The final catalog

The provisional full catalog was assembled from the just-determined primary and secondary provisional catalogs. Also added in was Polaris at the provisional coordinates ra=12.84, dec=89.34. Once the tie to the solar ra was made, then that ra offset could be added to the provisional ras to produce the final catalog. The ra2_err was previewed by adding the modern value of the ra of alphaAri to the provisional ra and then subtracting the modern 2020 ra of the star (c1).

First, the full provisional catalog. The primary and secondary provisional catalogs were concatenated, variables no longer needed (e.g. mdra) were removed, and Polaris was added in to get a provisional catalog of 734 stars. All ra/dec values, even the modern catalog values, were still for the year 2020. Here is a sample from that provisional catalog. The full version of this provisional catalog can be found here.

A final offset from the provisional ra of alphaAri had been measured as 32.064 degrees. This value was added to the provisional ra values in the provisional catalog to give the final estimate of the 2020 right ascensions for the catalog stars. That final catalog can be found here.

Here is a snippet of the final catalog.

Below are the plots for the differences between my catalog and the YBSC, in ra and dec. The standard deviation of the ra errors is 1.4 arc minutes, with a zero point offset of about 1 arc minute. I don't have any explanation for the curvature in the plot. The standard deviation of the dec errors is 0.7 arc minutes, with a zero point error of about 0.3 arc minutes. The dec errors are smaller because I referenced modern catalogs to compensate for mount altitude errors. Outliers have been removed either by eye (e.g. Polaris) or by 3-sigma clipping.

A coordinate-system-free way to look at the catalog accuracy is to ask what the distance error would be between the actual star and the detector center if the telescope were pointed at my catalog position. The sky errors have a mean value of 1.4 arc minutes and a standard deviation of 0.8 arc minutes about that value. Note the excess errors in the plot for stars that pass near my zenith (dec=39 deg).

The catalog is constructed. June 2022.

A few comments about imperfections in the construction of the final catalog.

I used my latitude as determined by my solar observations. It is off by at least 0.01 degrees (0.6 arc minutes) from the GPS value.

I used the YBSC right ascension as my star identifier, modified to avoid collisions between stars at similar ras, and rounded to the nearest 0.01 degree. Thus, there was an inherent 0.005 degree (0.3 arc minutes) error in all my working ra positions.

When I precessed the YBSC to my epoch of 2020 I used a simplified formula and thus the precession was not exact. This surfaced very prominently in the position of Polaris. In the final catalog I recalculated the position of Polaris, using the full precession formulas, but I did not go back and apply full precision to the rest of the stars, so there is an inherent precession error in all my positions.

I did not apply proper motion to the YBSC positions.

I took these shortcuts because I was not trying for maximum accuracy, just enough to allow comparision to Tycho's catalog. The journey was more important than the destination.

Tycho included visual estimates of the magnitudes of the stars in his catalog. I could not do that because my skies are so poor that most of his stars are not visible by eye. So I included the YBSC catalog values so that, for example, interested folks could plot my errors versus magnitude. I could have captured my camera images during each measurement and later used image processing to recover rough magnitudes, but that would have been a very large effort to little avail. I wanted this project to avoid image processing completely.

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