Measurements of double stars made with an altazimuth mounted telescope are subject to the same errors as those made with an equatorially mounted one. However, additional errors can be introduced in converting the zenithal position angle to the position angle. The observer's latitude and the equatorial coordinates of the star are required to calculate the paral-lactic angle. The accuracy to which these are known determines the accuracy to which the parallactic angle can be calculated and in turn sets a limit on the accuracy of the position angle.
The errors in the parallactic angle would be negligible if the zenithal position angle was timed accurately and if the latitude could be determined accurately (perhaps from an accurate survey map or a GPS). Furthermore, precessing the right ascension and declination of the star from the catalogue positions would ensure accurate values for the coordinates of the star.
The separation, of course, will not be affected by these factors. Neither will the position angle if a mechanism that compensates for field rotation (a field de-rotator, as one manufacturer calls it) is fitted to the telescope. However such a compensating mechanism would, as it rotates, cause a right-angled eyepiece holder to "fall over", placing the eyepiece at an awkward angle. This would not be a problem if a right-angle eyepiece holder was not used, such as when viewing straight through the telescope or using a camera.
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