Problem Calculating a Moon's Position

I'm writing a program to calculate positions of the sun, moon and
planets with an accuracy of about one arc second.

The program calculates geometric, astrometric and apparent positions
in ecliptical (heliocentric and geocentric), equatorial (geocentric
and topocentric) and horizon (topocentric) coordinates. The tests done
so far show that all seems to work fine with one exception:

the moon's topocentric astrometric coordinates.

Comparing with results from CalSky the (absolute) differences are
minimal at the North Pole (RA: approx. 3") and maximal at the Equator
(RA: approx. 11"). (Note: the moon's geocentric astrometric
coordinates are calculated correct; the problem refers only to the
topocentric coordinates.)

The astrometric coordinates do not contain contributions from
aberration. For this the contribution from stellar aberration (sun/
earth-system) is deducted from the moon's coordinates (moon/earth-
system). This correction is applied on the geocentric equatorial
coordinates, thus leading to correct geocentric astrometric
coordinates. Transforming these correct geocentric coordinates with
the observer-vector to topocentric coordinates results in the above
mentioned differences.

It is my understanding, that
(1) for astrometric coordinates of the moon only contributions from
spherical aberrations have to be removed from the calculated
coordinates. Aberration of the earth/moon-system has not to be added.
(They would however have to be added to apparent moon coordinates if
they were relevant in the accuracy range of 1", but they aren't.)
(2) the spherical aberration values don't change to the extend of the
observed differences (as mentioned above) when calculated with
topocentric instead of geocentric coordinates. (The orbit velocity of
the earth is about 30km/s compared to the maximal topocentric velocity
of 0.5km/s., thus leading to differences of about 1/60th of the
stellar aberration.)
(3) there seems no programming error to be involved since the
calculation passes through the same routines within the program
providing otherwise correct results.

Where may these differences come from?

Any hints on what may possibly be the cause for those differences are
welcome. Thank you.

Marcel
.

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