This explanation comes from David Bohlin, a senior scientist
in Code SR at NASA:
The reason for the gradations of light and color in the Shuttles
exhaust plume is a combination of the facts that the sun had
set at the Cape and the effect of the Rayleigh scattering of
sunlight as it passes through the Earth's atmosphere.
Rayleigh scattering of electromagnetic waves by gas
molecules is proportional to the inverse of the 4th power of
the wavelength, which explains why the sky is blue to our
eyes and the setting sun is red. That also explains the colors
of the plume. The lower part is in the shadow of the earth's
local western horizon (which can also be seen as the dark
horizontal band immediately above the horizon in the
background eastern sky). As you move up to a higher altitude
on the plume the setting sun comes into view, but the only
light getting through the long air-path length is the red end of
the spectrum so the plume looks red (as does the next higher
band of the background sky). As you go higher the sun is
effectively rising above the horizon to the plume, the air-path
length for the sunlight is diminishing so less blue light is being
scattered away, and the residual light moves to the yellow
part of the spectrum. Finally the upper part of the plume is in
full sunlight and appears white.
As for the apparent "convergence" of the shadow to the full
moon, my training in architectural drawing suggests to me
that this is a simple effect of perspective of how the more or
less rectangular shadow of the plume looks as it projects
through space in a direct line from the sun to the moon. The
sun is far enough away that the shadow retains structural
identity, just as does the earth's shadow on the moon during a
lunar eclipse.
Physics aside, though, this is a stunning picture that ought to
take its place in the pantheon of the most interesting ones
ever made of a Shuttle launch. It was possible only because
of the fact that the sky was absolutely clear from east to west
and the timing of the launch with the rising of the full moon. I
congratulate you getting it!!!

Got all that, now? Me, either.