Traditional corrections were applied for the inclination of the micrometer, irregularities of the pivots and the micrometer screw, clamp and circle differences, circle diameter corrections, variation of latitude, and refraction, as well as collimation, level, azimuth, and nadir.
Measurements of
the instrumental flexure determined from the horizontal
collimators were made for each transit circle but these exhibited
very large variations. Since a more consistent determination of the
flexure can be determined from the star observations
(Holdenried & Rafferty [1997]),
the flexure determined from the horizontal collimators
was not applied.
Since the formation of the most recent absolute catalog from the Six-inch,
the W1
,
showed that a more consistent determination of the flexure
can be extracted from star observations (Holdenried & Rafferty [1997]),
this method was
tried with the W2
observations. Although excellent results were
obtained from the Six-inch observations, the results from the Seven-inch
were not satisfactory, showing a systematic error that was a function of
zenith distance. The method involved using FK5 stars to solve for corrections
to the flexure and refraction, and using circumpolar stars to solve for a
correction to the latitude. This last step was necessary for an absolute
program such as the W1
;
however, in the case of the
Seven-inch data, it was felt that the below pole observations of the
circumpolar stars were the source of the systematic errors. Therefore,
another method was employed, fitting a cubic spline to reduce the residuals
of all Hipparcos stars but excluding the below pole
observations (which are not necessary for the differential reductions).
This new appoarch gave nearly
identical results for the Six-inch as the other method and
it removed the systematic differences seen in the Seven-inch
observations. For consistency the cubic spline method was used
on both the Six-inch and Seven-inch W2
observations.
Observations were grouped into "tours". Usually two tours
were taken per night, dividing the night in
half between two observers.
Each tour contained determinations of
the collimation, level, nadir, azimuth, and flexure
taken at two to three hour intervals for the nighttime tours.
For the Seven-inch transit circle, azimuth determinations
were made hourly due to apparent motions of the piers.
For each tour, observations were made of selected
groups of stars to determine corrections to the sidereal
time, azimuth, and refraction. In addition,
a subset of stars, following a concept developed by Küstner
and henced
referred to as Küstner stars,
distributed over the entire sky
was observed during each tour to check for nightly
variations of the instrument or atmosphere over large angles. The
IRS were grouped in
zones of 15
of declination and were observed with
FK5 reference stars to allow differential reductions for each tour.
As was explained previously, although
the catalog was planned to be absolute, the IRS were observed
in such a way as to allow differential reductions. Because the
differential reductions could be carried out in almost real-time,
they provided an opportunity to closely
monitor the quality of the observations.
Differential observations also are an effective
method of reducing the random and systematic errors in the data.
The requirement imposed by the even distribution in time and zenith distance of the clock, azimuth, refraction, and Küstner stars as well as the need to choose IRS and their reference stars while maintaining a balance of all observations over the Clamps and Circles necessitated the development of an automatic method of selecting the stars to be observed for each tour. The logical criteria for this Star Selector software were constructed by T. Corbin, while the software and system development was done by F.S. Gauss.
Declination errors | ||||||||||
Six-inch | Seven-inch | Total | ||||||||
Declination | ![]() |
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n | ![]() |
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n | mean | ![]() |
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n |
Range | mas | mas | stars | mas | mas | stars | epoch | mas | mas | stars |
+90 to +85 | 251 | 72 | 97 | 1990.76 | 251 | 72 | 97 | |||
+85 to +80 | 226 | 73 | 265 | 1990.72 | 226 | 73 | 265 | |||
+80 to +75 | 216 | 74 | 435 | 1990.68 | 216 | 74 | 435 | |||
+75 to +70 | 212 | 75 | 577 | 1990.71 | 212 | 75 | 577 | |||
+70 to +65 | 215 | 76 | 736 | 1990.73 | 215 | 76 | 736 | |||
+65 to +60 | 213 | 78 | 874 | 1990.76 | 213 | 78 | 874 | |||
+60 to +55 | 206 | 74 | 1018 | 1990.74 | 206 | 74 | 1018 | |||
+55 to +50 | 209 | 76 | 1156 | 1990.83 | 209 | 76 | 1156 | |||
+50 to +45 | 201 | 74 | 1277 | 1990.80 | 201 | 74 | 1277 | |||
+45 to +40 | 194 | 71 | 1416 | 1990.80 | 194 | 71 | 1416 | |||
+40 to +35 | 200 | 73 | 1533 | 1990.83 | 200 | 73 | 1533 | |||
+35 to +30 | 201 | 75 | 1579 | 142 | 189 | 16 | 1990.76 | 201 | 75 | 1579 |
+30 to +25 | 201 | 75 | 1765 | 210 | 114 | 191 | 1990.80 | 202 | 75 | 1765 |
+25 to +20 | 207 | 76 | 1748 | 227 | 91 | 236 | 1990.82 | 209 | 76 | 1748 |
+20 to +15 | 206 | 77 | 1782 | 219 | 72 | 228 | 1990.80 | 208 | 77 | 1782 |
+15 to +10 | 209 | 81 | 1811 | 218 | 65 | 210 | 1990.82 | 211 | 80 | 1811 |
+10 to ![]() |
201 | 79 | 1827 | 216 | 58 | 244 | 1990.85 | 203 | 78 | 1827 |
![]() ![]() |
194 | 80 | 1820 | 217 | 93 | 1792 | 1991.45 | 215 | 64 | 1822 |
![]() ![]() |
186 | 80 | 1727 | 218 | 87 | 1796 | 1991.58 | 211 | 63 | 1802 |
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183 | 59 | 282 | 227 | 86 | 1825 | 1992.15 | 225 | 84 | 1822 |
-10 to -15 | 179 | 57 | 207 | 220 | 80 | 1829 | 1992.16 | 218 | 80 | 1831 |
-15 to -20 | 173 | 62 | 204 | 223 | 80 | 1842 | 1992.16 | 221 | 79 | 1841 |
-20 to -25 | 173 | 70 | 200 | 221 | 78 | 1701 | 1992.14 | 219 | 77 | 1701 |
-25 to -30 | 165 | 86 | 186 | 221 | 76 | 1596 | 1992.14 | 220 | 76 | 1596 |
-30 to -35 | 124 | 148 | 67 | 217 | 77 | 1787 | 1992.18 | 217 | 77 | 1787 |
-35 to -40 | 220 | 77 | 1832 | 1992.17 | 220 | 77 | 1832 | |||
-40 to -45 | 225 | 78 | 1657 | 1992.25 | 225 | 78 | 1657 | |||
-45 to -50 | 222 | 78 | 1644 | 1992.22 | 222 | 78 | 1644 | |||
-50 to -55 | 222 | 77 | 1329 | 1992.16 | 222 | 77 | 1329 | |||
-55 to -60 | 227 | 79 | 1184 | 1992.27 | 227 | 79 | 1184 | |||
-60 to -65 | 228 | 79 | 1034 | 1992.22 | 228 | 79 | 1034 | |||
-65 to -70 | 235 | 81 | 799 | 1992.25 | 235 | 81 | 799 | |||
-70 to -75 | 247 | 83 | 648 | 1992.21 | 247 | 83 | 648 | |||
-75 to -80 | 266 | 87 | 494 | 1992.26 | 266 | 87 | 494 | |||
-80 to -85 | 275 | 84 | 310 | 1992.30 | 275 | 84 | 310 | |||
-85 to -90 | 298 | 79 | 111 | 1992.23 | 298 | 79 | 111 |
The locations of the two transit circles allowed
nearly 70
overlap in the declinations accessible to
each telescope. For those stars in this overlap region,
the observations were combined in a weighted mean.
The weights (given in Table 5)
were based on the mean standard deviation of a single observation
as a function of zenith distance and were an attempt to account
for the degradation suffered by observations made through large
air masses.
The weighted standard deviation of the mean is given with the position of each star. For the stars observed with both transit circles, the mean positions and their standard deviation of the mean as determined by each instrument are given as well as the weighted mean and weighted standard deviation of the mean of the combined data.
Tables 6 and 7 group
the average standard deviations of a
single observation, the average standard deviation of the mean,
and the number of stars into five degree zones of declination.
The average standard deviation of a single observation
was close to 200 mas in right ascension and 215 mas
in declination.
The average standard deviation of the
mean position for a star varied by the number of observations.
Since the majority of stars in each zone were IRS, which averaged
six (two on Circle One and four on Circle Two)
observations each, the average standard deviation of the
mean was close to 70 mas in right ascension and 77 mas in
declination. In the declination zone -5
to +5
the
Six-inch and Seven-inch observed the same IRS stars thus doubling the
number of observations each received, and this manifests itself
in a sharp drop in the average standard deviation of the mean.
A few double stars observed by both transit circles showed significant differences. For example, in some cases the image dissector on the Seven-inch transit circle could not split doubles that the observers on the Six-inch transit circle were able to resolve. In those situations, where it was clear that each telescope observed a particular double differently, the observations by one instrument or the other were dropped. Double stars outside the overlap zone for the two telescopes, of course, can not be compared in this way and may have undetected errors in their positions.
The purpose of the daytime observations of the Sun, Mercury, Venus, Mars, and bright stars was to create an absolute catalog tied to the dynamical reference frame. Because these observations were not necessary for the link to the ICRF and the quality of these observations makes it difficult to adjust them to the nighttime system, the daytime observations were not reduced.
Additional phase corrections | ||||
Mars | - | Six-inch | - |
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- | - |
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||
- | Seven-inch | - | ![]() |
|
- | - |
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||
Jupiter | - | Six-inch | - |
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- | - |
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||
- | Seven-inch | - |
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|
- | - |
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||
Saturn | - | Six-inch | - |
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- | (limb obs) | - | none | |
- | Six-inch | - | none | |
- | (ring obs) | - | none | |
- | Seven-inch | - | none | |
- | - | none |
The same corrections that were developed for the observations of the stars also were applied to the nighttime planetary observations. It is necessary to apply additional corrections to the observations of most of the planets due to their orbital motions, appearances, and distances. These additional corrections must be calculated using data from an ephemeris. For the major planets, ephemeris data from JPL's DE405 ([1998]) were used, and for the minor planets, USNO (Hilton [1999]) provided the ephemerides.
Corrections for orbital motion were applied to bring the mean,
measured position into coincidence with the meridian.
![]() |
(1) | ||
= | ![]() |
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(2) | ||
= | ![]() |
||
where:
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= | ![]() |
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Declinations were corrected for horizontal parallax using the following:
![]() |
(3) | ||
= | ![]() |
||
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= | ![]() |
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= | ![]() |
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Corrections for the visual appearance of each solar system object were based on their appearance in the transit circle and the method of measurement used.
The Seven-inch, observing with the image dissector, used digital centering algorithms developed by Stone ([1990]). Changes to these algorithms have caused the observations of Mars, Jupiter, and Saturn made between 1987 and 1992 to be dropped. The algorithm also had difficulty with Saturn as the rings tilted edge on during the last year of the program and these observations were also dropped. For Uranus, Neptune, and the minor planets the center of light was observed.
The Six-inch, observing visually, dealt with the planetary objects as follows:
Mars - The four limbs were observed for all the nighttime
observations, except for three when the center of light was taken.
Corrections for phase were applied using:
![]() |
(4) | ||
= | ![]() |
||
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|||
and
![]() |
(5) | ||
= | ![]() |
||
where:
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= | ![]() |
|
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= | ![]() |
|
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= | ![]() |
|
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= | ![]() |
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q | = | ![]() |
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Q | = | ![]() |
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i | = | ![]() |
|
Minor Planets - No visual appearance corrections were applied as all presented point source images. Jupiter - The four limbs were observed. Corrections for phase were applied using the same equations as were given for Mars. Saturn - The four limbs of Saturn were observed about 65% of the time, otherwise the edges of the rings were taken. Even though in previous catalogs no phase corrections were applied to the observations of Saturn, plots of the (O-C)s from the limb observations showed a systematic offset symmetrical around oppositions indicating the need for such an adjustment. The (O-C)s from the ring observations showed no such systematic offsets. Corrections for phase were applied to the limb observations using the same equations used for Mars and Jupiter. Uranus and Neptune - Center of light was observed and no corrections for phase were applied. Plots of the (O-C)s as functions of the phase corrections determined from equations above show systematic offsets symmetrical around opposition even after phase corrections given above were applied. The equations used for the Six-inch data, as well as the algorithms developed for the Seven-inch data, are based on the geometric changes in the appearances of these planets. The failures to account for all the phase effects are likely the result of limb darkening or other illumination effects. Empirically correcting for these residual effects is the cause for some concern in that the effects may be in the ephemeris rather than in the observations themselves. However, the Six-inch results for Saturn were able to clarify the situation when the observations of Saturn's limbs showed the systematic offsets while the observations of the rings did not (no such phase corrections could be determined for the Seven-inch Saturn observations because the algorithm used was fitted to both the limbs and rings). The empirically determined, additional phase corrections for Mars, Jupiter, and Saturn are shown in Table 8.
Copyright The European Southern Observatory (ESO)