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    Re: Star positions.
    From: Paul Hirose
    Date: 2013 Jan 05, 12:13 -0800

    Örjan Sandström wrote:
    > Today I tried to cobble together a long term almanac for stars using 2008 as 
    base, this as 2008-2011 was closest quadrennial I had covered by NA (For 
    Aries table).
    Örjan, accuracy is a little better if you use barycentric star
    coordinates with respect to the mean equator. The almanac coordinates 
    (geocentric apparent place with respect to the true equator) are not the 
    best basis for long term corrections because they include the periodic 
    effects of aberration and nutation.
    For example, let's look at the effect of aberration on the geocentric 
    apparent coordinates of Vega:
    80°42.23' +38°47.36' 2008 Jan 0.0 TT
    80°42.16' +38°47.21' 30
    80°42.00' +38°47.11' 60
    80°41.78' +38°47.08' 90
    80°41.56' +38°47.12' 120
    80°41.41' +38°47.23' 150
    80°41.35' +38°47.38' 180
    80°41.40' +38°47.52' 210
    80°41.54' +38°47.63' 240
    80°41.75' +38°47.68' 270
    80°41.97' +38°47.65' 300
    80°42.15' +38°47.54' 330
    80°42.23' +38°47.39' 360
    80°42.23' +38°47.36' 365.25
    The January coordinates are almost identical to your table. But SHA is 
    maximum in that month. By July it's .88' less, then it returns to 
    maximum at the end of the year. On the other hand, declination is near 
    its mean at Jan 0, minimum at day 90, and maximum at 270. In the almanac 
    that's not so easy to see because precession and nutation also affect 
    the coordinates. At .01' precision, even proper motion is noticeable in 
    one year. To eliminate those factors in the above table, Vega, the 
    equator, and the equinox were fixed at their true orientation at Jan 0.
    Because the maximum aberration of any star is only about .3' (great 
    circle), it's reasonable for a long term almanac to ignore aberration. 
    That is, use barycentric or heliocentric coordinates instead of 
    geocentric apparent coordinates.
    It also helps to refer the coordinates to the mean equator, not the true 
    equator. Tha latter causes a periodic variation of SHA and declination 
    due to nutation. For example, here is the barycentric SHA of Vega with 
    respect to both the mean equator and true equator. The difference is due 
    to nutation.
         mean      true  nut.
    80°41.85' 80°41.78' -.07 2008 Jan 0 0h TT
    80°41.34' 80°41.22' -.12 2009
    80°40.84' 80°40.68' -.16 2010
    80°40.33' 80°40.15' -.18 2011
    80°39.82' 80°39.64' -.18 2012
    80°39.31' 80°39.15' -.16 2013
    80°38.80' 80°38.68' -.12 2014
    80°38.30' 80°38.23' -.07 2015
    80°37.79' 80°37.78' -.01 2016
    80°37.28' 80°37.32' +.04 2017
    80°36.77' 80°36.87' +.10 2018
    80°36.26' 80°36.40' +.14 2019
    80°35.76' 80°35.92' +.16 2020
    80°35.25' 80°35.41' +.16 2021
    80°34.74' 80°34.89' +.15 2022
    80°34.23' 80°34.35' +.12 2023
    80°33.72' 80°33.79' +.07 2024
    80°33.21' 80°33.23' +.02 2025
    The table above includes the proper motion of Vega, which amounts to 
    .08' SHA in the 17 years. Nutation affects SHA by about plus or minus 
    .17' over this period. The dominant term has a 19-year cycle, but a 
    30-day table interval would show high frequency nutation components too.
    If you don't remove aberration and nutation from the star coordinates, 
    the error is only a few tenths of a minute (great circle distance). And 
    it's a constant offset - does not increase with time - so perhaps for 
    you this is not significant. It is more important to have the correct 
    rate of change. In the case of Vega, my table (left column) shows that 
    your rate of -.51' / year is correct. I have not checked any other 
    values in your table, however.
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