements decayed they heated Earth from within.  

In concert, these mechanisms plus further gravitiational compaction of the
ball of stuff, released enough heat to cause partial melting to begin. 
Metallic iron or alloys of iron-nickel-sulfur are among the first things to
melt out of the proto-planet.  As they melt, they form droplets that can
begin to migrate under the influence of gravity.  Because the iron melt is
denser than the silicate residual, as the droplets coalesce and get big
enough, they migrate downward, which releases more potential energy, first
as kinetic energy and ultimately as heat, which accelerates the melting.  

As shown in this web site, it would take about a half-billion years for
the temperature to rise sufficiently by these processes alone
http://www.indiana.edu/~geol105/images/gaia_chapter_3/earth_differentiation.htm


Some geologists think now, however, that it may have happened much earlier
in earth's history.  The moon is now generally accepted to have formed from
a collision between a young Earth and a Mars-sized proto-planet, which
completely melted both bodies (and in fact turned a good part of them to
vapor, which then condensed back into liquid as the bodies cooled and
separated). See http://www.spike.com/video/naked-science-birth/2685304.

This may have occurred very early in Earth's history (perhaps only 60
million years after the birth of the solar system, instead of 600 million
in the classical model.  http://news.nationalgeographic.com/news/2007/12/071219-moon-collision.html

Either way, as a result of radioactive decay and collisions, there is
plenty of heat available to melt the earth and allow differentiation of the
iron-nickel core from the silicate mantle and crust.  

Dave Smith