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Re: Long Term Almanac for navigational stars
From: Rafal O.
Date: 2018 Dec 2, 12:45 -0800

Hello,

Few more days while I was working on Long Term Almanac for Sun and here are some statistical analysis. These data depend on an attempt to create LTA for years 1900-2099 and chosen start epoch 2000. As the previous LTA for navigational stars it also base on tabular metod. If one wants to use simple calculator or slide rule to perform one multiplication one can use it as well. For each day of the selected epoch (Y2000) one sees GHA and dec for Sun at 00:00:00. Then one needs to apply one linear correction (here is one multilication than can be avoided by using lookup table) to the tabulated values.

To check if the approach is valid I compare exact data taken from SkyField with the estimated ones. Below I present data for quantiles 25%, 50%, 70%, 80%, 90%, 95%, 99% and 100%. For example for January 90% of GHA error were below 10", for declination it was <12". For all months 90% data were within 0.3' for both GHA and dec. The 90% quantile was 0.4', respectively.

I hope that within few weeks I finish my work and will be able to present some PDF with examples and tables. To make this project not depended on other sources it will need also GHA Aries that is also analyzed.

In summary: looks like that I can provide Long Term Almanac for Sun, GHA Aries and all 57 navigational stars that should be usable for time interval 1900-2100 (and even more). It needs only few lookup in the auxillary tables and needs only additions / substractions.

Best wishes,
Rafal

==> SunLTA-E2000-Y1900-2099-M01.log <==
Quantiles: key(gha):
0.25: 1.84
0.50: 3.86
0.70: 5.81
0.80: 7.16
0.90: 9.60
0.95: 11.81
0.99: 16.95
1.00: 28.03
Quantiles: key(dec):
0.25: 1.27
0.50: 3.20
0.70: 5.70
0.80: 7.84
0.90: 11.22
0.95: 14.02
0.99: 21.52
1.00: 36.41
==> SunLTA-E2000-Y1900-2099-M01-R2-v2.log <==
Quantiles: key(gha):
0.25: 1.59
0.50: 3.44
0.70: 5.51
0.80: 6.79
0.90: 8.77
0.95: 11.05
0.99: 14.36
1.00: 18.54
Quantiles: key(dec):
0.25: 1.08
0.50: 2.53
0.70: 4.45
0.80: 6.12
0.90: 8.33
0.95: 10.64
0.99: 15.67
1.00: 21.05
==> SunLTA-E2000-Y1900-2099-M02.log <==
Quantiles: key(gha):
0.25: 2.02
0.50: 4.61
0.70: 7.55
0.80: 9.63
0.90: 12.73
0.95: 15.40
0.99: 20.33
1.00: 29.98
Quantiles: key(dec):
0.25: 1.32
0.50: 3.47
0.70: 6.06
0.80: 8.09
0.90: 11.55
0.95: 14.45
0.99: 22.46
1.00: 35.10
==> SunLTA-E2000-Y1900-2099-M03.log <==
Quantiles: key(gha):
0.25: 1.96
0.50: 4.17
0.70: 6.78
0.80: 8.79
0.90: 11.98
0.95: 14.86
0.99: 21.81
1.00: 37.81
Quantiles: key(dec):
0.25: 1.86
0.50: 4.71
0.70: 8.43
0.80: 11.30
0.90: 15.68
0.95: 19.61
0.99: 29.06
1.00: 43.91)
==> SunLTA-E2000-Y1900-2099-M04.log <==
Quantiles: key(gha):
0.25: 1.63
0.50: 3.58
0.70: 5.54
0.80: 6.88
0.90: 9.34
0.95: 11.48
0.99: 16.92
1.00: 27.22
Quantiles: key(dec):
0.25: 1.71
0.50: 4.25
0.70: 7.68
0.80: 10.32
0.90: 14.35
0.95: 18.12
0.99: 26.76
1.00: 38.96)
==> SunLTA-E2000-Y1900-2099-M05.log <==
Quantiles: key(gha):
0.25: 1.61
0.50: 3.92
0.70: 6.21
0.80: 7.74
0.90: 9.95
0.95: 11.93
0.99: 15.49
1.00: 20.34
Quantiles: key(dec):
0.25: 1.45
0.50: 3.66
0.70: 6.62
0.80: 8.99
0.90: 12.49
0.95: 15.76
0.99: 23.60
1.00: 35.49
==> SunLTA-E2000-Y1900-2099-M06.log <==
Quantiles: key(gha):
0.25: 2.71
0.50: 5.91
0.70: 9.72
0.80: 12.71
0.90: 17.55
0.95: 22.40
0.99: 32.42
1.00: 49.47
Quantiles: key(dec):
0.25: 0.40
0.50: 0.91
0.70: 1.52
0.80: 1.99
0.90: 2.78
0.95: 3.54
0.99: 5.90
1.00: 10.32
==> SunLTA-E2000-Y1900-2099-M07.log <==
Quantiles: key(gha):
0.25: 2.21
0.50: 4.86
0.70: 7.33
0.80: 9.20
0.90: 12.31
0.95: 15.48
0.99: 23.17
1.00: 39.81
Quantiles: key(dec):
0.25: 1.13
0.50: 2.84
0.70: 5.08
0.80: 6.74
0.90: 9.50
0.95: 12.00
0.99: 17.92
1.00: 28.12
==> SunLTA-E2000-Y1900-2099-M08.log <==
Quantiles: key(gha):
0.25: 1.87
0.50: 4.22
0.70: 6.36
0.80: 7.80
0.90: 10.31
0.95: 12.58
0.99: 18.44
1.00: 30.58
Quantiles: key(dec):
0.25: 1.60
0.50: 4.02
0.70: 7.20
0.80: 9.55
0.90: 13.59
0.95: 17.11
0.99: 25.64
1.00: 40.28
==> SunLTA-E2000-Y1900-2099-M09.log <==
Quantiles: key(gha):
0.25: 2.24
0.50: 5.02
0.70: 8.19
0.80: 10.55
0.90: 14.27
0.95: 17.85
0.99: 25.82
1.00: 42.02
Quantiles: key(dec):
0.25: 1.61
0.50: 3.75
0.70: 6.63
0.80: 8.97
0.90: 12.48
0.95: 15.81
0.99: 24.03
1.00: 38.40
==> SunLTA-E2000-Y1900-2099-M10.log <==
Quantiles: key(gha):
0.25: 2.36
0.50: 5.32
0.70: 8.48
0.80: 10.94
0.90: 14.68
0.95: 18.14
0.99: 25.41
1.00: 38.06
Quantiles: key(dec):
0.25: 1.71
0.50: 4.13
0.70: 7.17
0.80: 9.73
0.90: 13.61
0.95: 17.25
0.99: 26.90
1.00: 42.86
==> SunLTA-E2000-Y1900-2099-M11.log <==
Quantiles: key(gha):
0.25: 1.56
0.50: 3.50
0.70: 5.46
0.80: 6.89
0.90: 9.00
0.95: 10.52
0.99: 13.56
1.00: 21.58
Quantiles: key(dec):
0.25: 1.43
0.50: 3.49
0.70: 6.17
0.80: 8.24
0.90: 11.74
0.95: 14.77
0.99: 23.25
1.00: 38.31)
==> SunLTA-E2000-Y1900-2099-M12.log <==
Quantiles: key(gha):
0.25: 2.43
0.50: 5.23
0.70: 8.40
0.80: 10.93
0.90: 15.17
0.95: 19.58
0.99: 29.26
1.00: 51.14
Quantiles: key(dec):
0.25: 0.50
0.50: 1.05
0.70: 1.65
0.80: 2.08
0.90: 2.82
0.95: 3.66
0.99: 6.59
1.00: 13.05

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