Binary star astrometry is all about two quantities, angular separation and position angle. In a binary star system, the angular separation is the angle between the two stars subtended on the sky, while the position angle is the orientation of the axis connecting the two stars with respect to north. By convention, north is at 0° and east is at 90°.
Making measurements from a perfect image is easy. Due to the circular aperture of the aberration-free telescope that generated this perfect image, an unresolved star along the optical axis has a point-spread function (the two-dimensional intensity distribution in the image of energy from the star) that is radially symmetric, with a bright central core, and a succession of concentric rings. This pattern is known as an Airy disk (see Chapter 10).
The Airy disk is radially symmetric: there is a point that can be determined to be the centre. If there are now two Airy disks, one from each unresolved star in a binary star system, getting the astrometric information is straightforward - determine the angle and distance of separation in the units of the image, and use knowledge of the scale and orientation of the image with respect to the sky to get astrometric information suitable for publishing.
This scenario changes with the introduction of seeing - short time-scale variations of the image intensity introduced by the atmosphere. If the separation of the two stars is smaller than the size of the seeing disk, the astronomer risks being unable to distinguish between the two stars.
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