Update on the prediction for the relative positions of the binary star Xi Bootis

In my previous post I described a program to calculate the relative positions of a binary star for any given date. Using this program I can now verify the prediction that I had obtained previously using Roger Wesson's online calculator (or perhaps, more honestly, I can ensure that my code is performing the same as Roger's). Using the parameters for the Xi Bootis in that previous post Roger's utility predicted that separation and PA of Xi Boo on the 1st May 2024 (2024.333) was 4.81 arcseconds and 289.8 degrees, respectively. Running my code using the same input values I get that the PA is 289.8163749 degrees and the separation is 4.814400629 arcseconds which agrees exactly with Roger's results to the same number of decimal places as he quotes.

To make sure that my program works in a wide variety of cases I have also recomputed the predicted positions of these stars over the period 2024 to 2174 in gaps of 10 years (again refer to my earlier post) and, again, to the same number of decimal places I see no difference between the results of my code and those of Roger's. This is all good!

I have since realised that the BAA produces tables of ephemerides of visual binaries in the BAA Handbook (see page 111 for the 2025 book). I notice that the orbital elements they use come from the Sixth Catalog of Orbits of Visual Binary Stars at the US Naval Observatory. For Xi Bootis (ADS number 9413) they give the following parameters:-

Orbital Period P (years) : 152.9614

Date of periastron T : 1909.6213

Semi-major axis of orbit a (arc seconds): 4.93454

Eccentricity of orbit e : 0.51385

Inclination of orbit to plane of sky i (degrees) : 140.453

Argument of periastron ω (degrees) : 25.492

PA of ascending node Ω (degrees) :168.795

Using these parameters for Xi Bootis in my program for the 1st May 2024 (2024.333) I get that the PA is 290.9 degrees and the separation 4.97 arcseconds (as opposed to 289.8 and 4.81 found previously). This is slightly better in agreement with my observation for this date of 291 +/- 3 degrees and 5.5 +/- 0.4 arcseconds, respectively.

Finally, just to check my results against those of the BAA, using these parameters I get for 2025.0 that the PA is 289.8 degrees and the separation is 4.91 arcseconds. The BAA gets 289.7 and 4.91. For 2026.0 I get 288.2 and 4.82 and the BAA gets 288.1 and 4.82. So the BAA seems off by 0.1 in the PA each time.

All text and images © Duncan Hale-Sutton 2025