Comment 105 for bug 575621

Ok, let me see if I'm following you correctly -

On 2/1/2013 1:42 PM, Alexander Wolf wrote:
> Hmm...
>
> Just a fact: we use Espenak & Meeus (2006) algorithm for computation of
> ΔT, which based on Morrison and Stephenson (2004) equations. The revised
> value used for the Moon's secular acceleration, which originally used
> in this algorithm, is n-dot = -25.858 arc-sec/cy*cy (-0.12932224). For
> solar eclipse on 484/1/14 original algorithm give a value of ΔT = 5838.3
> s (http://eclipse.gsfc.nasa.gov/SEsearch/SEsearchmap.php?Ecl=04840114).

Yes, I see that now. Below the map it says "These eclipse predictions
were generated for the Moon's center of mass using the VSOP87/ELP2000-82
ephemerides <http://eclipse.gsfc.nasa.gov/SEcat5/ephemeris.html> and a
value of ΔT = *5838.3 s*". So what you're saying is that if our
implementation is correct, it should result in a similar ΔT value, close
to 5838.3 seconds.

> Stellarium with double t = (year-1955)/100; and return -0.12932224 * t *
> t; give a value of ΔT = 5840.95 s.

So this is the value actually produced by the Stellarium code after
correcting 1995 to 1955? This looks pretty good, only differing by about
3 seconds.

> Stellarium with double t =
> (year-1955)/100; and return -1.9170656 * t * t; (latest fix) give a
> value of ΔT = 5490.55 s.

And this is the result of the latest fix I suggested. Stellarium is
giving me this same number on my computer. Not such a good match. It
differs by about 348 seconds, or close to 6 minutes, from what the NASA
site reports.

>
> If http://eclipse.gsfc.nasa.gov/ use as etalon then better values
> Stellarium given with n-dot = -25.858 arc-sec/cy*cy (-0.12932224). If we
> use SOLEX as etalon then I need know, which exactly algorithm was used
> for ΔT computation.

I think a good initial goal would be just to correctly implement the
DeltaT polynomials used by the NASA eclipse pages. And from what you're
showing us here, it seems that the -26 to -25.858 correction is the one
that comes closest to doing that.

Still there's an empirical concern, that perhaps these polynomials don't
do an adequate job of matching the 484/1/14 eclipse. I haven't actually
seen an account of what was seen and recorded and at what exact
location, but with the -26 to -23.895 correction I find a total eclipse
in progress right at sunrise just 1 degree east of Athens, while with
the -26 to -25.858 correction I don't think there is a total eclipse
within one degree of Athens, and the fullest eclipse that does occur
happens below the horizon before sunrise.

So... correcting from -26 to -23.895 does seem to give a nicer result
for that particular eclipse, but from what you've shown us it appears to
be the wrong way to fix it. If that eclipse isn't being correctly
reproduced, we probably need to find another set of equations that's
designed to place this eclipse a bit later, and introduce that as an
alternative DeltaT approach that a user can choose. The equation that
Victor derived would probably do a good job with this.

Allan