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Hello,

    Few weeks ago I posted few mails about Pub 249 Vol 1 for epoch 2020. This tables were recalculated and printed with 0.1' and 0.1° accuracy for Hc and Zn, respectively. I also presented method to apply some corrections if i.e. SHA, declination or even AP latitude changes. There were some discussion whether such tables are needed with such accuracy. One of the remark was that it needed an additional information about how SHA and declination changes between the chosen epoch and the sight time.

    This led me to consider how one can correct such values. In fact I was wondering if we can provide an easy to use Long Term Almanac for selected stars. The goal was that it bases only on few lookup tables, no multiplication, no divisions. Only addition and substractions. The resulting accuracy should be as good as possible (below 0.3') and such LTA should lasts for very long period of time.

    I made analysis of SHA and dec using python. Firstly with pyephem, then by skyfield (using JPL de435 data). Here I present some example:

1855/01/15 Rigel
epoch: 2000
d(year) = 145

SHA:
Corrections due to -145 years (d1):
4329+1732+216=6277

Corrections due to non-linear effects (d2):
6277-2=6275

Corrections due to Earth's nutations:
6275-(-11)=6286 arcsecons = 3600 + 2686 = 1°44'46"

Initial value for 2000/01/15:
281°21'32"

Corrected value for 1855/01/01:
281°21'32" + 1°44'46" = 282°65'78" = 283°06'18"
JPL de435 returns +283°06'19", error or 1 arcseconds.

From this daily pages (https://www.esauboeck.com/images/1855.jpg), see https://www.esauboeck.com/Bowditch.html
I get RA 5h07m34.23s that corresponds to 283°06'27". See, also how error for SHA and dec behave with time.

For this 400 years long time interval errors' quantiles are as follows:

Quantiles:
SHA |      25% |      50% |      75% |      85% |      95% |      99% |     100%
  d3 |     0.23  |     0.45  |     0.80   |     1.11   |     1.75 |     2.79 |     3.79
dec |      25% |      50% |      75% |      85% |      95% |      99% |     100%
  d3 |     0.11 |     0.24 |     0.41 |     0.50 |     0.67 |     0.83 |     0.99

For SHA in 95% of cases one gets error below 2", for declination: <1". If one decides to work only with i.e. 100 years time interval then these two page long entries for one star would fit into one.

Best regars,
Rafal