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Cliff Sojourner wrote:

> how are almanac tables tested?  how do you know you can
> trust the generated table?

In 3 stages (at least).

Almanacs are produced from fundamental ephemerides. Putting aside trivial
problems such as printing errors, s/w errors, truncation problems, which can
easily be eliminated, all deviations from the theoretical values are the result
of an intentional trade-off between size and versatility of the almanac versus
its accuracy. As such, the deviations are voluntary, and predictable. If it is
said that an almanac is precise to 0.1' of arc, it means that there is no
greater deviation than that from the value obtained by rigorous methods from the
fundamental ephemerides.

The fundamental ephemerides are produced by numerical integration from dynamical
theory and least-square-fitted observational data. One can estimate the errors
due to finite step size of integration or truncation of terms. Then the result
must be published in a suitable format, for instance, Chebyshev polynoms. This,
again, causes _predictable_ approximation errors. It is in this sense that one
can say that a certain fundamental ephemeris is precise to, say 1 mas level, or
whatever.

One can, of course, hardly predict errors stemming from an inadequate theory or
inaccurate observations. This is, finally, where empirical verification comes
into play. More and better observations lead to better initial conditions for
the equations, may even result in a new theory, which yields better fundamental
ephemerides, from which a better almanac or star-gazing program can be produced.

It almost goes without saying that to go out and check the position of the sun
against one's almanac or the xyz star gazing program is quite a silly exercise.
I always find it hilarious, when the "Ocean Magazine" and the "Cruising
Navigator" do exactly this: "We have tested the "Admiral's Sight Reduction
Suite, Professional Edition, and found it to be accurate within half a mile when
compared to GPS in 12 foot seas"


> why should I believe one program is better (more
> accurate) than another?

Where commercial computer programs are concerned, this is mostly a thing of the
past when computers were so slow and small that one had to make compromises.
Nowadays, when all almanac programs come on CD roms and need 64 MB of memory
just to bring the first window onto the screen, there is very little
justification for truncating the theory of the moon after 200 terms. Nowadays, a
program does either the right thing (i.e. using JPL ephemerides and NOVAS
algorithms) or the wrong thing. In the latter case, throw it away. At any rate,
the documentation of a good professional ephemeris program should tell you
exactly what the underlying theory or fundamental ephemerides and algorithms
are, so that you can understand the limitations and use it correctly. If it
doesn't, forget the program.

Regards

Herbert Prinz

   

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