The SOFA functions are not working correctly – iauAtoc13 and iauIcrs2g / iauG2ic

Good day!

I. Testing of function SOFA.iauAtoc13.
Observation points on the Earth’s surface are being investigated.

Array of observation points –

Longitude – from 0 to 360 with discreteness 10,
Latitude – from -90 to +90 with discreteness 10 –
704 observation points.

At each observation point,
the points of the hemisphere
visible from this observation point are examined –

R – from 0 to 360 with dicreteness 10,
D – from 0 to 180 with dicreteness 10.
704 points of hemisphere.

Summary 704 X 704 = 495 616 points

For each observation point under study
the coordinates of each investigated point of the hemisphere are
taken by the initial test subjects
ICRS coordinates.

Testing.

1. The program SOFA.iauAtco13 –
by the coordinates of the observation point and
ICRS-coordinates of the next point of the hemisphere,
( source ICRS coordinates )
the horizontal coordinates of
this point of the hemisphere are determined.

2. The program SOFA.iauAtoc13 –
the obtained horizontal coordinates are
converted back to
ICRS coordinates
( results )

3. The resulting ICRS coordinates are compared
with the source ICRS coordinates, the
difference between them is recorded in the
corresponding protocol.

Ideally, the difference
between the resulting ICRS coordinates
and the source ICRS coordinates
should be minimal,
due only to the underestimation of atmospheric conditions.

However, the results of the experiment are discouraging –
for the hemispheres of all observation points,
the difference in direct ascension ranges from -360° to 360°,
the difference in declination from -270° to 90° (?).

Below are three ABBREVIATED TABLES,
with the results of calculations rounded to whole
at three observation points –
at the North Pole, at the South Pole and in the London area.

At the North Pole,
the difference across the ENTIRE HEMISPHERE of VISIBILITY is
in right ascent
from -360° at
Longitude = 70, Latitude = 90, R_ICRS_Src = 0, D_ICRS_Src = 90,
to 360° at
Longitude = 240, Latitude = 90, R_ICRS_Src = 360, D_ICRS_Src = 0,
in declination
from -90° to 90°.

NORTH POLE, Longitude = 0°, Latitude = 90°
1 2 3 4 5 6 7 8 9 10 11
1 Ra_ICRS_Src 0 0 0 0 0 0 0 0 0 0 0
2 Dec_ICRS_Src 0 20 40 60 80 90 100 120 140 160 180
3 Ra_Horizont 360 360 0 0 0 171 180 180 180 180 180
4 Dec_Horizont 0 20 40 60 80 90 80 60 40 20 0
5 Ra_ICRS_Res 330 100 100 100 100 289 280 280 280 280 338
6 Dec_ICRS_Res 90 70 50 30 10 0 10 30 50 70 90
7 Ra_ICRS_Delta 330 100 100 100 100 289 280 280 280 280 338
8 Dec_ICRS_Delta 90 50 10 -30 -70 -90 -90 -90 -90 -90 -90

At the South Pole,
the difference across the ENTIRE HEMISPHERE of VISIBILITY is
in right ascent
from -360° at
Longitude = 270, Latitude = -90, R_ICRS_Src = 360, D_ICRS_Src = 90,
to 360° at
Longitude = 270, Latitude = -90, R_ICRS_Src = 0, D_ICRS_Src = 90,
in declination – from -270° to -90°.

SOUTH POLE, Longitude = 0°, Latitude = -90°
1 2 3 4 5 6 7 8 9 10 11
1 Ra_ICRS_Src 0 0 0 0 0 0 0 0 0 0 0
2 Dec_ICRS_Src 0 20 40 60 80 90 100 120 140 160 180
3 R_Horizont 360 360 0 0 0 171 180 180 180 180 180
4 D_Horizont 0 20 40 60 80 90 80 60 40 20 0
5 R_ICRS_Res 33 280 280 280 280 92 100 100 100 100 28
6 D_ICRS_Res -90 -70 -50 -30 -10 0 -10 -30 -50 -70 -90
7 R_ICRS_Delta 33 280 280 280 280 92 100 100 100 100 28
8 D_ICRS_Delta -90 -90 -90 -90 -90 -90 -110 -150 -190 -230 -270

In the London area,
the difference across the ENTIRE HEMISPHERE of VISIBILITY is
by right ascent
from -344° at
Longitude = 0, Latitude = 50, R_ICRS_Src = 360, D_ICRS_Src = 40,
to 328° at
Longitude = 0, Latitude = 50, R_ICRS_Src = 30, D_ICRS_Src = 40,
in declination – from -130° до 50°.

LONDON, Longitude = 0°, Latitude = 50°
1 2 3 4 5 6 7 8 9 10 11
1 Ra_ICRS_Src 0 0 0 0 0 0 0 0 0 0 0
2 Dec_ICRS_Src 0 20 40 60 80 90 100 120 140 160 180
3 Ra_Horizont 360 360 0 0 0 171 180 180 180 180 180
4 Dec_Horizont 0 20 40 60 80 90 80 60 40 20 0
5 Ra_ICRS_Res 280 280 16 100 100 292 280 280 280 280 280
6 Dec_ICRS_Res 50 70 90 70 50 -39 -30 -10 10 30 50
7 Ra_ICRS_Delta 280 280 16 100 100 292 280 280 280 280 280
8 Dec_ICRS_Delta 50 50 50 10 -30 -129 -130 -130 -130 -130 -130

Conclusion.

The SOFA.iauAtco13 program works correctly,
with some minor comments,
the SOFA.iauAtoc13 program DOES NOT WORK CORRECTLY.

II. Testing of functions iauIcrs2g and iauG2icrs

Mutual inverse transformations
a. ICRS coordinates Source ==> Galaxy coordinates ==> ICRS coordinates Result,
Difference = ICRS coordinates Result – ICRS coordinates Source
b. Galaxy coordinates Source ==> ICRS coordinates ==> Galaxy coordinates Result
Difference = Galaxy coordinates Source – Galaxy coordinates Result

Array of testing coordinates –
right ascent – from 0 to 360 with discreteness 10,
declination – from -90 to +90 with discreteness 10 –
704 pairs of coordinate.

Difference by right ascent – from -360° to 360°
Difference by – 0

Conclusion.

The SOFA.iauIcrs2g or/and SOFA.iauG2icrs programs
DOES NOT WORK CORRECTLY.