It's been about a decade since I've done any celestial observations, and at that time I was using a manual total station with a solar filter. Very simple.
A couple of years ago, I bought a Wild T-2 and that really got me interested in doing celestial observations again. I observed the Sun on Sunday. One thing I found out is that I need to develop better skills at reading the circle. I had several observations that were off by 10' because I didn't read the scale correctly. Since it was my first field use of the T-2, I wasn't too upset by this. I'm sure that as I practice, I'll be able to read the scale quickly and accurately and be able to reflexively use the adjustment knobs without having to hunt for them.
I did two sets of 8 observations (four observations in face 1 and four observations in face 2)
I used the USNO application, and as Ashton commented, I simply had the application determine the azimuth of the Sun at the UTC for each of my observations. Eventually I'll develop a program to perform the calculations, but for the first few times, I wanted to be able to quickly reduce the observations to see if my field procedures and equipment were proper. As discussed above, the semi-diameter of the Sun must be applied (since I was using trailing edge by projection onto a white sheet of paper, watching for the vertical crosshair to disappear). This required a few steps, but ultimately appears to have given good results.
My first set of eight observations gave an azimuth to target of 7°08'23.7" with an extreme spread of 24.7" and a standard deviation of 9". One of my observations was off by 20' and another by 10', almost certainly from misreading the circle.
My second set of eight observations gave an azimuth to target of 7°07'57.5" with an extreme spread of 25.5" and a standard deviation of 8". I had four observations that were off by 10', almost certainly from misreading the circle.
So the difference between the average of the two sets is 26.2".
As I said before, the instrument is a Wild T-2 (direct reading to 1 arc-second) with an erect image. I was sighting the strobe on a radio tower that is about 7,000' away. I used my cell phone with an GPS app that gives UTC for time and used a stopwatch to clock each pointing. I'm hoping to incorporate a shortwave radio for time in the near future. Position was determined by the same cell phone GPS app. As mentioned, pointing was accomplished by projecting the image on a white sheet of paper on a clipboard, a method that works well for theodolites but not for total stations. I know my sighting of the Sun needs improvement. Catching the crosshair on the trailing edge felt a little loose.
Even though I had some decent consistency in the two observations, I still wasn't sure if they were accurate or if I had some large bias in my results, so early this morning I took my robot (GeoMax Zoom 95, with 2 arc-second accuracy) out and did observations on Polaris. One problem that I encountered is that I don't think my robot has an illuminated crosshair. I worked around it by indirectly shining a flashlight into the objective lens. This worked well, except that it required the use of my hand, which was also busy holding the stopwatch while the other hand manipulated the horizontal and vertical motion knobs.
I was pleased with my results. I turned one set of eight observations (four in face 1 and four in face 2). The average azimuth was 7°07'10.3" with an extreme spread of 25.8" and a standard deviation of 9". I was turned to the same strobe that I used in the day-time Solar observations. I say it was the same strobe, the day-time strobe is white and the night-time strobe is red, but I'm pretty sure it's the same housing and reflectors.
So my azimuths thus far are 7°08'23.7", 7°07'57.5, and 7°07'10.3". This is a pretty ugly spread, but there don't appear to be any large-scale errors. I'm sure the consistency will improve as I continue to practice.
I'm looking forward to attempting a celestial resection to determine Latitude and Longitude. I'd never heard of this process before, but it's based on the vertical angles observed to a pair of stars. The vertical angle needs to be extremely precise and atmospheric refraction must be accounted for. To test, I observed the vertical angles of Polaris while I was pointing so I could compare to the computed position of Polaris given by the USNO app to see how they compared.
To see how the vertical angle from both face 1 and face 2 would average, I noted the difference of the observed altitude to the face 1 observations to the computed altitude from USNO, and the difference in the face 2 observations to the computed altitude from USNO. Face 1 was -8.4" on average from the computed altitude. Face 2 was +7" on average from the computed altitude. This would suggest that the average of the eight altitude observations were different from the computed altitude by -1.5". From what I've read, using a 1-second instrument should yield a latitude and longitude within 2 or 3 arc-seconds with the resection method. It looks like I might be able to do just that.
I taught a course in Geodetic Astronomy at the University of New Orleans in the early 1980s. I found the course and Lab pretty easy to conduct and students were able to follow with success when I introduced the simple programmable calculator functions based on Jean Meeus. We used the old Smithsonian Astrophysical Observatory (SAO) Star Catalog and compared it to the (at the time) FK-4 Apparent Places of Fundamental Stars. Observations and calculations were easy, almost trivial. We were using one-second theodolites and one zero-point one-second theodolite (BC-4). All that old gear is now taken out once every other year for a single Lab at LSU ... whenever I get enough students for the course to "make" sufficient enrollment. I don't bother with the old HP-41CV software anymore, but that sure made it an easy task, way back then. Guess it could be resurrected nowadays with the HP41 software for iPhones ... If you restrict yourself to stars, all you need is Meeus and a Star Catalog and you'll be good to better than one arc second. The current "Explanatory Supplement to the Almanac" will work also, if you're not of the faint of heart. Meeus just cuts to the chase.
One important item that is often overlooked when using an older instrument is mislevelment, or more properly the inclination of the standing axis. Newer instruments that have dual axis compensation greatly minimize this effect. This is NOT corrected by D-R. It is amplified on steeper sights (i.e. polaris
The T2 that I have has a compensator which makes it easy to either level up very accurately or be able to apply a correction. I explain this in a paper I wrote many years ago (1997). Here is a link... https://rpls.com/?attachment=1614808&document_type=document&download_document_file=1&document_file=107
From the manual...
The Stellarium app (Windows, Mac, Linux, phone, web) will provide ephemeris for most of the celestial objects (over 600,000).
