Project M Separation And Position Angle Of Binary Stars

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Binary stars provide important laboratories for determination of a variety of fundamental stellar properties. The widely-spaced "visual binaries'' are particularly important because we can hope to observe their orbital motion, thereby measuring the star's paths around their common center of mass. That information can be used to determine the masses of the two stars. It is one of the very few unambiguous, direct ways of determining stellar mass. It thus provides an important anchor to sophisticated models of stellar spectroscopy and stellar evolution.

You may have seen diagrams showing well-determined orbital motion of binary stars. Figure 5.4 is a typical example. Considering the long history of binary-star observation, and the fundamental importance of determining their orbits, you may be surprised at how few binary star orbits are considered "well determined''. Astronomy is often seen as a science filled with big numbers, including great mountains of data. I've see diagrams that show the red shift of nearly 1 million galaxies [5]. Over 100,000 binary stars are listed in the latest Washington Double-Star Catalog, but the current Sixth Orbit Catalog of Binary Stars contains fewer than 2,000 "well-determined" binary star orbits.

Even more surprising (to me, at least) is the list of "neglected" binaries. These are star systems with separation >3 arc-sec and brighter than 11th magnitude (hence most are within the range of a careful amateur CCD astronomer) that have not been measured for more than 20 years. The "neglected binaries'' list amounted to over 6,400 star systems, as of this writing [6]. There is room for significant amateur astrometry contributions to this important field!

Your well-taken and processed CCD image of the field containing a double-star can be analyzed by your astrometry software to determine the separation and position angle of a binary pair. You use your processed image and software to determine the RA-Dec position of the primary star of the pair, and then repeat the process to determine the RA-Dec position of the secondary star. These positions allow you (or the software) to determine the separation (p) and position angle (<) of the secondary, relative to the primary.

Since many popular CCD image-processing programs will output the coordinates of the two stars, but will not calculate the separation and position angle, here are

Position Angle Astronomy
Figure 5.4. Example of a "well-determined" binary star orbit. (Used with the kind permission of the United States Naval Observatory)

the necessary equations [7]:

RAP = RA of primary star (in radians)

Dp = Declination of primary star (in radians) RAS = RA of secondary star (in radians) Ds = Declination of secondary star (in radians) The separation is given by

and the position angle is calculated by

Some astrometry software will give the separation and position angle directly, so that you don't have to do the calculations. Check the user's manual of the software that you use.

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