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A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Star positions.
From: Paul Hirose
Date: 2013 Jan 05, 12:13 -0800
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. --