Calibration Pairs

Table 15.1 lists bright and wide pairs whose position angles and separations can be predicted with sufficient accuracy to calibrate a filar micrometer. The data used for this has been taken from the Observations Catalogue at USNO, courtesy of Dr B. D. Mason. The Catalogue contains all published observations irrespective of accuracy so some of the measures have been excluded from consideration. Sixteen bright pairs have been chosen to cover the north, the equator and the south for all times of year. The southern pairs are considerably less frequently observed and the predicted positions are therefore less reliable.

Although some of these pairs are real, if very slow-moving, binaries the observed arc is less than 5° in most cases and so motion is assumed to be linear. A weighted, least-squares straight line fit to the data has been made in all cases with the weighting being made arbitrarily. It was decided to give micrometer measures a weight equal to the number of nights whilst photographic measures (and also Hipparcos and Tycho measures where applicable) were given a weight of 50. As an example Figure 15.5 shows the observations of Z UMa (= X1744) from around 1820 to the present day, more than 350 in total. The effect of long sets of photographic measures made after 1950 is to dominate the fit but the earlier measures also fit the line reasonably well lending confidence to the predicted positions. In separation, there has been no significant change since observations began.

In each case in Table 15.1 it was first necessary to correct the observed angles for precession, bringing them up to the year 2000.0. The values given in the table for future years have also been corrected for precession to those epochs allowing an immediate comparison to be made with observations.

Figure 15.5. The measures of Mizar in separation and position angle 1820-2000.

Errors of Measurement

When any quantity is measured errors can arise in the process. These can be two kinds. Firstly, random or accidental errors which are caused by natural fluctuation when making, for instance, a number of measurements of the separation of a double star with a filar micrometer. If you take say six readings at each position of the movable wire, the numbers will differ slightly. Taking the arithmetic mean of these numbers yields a figure which can be taken to be a fair representation of what the value being measured should be. This can be converted into an angular separation in the usual way. If the pair being measured is a binary star of known separation then if the same measurement is

Figure 15.5. The measures of Mizar in separation and position angle 1820-2000.

1800

1850

1900 Epoch

1950

2000

Figure 15.5.

(continued)

repeated on several other nights and the subsequent mean values all indicate a greater separation than expected then you may suspect the existence of a systematic error. It may be that the current orbit is not predicting the correct separation for the time of observation but it could also mean that the screw value for the micrometer is not correct. If the screw value is based on a single standard pair then there is room for systematic error to come in - it may be that the separation assumed is not correct. This can be tested by observing other standard pairs to see if the same screw value is obtained. If it is then the binary orbit can be suspected.

This is a particularly interesting and vital area which needs to be considered regularly if micrometric measures are to be regarded as stable and reliable.

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