Meridian altitude measurements

Meridian measurements were fairly direct - they were the angle of the altitude axis when the centered star being tracked passed through az = zero or 180 degrees. If the crossing was at az = 0 then the star was north of the zenith. If the crossing was at az = 180 then the star was south of the zenith.

At the start of my serious data collection, the meridian stars arrived rapidly, so rapidly that the data collection became almost a computer game. 700+ stars over 360 degrees gives an average separation of half a degree in right ascension. The Earth rotates a half degree in 2 minutes of time. This is enough time for the scope to slew to the next star, but the stars are not distributed so evenly. Here is a histogram of the ra separations of the stars in Tycho's catalog:

Only a third of the stars are separated by half a degree or more. 157 stars have ras within 0.1 degree of each other. The Earth rotates 0.1 degrees in 24 seconds, not much time to slew and center! I often had to miss a star in order to get the scope to the next star after that one, hoping to catch the missed star on another night. The meridian passage of a star happens only once in a night, so there is no going back the same night to pick it up. Worse is the need to make a long slew in az, along with the shorter slew in alt, to get to a star that passes north of the zenith if the previous star was southerly. I would sometimes break the meridian stars for a night into two groups, those north-of-the-zenith and those south-of-the-zenith, because there would be no need for the long az slews. Later, as I accumulated more and more altitude measurements, the activities moved more to filling in gaps in the data and the hectic pace of the early days slowed considerably.

The other complication for meridian altitude data was the effects of refraction and flexure. Here is a plot of the altitude data for stars south of the zenith on one night. If refraction dominated, then the altitude errors would be largest for the stars at the lowest altitude. Here the opposite was true. This meant some other effect was in play. I expect, but can't be sure, that it was flexure in the optical train. I tried some lab experiments, adding weights to various parts of the scope tube, but wasn't able to convince myself that I had identified the culprit.

The fit here is a simple parabola, but other nights showed different corrections were needed, so I wasn't able to develop a stable flexure model. After the fit is subtracted, the system noise level becomes visible. The residuals to the fit all fall within one arc minute (0.016 deg), and the standard deviation for the 72 points is 0.006 deg (20 arcsec). I had to go through this fitting process for every night of data, and the northerly stars sometimes required a separate fit of their own.

My ability to make meridian altitude measurements thus falls short of what Tycho was able to do with his multiple instruments 400 years ago. I had to fall back on current star catalogs to take out my instrument error, an option not available to Tycho.

The actual tedious measurement technique can be sampled here, with this video.

At the end of data collection, I condensed the altitude data from the list of all measurements to produce a list of all the stars observed, along with their averaged altitude and the standard deviation of those measures. This is then input to the final catalog assembly process, where it is integrated with the separation data. The condensed meridian altitude list can be found here. This list is very succinct. It contains only the 2020_ra (which is used as the ID of the star), number of altitude measurements, the average altitude, and the sigma. No other star info. In the 'nalts' column there is the occasional '-1' indicating a zenith star, for which there are no directly measured altitudes. The altitude information comes from the zenith star recovery effort mentioned on an earlier page.

The list of stars (here) was later used as a look-up table to find the name of the star, its modern catalog magnitude and declination, and to guide the integration of this altitude data into the catalog formation.

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