In order to easily observe the changing position of Barnard's star, a large print scale and therefore a long focal length is necessary. An 80-mm f/11 refractor or 90-mm Maksutov is recommended for these photographs. Accurate polar alignment of the telescope is imperative. An 80-mm f/5 refractor can be used but it will take twice as long between photographs to detect appreciable motion in the star.
The afocal procedure for binary star photography is used here. With an 80-mm f/11 refractor, use a 6-mm wide field eyepiece such as Orion Expanse. A 9-mm eyepiece can be used with a 90-mm Maksutov. A 6-mm eyepiece combined with a 2x Barlow lens will work with an 80-mm f/5 refractor. The 90-mm Maksutov has the advantage of a short tube and fewer tracking problems. Since the change in the star's position is primarily in the declination direction, a slight amount of star trailing in the photograph will not obscure its proper motion.
Record the date, time and Julian day of your observation. Take several pictures and choose the best for printing. Before printing, crop the image to 100 mm x 100 mm to enlarge it. This will produce a print scale of about 1 arc second/mm. Save the image on a disk for later use.
Follow the first observation by another about a year later. In this period, Barnard's star will have moved about 10 arc seconds in declination. Use the same printing and cropping procedure you used for the previous photograph. The change in the position of the star should be on the order of 10 mm for the one-year period between the observations. The change can be seen easily by placing a transparent copy of the first observation over a print of the second.
A more quantitative measurement of the proper motion of Barnard's star can be obtained by printing each of the observations on a separate 1 mm x 1mm grid of rectangular coordinate paper. By referring to the grid lines, measure the vertical distance between two widely separated stars of known declination and use it to establish a print scale in arc seconds/millimeter. Then measure the vertical distance between Barnard's star and some other star of known declination. Using this distance and the plate scale, calculate the declination of Barnard's star. Repeat the procedure for the print taken a year later. The difference between the two declinations divided by the Julian day difference will be the proper motion of Barnard's star in declination in arc seconds/year.
References and Additional Reading
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