Hi John,

"... I know that at some point the ephemeris data for the earth
and moon start to break down, but let's assume that they are pretty
accurate for at least the next 800 years."

That's probably a very safe assumption. There's little question
but what the major source of trouble for such "future" events is
Delta-T.

And you are right: Guide _does_ have to make assumptions about
Delta-T to compute future events of this sort. Such "assumptions"
might be better called "guesstimates". I know of no formal error
estimates for Delta-T, and I'd think the uncertainties would be so
great that they could only be guessed at, especially for more
distant eras. The formula I suggested in my previous e-mail is
simply a decent fit to current behavior, and it'll probably hold
good to within a second or so for the next few years. But beyond
that... maybe Delta-T will take another detour, as it did a few
years ago.

"...The further out in time we go isn't there an increased
danger that the points on the earth's surface Guide predicts will
be in the eclipse path may be incorrect simply because a faster
or slower deltaT value will place a different point under the
moon's shadow cone at that time?"

Exactly. (The same applies to the distant past, but at least
we have _some_ actual data with which to work: cases where somebody
wrote on a clay tablet, "A dragon ate the sun today, then spit it
back out." That gives us a rough idea of what Delta-T was back then.
But for the distant future... well, no one has come back in a time
machine yet to tell us what Delta-T will be centuries from now. We
just have to wait to find out.)

-- Bill