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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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©Copr 92-2012 Omar F. Reis - All rights reserved