I was doing some more investigation today, but the above two posts arrived before I finished composing this one. Still, here are the numbers I got with my knocked-up Excel spreadsheet are (with NGP 2000.0 as provided in Dr. G's post of Wed Mar 03, 2004 11:56 pm: R.A. = 12h51.4m, Dec. = +27° 07.7', and also l
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Star RA 2000.0 Dec 2000.0 Alpha 2000.0 Delta 2000.0 Lambda 2000.0 Beta 2000.0
Proxima: 14h 29m 43s -62 40' 46" 217.4291667 -62.6794444 314.0120931 -1.92883518
Sirius: 06h 45m 08.9s -16 42' 58" 101.2870833 -16.7161111 227.3023151 -8.88218738
UV Ceti: 01h 39m 01.3s -17 57' 01" 24.7554167 -17.9502778 175.5772091 -75.69291764
Delta Pavonis: 20h 08m 43.6s -66 10' 55" 302.1811667 -66.1819444 329.8351385 -32.42034218
These numbers agree extremely well with Dr. Ganymede's, but not so well with Grant's. It means Dr. G's equations are now correct, but the input data may be inaccurate.
There's no need to bother with 1950.0 if the star and galactic data are for 2000.0. The only reason we got into precession from 1950.0 was because the equations in Grant's post of Mon Mar 01, 2004 7:10 pm were using 1950.0 galactic data.
By the way, note that Grant's R.A. for UV Ceti is 24.755529°, different from Dr. G's at 24.75541667°, so there's a duff input somewhere...
Otherwise, the funny thing about my differences from Dr. G's numbers is that I made the Excel spreadsheet again earlier today under Win NT 4.0 with Excel 97 and all the numbers were exactly the same as Dr. G's. Now I return to the Excel 2000 spreadsheet I made last night, and I get slight differences (non-identical numbers are Proxima Dec., UV Ceti R.A., UV Ceti Dec., and Delta Pav. Dec.). Which Excel do you use Dr. G? We may have a slight change in the ATAN2() algorithm, or treatment of rounding errors, between Excel's 97 and 2000.
However, I think Grant has the more accurate data. One source of lost accuracy is that that 33° (galactic longtitude of the ascending node of the galactic plane on the celestial equator) was too rounded for 1950.0, and must even change for 2000.0. Also, maybe even the NGP co-ords for 2000 at http://www.projectrho.com/smap04.html
are still not as precise as what Grant is using. I tried tweaking NGP Alpha, Delta and that 33° around the final significant digits, and I find I can get close to Grant's numbers - but an iteration with three inputs is too complicated to succeed quickly. Whatever, those figures I gave in my post of Wed Mar 03, 2004 7:11 pm under "Near Star weirdness" (http://www.shatters.net/forum/viewtopic.php?t=4538
) are definitely wrong, so please ignore them.
Note also those R.A. and Dec. co-ordinates of the NGP in epoch 2000.0 at http://www.projectrho.com/smap04.html
give the NGP and the Galactic Centre, but you'll need that l
= 33° figure instead, and it should be precisely computed. However, I used my spreadsheet to trim l
until the 2000.0 R.A. and Dec. for the galactic centre was Lambda = 0° and Beta = 0° precisely: I found l
1. Dr. G's equations appear to work correctly, just stick consistently to 2000.0 data.
2. There may be slight numerical errors in Excel 97 (?).
3. You need to ensure accuracy of NGP co-ords, GC co-ords and/or l
. If you want arcmin accuracy for Lambda and Beta you'll need more than arcmin accuracy for the inputs.
4. Someone's UV Ceti R.A. is slightly wrong - I think it's Dr. G's.