technical note - the proper motion of the stars Aug/04 - Omar Reis

In July/04 I was informed via e-mail of a possible problem in the Online Nautical Almanac software. The message reported a difference in the celestial position (GHA and declination) for certain stars, specially with early dates ( year 1800 ). The message also pointed to the probable cause of the problem: failure to consider the proper motion of the stars.

I went on to investigate how proper motion of stars (which was not considered in the previous Almanac versions) affected the position of stars. Proper motion of stars ( the moviment of stars in the celestial sphere ) is generally slow. On average, stars move 0.1" / year ( or 10 arcseconds each century ). However, I found that some stars move faster, as Mr. Reed pointed.

A report on the problem ( see below ) was sent to the irbs navigation "NavL" mailing list. The issue affected softwares that use the Navigator celestial engine, including the Online nautical almanac, the Star Finder and Navigator software. Service release version 4.5 of the Navigator software and version 2.6 of the Online Nautical Almanac corrected the problem. The message thread can be found in the irbs Navigation Mailing List of July/04.

Here is the report:

Navigator nautical almanac and proper motion of the stars

In response to Mr. Reed's message pointing the 
problem with star positions in the Online Almanac, 
I have researched the issue. These are my conclusions. 
 
I have applied the proper motion correction to the 
navigation stars ( the 60 listed in the almanac) 
and calculated 3 columns (all results in arc minutes):
 
- RA component of the proper motion (DRA)
- Declination component of the proper motion  (DDec)
- Proper Motion ( vectorial sum of the previous two - Dpm )
 
These proper motion components (or "Deltas") were 
computed between the date of the base almanac 
(epoch 1993.0) and the given epoch. The generated 
tables are included in the P.S below. 
 
In the epoch 1950.0 we have:
 
- Little change ( <=0.1' ) in 40 of the 60 stars. 
- Seven stars have moved more than 0.5'  
- Of these, the most notable are:
 
              Dpm  
Rigil Kent    3.2'
Arcturus      1.6'
Polaris       1.1'
Zuben-ubi     1.1'
 
For these, the proper motion delta is 
indeed significant.
 
For epoch 1800.0 we have:

              Dpm 
Rigil Kent   22.7'
Arcturus      6.5'
Polaris       9.0'
Zuben-ubi     4.5'
 
Large numbers for this early date.
 
For current epoch (jul/2004), the PM
delta for the same stars is:
  
              Dpm
Rigil Kent    0.6'
Arcturus      0.4'
Polaris       0.2'
Zuben-ubi     0.3'
 
Differently from what I used to think,
there is clearly the need to apply
the proper motion correction.
 
I have already fixed the problem 
in the almanac application.
 
Thanks to Mr. Reed, for pointing the 
problem & solution, and thanks to 
Mr. Huxtable, for being so helpful.

Omar Reis


P.S. report data

>>>> 1950 JAN. 1, 2, 3
 STARS        (w/o PM )       (with proper motion )      Deltas
------------------------------   -----------------  ----------------
 Name         SHA      Dec        SHA      Dec      DRA   DDec  Dpm
                 ░  '     ░  '     ░  '     ░  '     '     '     '
 Acamar      315 54.2 S40 30.3  315 54.2 S40 30.3   0.0   0.0   0.0  
 Achernar    336 01.7 S57 29.7  336 01.8 S57 29.7  -0.1   0.0   0.1  
 Acrux       174 03.4 S62 49.0  174 03.4 S62 49.0   0.0   0.0   0.0  
 Adhara      255 49.8 S28 54.0  255 49.8 S28 54.0   0.0   0.0   0.0  
 Albireo      67 49.9 N27 51.0   67 49.9 N27 51.0   0.0   0.0   0.0  
 
 Aldebaran   291 44.0 N16 24.7  291 44.0 N16 24.8   0.0   0.1   0.1  
 Alioth      167 02.1 N56 13.6  167 02.2 N56 13.6  -0.1   0.0   0.1  
 Alkaid      153 36.6 N49 33.4  153 36.4 N49 33.4   0.1   0.0   0.1  
 Al Na-ir     28 43.6 S47 12.7   28 43.7 S47 12.6  -0.1   0.1   0.2  
 Alnilam     276 34.6 S 1 13.8  276 34.6 S 1 13.8   0.0   0.0   0.0  
 
 Alphard     218 42.8 S 8 26.3  218 42.8 S 8 26.3   0.0   0.0   0.0  
 Alphecca    126 51.6 N26 52.6  126 51.7 N26 52.6  -0.1   0.1   0.1  
 Alpheratz   358 33.1 N28 48.9  358 33.2 N28 49.0  -0.1   0.1   0.2  
 Altair       62 54.8 N 8 44.2   62 55.2 N 8 43.9  -0.4  -0.3   0.4  
 Ankaa       354 02.4 S42 35.2  354 02.6 S42 34.9  -0.2   0.3   0.3  
 
 Antares     113 25.4 S26 19.5  113 25.4 S26 19.5   0.0   0.0   0.0  
 Arcturus    146 40.3 N19 24.9  146 39.4 N19 26.3   0.8   1.4   1.6  
 Atria       109 10.9 S68 56.5  109 11.0 S68 56.5   0.0   0.0   0.0  
 Avior       234 37.2 S59 20.6  234 37.2 S59 20.6   0.0   0.0   0.0  
 Bellatrix   279 23.0 N 6 18.5  279 23.0 N 6 18.6   0.0   0.0   0.0  
 
 Betelgeuse  271 52.7 N 7 24.2  271 52.7 N 7 24.2   0.0   0.0   0.0  
 Canopus     264 16.8 S52 39.9  264 16.8 S52 39.9   0.0   0.0   0.0  
 Capella     281 44.7 N45 57.0  281 44.8 N45 57.3  -0.1   0.3   0.3  
 Castor      247 08.6 N32 00.1  247 08.4 N32 00.1   0.1   0.1   0.1  
 Deneb        50 04.6 N45 06.0   50 04.6 N45 06.0   0.0   0.0   0.0  
 
 Denebola    183 22.6 N14 50.9  183 22.2 N14 51.0   0.4   0.1   0.3  
 Diphda      349 43.6 S18 15.7  349 43.8 S18 15.7  -0.2   0.0   0.1
 Dubhe       194 49.6 N62 01.0  194 49.5 N62 01.1   0.2   0.0   0.1  
 Elnath      279 12.8 N28 34.1  279 12.8 N28 34.2   0.0   0.1   0.1  
 Eltanin      91 08.9 N51 29.4   91 08.9 N51 29.4   0.0   0.0   0.0
 
 Enif         34 34.3 N 9 38.6   34 34.3 N 9 38.6   0.0   0.0   0.0  
 Fomalhaut    16 16.4 S29 53.6   16 16.7 S29 53.5  -0.3   0.1   0.1  
 Gacrux      172 54.6 S56 49.9  172 54.6 S56 49.7   0.0   0.2   0.2  
 Gienah      176 41.7 S17 15.7  176 41.6 S17 15.8   0.1   0.0   0.0
 Hadar       149 56.6 S60 07.8  149 56.6 S60 07.8   0.0   0.0   0.0
 
 Hamal       328 54.6 N23 13.7  328 54.8 N23 13.9  -0.1   0.1   0.1
 Kaus Austr.  84 47.7 S34 25.0   84 47.7 S34 24.9   0.0   0.1   0.1
 Kochab      137 18.2 N74 21.2  137 18.1 N74 21.2   0.1   0.0   0.0
 Markab       14 26.2 N14 56.1   14 26.2 N14 56.1   0.0   0.0   0.0
 Menkar      315 04.9 N 3 53.8  315 04.9 N 3 53.8   0.0   0.1   0.1
 
 Menkent     149 04.8 S36 07.8  149 04.4 S36 07.5   0.5   0.4   0.4
 Miaplacidus 221 49.9 S69 30.3  221 49.5 S69 30.4   0.3  -0.1   0.3
 Mirfak      309 48.8 N49 41.4  309 48.8 N49 41.5   0.0   0.0   0.0
 Nunki        76 57.9 S26 21.9   76 57.9 S26 21.9   0.0   0.0   0.0
 Peacock      54 34.8 S56 54.2   54 34.8 S56 54.2   0.0   0.1   0.1
 
 Polaris     335 14.3 N89 01.5  335 16.5 N89 01.5  -2.2   0.0   1.1
 Pollux      244 26.2 N28 09.0  244 25.7 N28 09.0   0.5   0.0   0.5
 Procyon     245 49.9 N 5 20.7  245 49.4 N 5 21.4   0.5   0.7   0.8
 Rasalhague   96 51.1 N12 35.3   96 51.2 N12 35.5  -0.1   0.2   0.2
 Regulus     208 34.3 N12 12.8  208 34.1 N12 12.8   0.2   0.0   0.2
 
 Rigel       281 57.7 S 8 15.3  281 57.7 S 8 15.3   0.0   0.0   0.0
 Rigil Kent  141 03.3 S60 37.2  140 58.0 S60 37.7   5.3  -0.5   3.2
 Sabik       103 07.7 S15 40.0  103 07.8 S15 40.1   0.0  -0.1   0.1
 Schedar     350 35.4 N56 16.0  350 35.5 N56 16.1  -0.1   0.0   0.1
 Shaula       97 27.3 S37 04.4   97 27.3 S37 04.3   0.0   0.0   0.0
 
 Sirius      259 15.9 S16 39.5  259 15.5 S16 38.6   0.4   0.9   0.9
 Spica       159 21.8 S10 54.1  159 21.8 S10 54.1   0.0   0.0   0.0
 Suhail      223 27.4 S43 13.5  223 27.4 S43 13.5   0.0   0.0   0.0
 Vega         81 11.6 N38 44.2   81 11.8 N38 43.9  -0.2  -0.2   0.2
 Zuben-ubi   137 58.8 S15 50.2  137 57.7 S15 50.2   1.1   0.0   1.1
 
 
 
>>>>      1800 JAN. 1, 2, 3
 STARS       (with proper motion)
------------------------------
 Name          SHA      Dec      DRA   DDec  Dpm
                ░  '     ░  '     '     '     '
 Acamar      317 19.4 S41 06.2   0.2  -0.1   0.2 
 Achernar    337 25.3 S58 15.3  -0.6   0.1   0.1 
 Acrux       176 09.7 S61 59.1   0.2   0.0   0.1 
 Adhara      257 18.1 S28 41.4   0.0   0.0   0.0 
 Albireo      69 20.5 N27 31.8   0.0   0.0   0.0 
 
 Aldebaran   293 53.3 N16 07.2  -0.2   0.6   0.6 
 Alioth      168 40.7 N57 02.4  -0.6   0.0   0.6
 Alkaid      155 04.8 N50 18.2   0.6   0.0   0.6 
 Al Na-ir     31 04.8 S47 56.5  -0.6   0.5   0.6
 Alnilam     278 28.7 S 1 19.0   0.0   0.0   0.0
 
 Alphard     220 33.3 S 7 47.0   0.0  -0.1   0.1
 Alphecca    128 26.9 N27 22.7  -0.4   0.3   0.4
 Alpheratz     0 29.8 N27 59.3  -0.5   0.5   0.7
 Altair       64 44.9 N 8 19.7  -1.8  -1.2   1.5
 Ankaa       355 53.4 S43 23.8  -0.9   1.3   1.5
 
 Antares     115 43.6 S26 00.0   0.0   0.1   0.1
 Arcturus    148 22.0 N20 13.0   3.7   6.4   6.5
 Atria       113 10.7 S68 40.8  -0.2   0.1   0.2
 Avior       235 23.0 S58 51.5   0.2  -0.1   0.1
 Bellatrix   281 23.7 N 6 10.9   0.0   0.0   0.1
 
 Betelgeuse  273 54.6 N 7 23.0  -0.1   0.0   0.1
 Canopus     265 06.7 S52 34.8  -0.2  -0.1   0.1
 Capella     284 31.3 N45 48.8  -0.4   1.4   1.4
 Castor      249 31.8 N32 20.4   0.7   0.3   0.5
 Deneb        51 21.2 N44 33.5   0.0   0.0   0.0
 
 Denebola    185 16.8 N15 41.4   1.6   0.4   1.7
 Diphda      351 36.6 S19 05.1  -0.8  -0.1   0.8
 Dubhe       197 07.0 N62 49.9   0.8   0.2   0.8
 Elnath      281 35.2 N28 27.2  -0.1   0.6   0.6
 Eltanin      92 01.0 N51 30.2   0.0   0.1   0.1
 
 Enif         36 24.7 N 8 57.0  -0.1   0.0   0.1
 Fomalhaut    18 20.6 S30 41.4  -1.2   0.5   1.1
 Gacrux      175 00.3 S55 59.3  -0.2   0.8   0.9
 Gienah      178 37.4 S16 25.7   0.5  -0.1   0.4
 Hadar       152 36.8 S59 24.6   0.2   0.1   0.2
 
 Hamal       331 01.9 N22 31.5  -0.7   0.5   0.7
 Kaus Austr.  87 17.0 S34 29.7   0.1   0.4   0.4
 Kochab      137 13.1 N74 58.1   0.4   0.0   0.3
 Markab       16 18.3 N14 07.5  -0.2   0.1   0.1
 Menkar      317 02.6 N 3 18.8   0.0   0.3   0.3
 
 Menkent     151 17.3 S35 23.4   2.1   1.7   2.2
 Miaplacidus 222 13.4 S68 53.2   1.4  -0.3   1.4
 Mirfak      312 30.3 N49 09.9  -0.1   0.1   0.1
 Nunki        79 17.3 S26 33.6   0.0   0.2   0.2
 Peacock      57 31.8 S57 23.6  -0.1   0.3   0.3
 
 Polaris      13 18.4 N88 20.9  -9.7   0.1   9.0
 Pollux      246 43.1 N28 31.3   2.3   0.1   2.2
 Procyon     247 47.0 N 5 45.0   2.3   3.3   3.8
 Rasalhague   98 35.6 N12 41.6  -0.4   0.7   0.8
 Regulus     210 33.7 N12 57.1   0.8   0.0   0.8
 
 Rigel       283 45.8 S 8 25.3   0.0   0.0   0.0
 Rigil Kent  143 32.1 S60 00.8  23.9  -2.2  22.7
 Sabik       105 16.9 S15 29.5  -0.1  -0.3   0.3
 Schedar     352 44.2 N55 26.7  -0.3   0.1   0.2
 Shaula      100 00.2 S36 58.4   0.0   0.1   0.1
 
 Sirius      260 54.5 S16 25.8   1.8   3.9   4.1
 Spica       161 20.5 S10 07.2   0.1   0.1   0.1
 Suhail      224 50.2 S42 36.9   0.1   0.0   0.0
 Vega         82 27.9 N38 35.2  -0.8  -0.9   1.1
 Zuben-ubi   139 58.7 S15 13.1   5.1   0.2   4.5
 
 
 


 

 


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Omar F. Reis - All rights reserved