Right Ascension zero point
There was a simple but profound problem in the early days of astronomy, which was to establish the 'absolute' position of the stars in the sky. The stars can be measured relative to each other, but then one can only produce a catalog of relative positions. It is possible to pick a star, say Vega, and assign it the coordinates (zero, zero), but this leads to a number of problems such as how to compare positions to other catalogs that used a different method.
A more natural way was to recognize that the rotation of the earth suggests a set of coordinates related to the apparent fixed north rotational pole of the sky. Because the stars, at night, seemed to rotate about the pole, a coordinate that reflects a star's distance from the pole, a sort of 'latitude', gives that coordinate an 'absolute' reference point. This coordinate became known as declination, defined as 90 degrees minus the star's distance from the pole.
In the perpendicular direction, the direction of rotational movement, there is no natural absolute reference point and one is back to picking some star as the reference point in that coordinate ('longitude'). The problem was solved by letting the Sun, and the Earth's orbital motion, determine a spot on the sky that could be used for the stellar 'longitude' reference point. The definition of that longitudinal reference point was the point in the sky where the Sun was located at the spring equinox. This coordinate became known as the 'right ascension' and the reference point, known as the 'First point of Aries', was where right ascension was zero. It was only later found out that this point moves slowly across the sky over the centuries, a process known as precession.
All this was fine, but it creates one essential observational problem: the right ascension zero point is defined by the position of the Sun, but the stars cannot be observed during the day. When the stars appear at night, the Sun is gone, so how to use it as a reference? Tycho found an ingenious solution.
Sun->Venus->Star: Although the stars are not visible during the daytime, the planet Venus can be seen by the unaided eye (telescopes had not been invented yet in Tycho's time) even while the Sun is up. And, Venus can often be seen in the morning or evening sky when some stars are still visible. This allowed Tycho to measure the right ascension of Venus relative to the Sun during the day, and then use that same right ascension (adjusted for the slow orbital motion of Venus) to measure the position of bright stars, thus transferring the right ascension of the Sun to the nighttime stars.
The Sun's right ascension can be found on any clear day through the measurement of the Sun's meridian altitude. See the second illustration on this page. Also, the position of the Sun had been studied for millenia before Tycho, so formulas that gave the Sun's position accurately were available to him. These formulas, formatted as tables of numbers, provided a solar 'ephemeris', but its usefulness depended on the knowledge of time and Tycho's clocks (the best available in 1580) still had poor accuracy.
I decided to try Tycho's methods, but they proved difficult for me due to my poor horizons. I could only observe Venus when it was in the evening western sky (my eastern horizon is blocked by trees) but its evening apparition in 2021 was not particularly advantageous. When the Sun had set far enough for the brighter stars to become detectable by my instrument, Venus was already at a very low altitude, typically below 20 degrees, and sinking fast. I was really only able to get one evening's useful measurements of Antares (alphSco) relative to Venus. I also found that my measurements of the Venus-to-Sun separation angles were noisy and rendered the right ascension transfer unfeasible.
Here is a screenshot from one of my attempts to measure the separation angle between the Sun and Venus. Venus is the small dot near the center of the reticle. The blemishes on the solar disk are almost all dust particles on my pellicle, not sunspots.
Here is a sample of the calculation of alphaSco's right ascension by way of the JPL Horizon's position of Venus on two different days. The September 30 results are off (ra_err) by several arc minutes and rejected as outliers in later analysis. The objects are boxed in blue, the low altitudes in green, the JPL values in orange, and the final measured right ascension (relative to Venus) boxed in red.
Sun->Jupiter->Star: With Venus marginally useless, I turned to Jupiter. Jupiter would not have been available to Tycho's eyes in the daytime, but I found that my instrument could image it. The idea was simply to use Jupiter in place of Venus to transfer the solar right ascension. This was moderately successful, and I was able to obtain Jupiter-star separation measurements on several nights. But this approach had a defect that I didn't appreciate at first, in that Jupiter, an extended object fainter than Venus, was only visible during the day when it was well away from the Sun. When I went to measure Jupiter's separation from the Sun at the time of the transfer operation, it was much closer to the Sun than my earlier observations and the increased brightness of the daytime sky at Jupiter's position made it impossible to find. Thus, I was not able to measure the Jupiter-to-Sun separation angle that I needed for the right ascension transfer.
Here is Jupiter imaged in the daytime. Its altitude was 37 degrees, the exposure time was 2.3 milliseconds, and the aperture is 37 mm.
Here is Jupiter superimposed on the Sun's disk, as seen through the local tree line. It is barely visible in the center of the solar disk.
I had decent luck with Jupiter and its star field. Here is my spreadsheet for getting the stellar right ascensions from the JPL position of Jupiter. The objects are boxed in blue, the altitudes in green, the JPL value in orange, and the final measured right ascension (relative to Jupiter) boxed in red. When these measured right ascensions are compared to the modern catalog values (ra2), the resultant errors are acceptable - on the order of an arc minute or two.
Sun->Star: With neither of these efforts working out as well as I wanted, my last approach was to observe a star in the daytime and do a direct Sun-to-star right ascension transfer. I tried this many times but found, as I had with Venus, that any Sun-to-object measurements that I made turned out to be very noisy and not useable. My guess was that this difficulty arose from my lack of a pair of solar filters that could cover both apertures. I had provided only the direct path with a solar filter option. Because of this, I could not perform the zeroing operation I normally used for pitch (separation) measurements. I could not drive the pitch to zero and get two solar images on the detector.
Here is alphaCMa (Sirius) superimposed on the center of the solar disk. The exposure time is 891 microseconds. There is a small sunspot group on the upper right of the disk, but all other smudges are from the optics.
With this inability to do the right ascension transfers from the Sun, I was forced to use the modern ephemeris positions for Venus and Jupiter to establish their right ascensions, which then enabled me to transfer the offsets to the stars. Tycho did a better job than I did!
The final result of all this effort was an estimate of the actual right ascensions in the provisional catalog, which assumed that the ra of alphaAri was zero. I now had measurements of the offset of several provisional stars relative to modern values of the ra of Jupiter and Venus.
Below is a summary of the ra zero point measurements: the reference object is outlined in blue, the target star in green, the absolute ra of the target star (c3+c8) in purple, and the offset of the provisional ra to the true ra in red. The bottom two numbers in the red column are the mean value of the eight estimates and the standard error in that estimate, all in degrees. The standard error is about one arc minute. The estimated absolute ra of alphaAri is 32.064 degrees (in 2020). This value of 32.064 degrees is to be added to the provisional ras in our provisional catalog to complete the construction of the catalog. The modern value for the ra of alphaAri (precessed to 2020) is 32.08 degrees.
