Proper motion of stars

1) You did not answer the question in the question thread on this website, therefore it expired. I did not receive private email. We discuss Stellarium here.

2) Comparing and testing is important, thanks for some examples. But don't use Stellarium as reference, yet.

3) Excluding refraction correction in Stellarium is of course important, as incorrect reading from the screen may happen. If this source of error can be excluded, we can continue investigating. V0.14.1 was indeed the first version to give (I hope) correct values for ecliptic obliquity and precession.

4) I do not know the algorithms used by CdC or by you. How do the 3 of us compare e.g. against NASA/JPL Horizons? I would assume that this can be used as reference. Can you look this up and add data here?

5) Stellarium (AFAIK; but I did not work on this part) only corrects a linear term of proper motion (please correct me if I am wrong?). If the others correct for space motion, results may differ.

6) Tycho died in 1601. I don't know his catalog in detail, he certainly corrected for precession, did he also give actual observation data from previous years?

Ad 1) OK, now I know how to do it.

Ad 2) I will refrain from using Stellarium as a reference for my investigation.

Ad 3) Refraction is definitely nor an issue. I did not take readings from the screen but read the Dec values from the info section on the screen. As an example, the Dec value of HIP 19849 (o2 Eridani) read from RA/Dec (on date) line is -8 deg -15' -45,0". This value is not affected by change in altitude and is thus independent on refraction.

Ad 4) The basis for my calculations is the Hipparcos-2 catalogue. The DEC values are then corrected for proper motion (linearly) and precessed to the epoch of Tycho's catalogue. The precession formula used is from: Duffett-Smith,P. and Zwart, J.: Practical Astronomy with your Calculator or Spreadsheet, Cambridge, Cambridge University Press (2011), Section 34.
The method used by CdC is described in the link below.

https://www.ap-i.net/skychart/en/documentation/computation_method_and_precision

I am not familiar with the NASA/JPL Horizon system but it seems that this is relates only to solar system objects. I do, however, have a reference for these calculation: Rawlins, D., "Tycho's 1004-star catalog" (PDF). DIO, the International Journal of Scientific History 3 (1), 1993. This article contains RA and Dec values for the entire Tycho catalogue, and Rawlins values are identical to those of CdC within the precision given.

Ad 5) CdC corrects for space motion while mine do not. Still my values are very close to those of CdC (on average 4").

Ad 6) Tycho's 1004 star catalogue was completed in 1598 but he adjusted his celestial coordinates to the end of the year 1600. As he was still using the Julian calendar 10 days must be added to his epoch. He based the catalogue on several thousands of observations. I have made a preliminary study of the accuracy of the observations and it is about 1'.

I hope this clarifies the points raised above.

This question was expired because it remained in the 'Open' state without activity for the last 15 days.

(After receiving private mail by OP to reopen)

I had thought your statement (2) requires no further comment.

I cannot give further comments. Stellarium is not perfect yet. I did not program the stellar catalog and did not investigate the stellar motions so far.

Stellarium was never intended to be used as highly accurate reference, but as a nice visualisation with some (undocumented) omissions in accuracy in a false assumption that speed was more important. I am working on improving that, but this is a long process.

Stellarium is open-source, so please look into the code and improve it. The catalog in DIO should be a valid reference to compare.

See comment #4

Stellarium uses simple linear model for proper motion of stars. Plus we use data from 1991 for stars and this data is not very accurate now and our catalogs do not include radial velocity for stars for correct calculation.