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Re: Long Term Almanac for navigational stars
From: Rafal O.
Date: 2018 Dec 3, 01:39 -0800

Hello,

Statistical analysis for GHA Aries revealed that all errors are within 2" from the exact values:

==> GHA-Aries-E2000-Y1800-2199-M01.log <==
----------------------------------------
Quantiles: q(0.25: 0.12, 0.50: 0.26, 0.70: 0.39, 0.80: 0.47, 0.90: 0.60, 0.95: 0.71, 0.99: 0.87, 1.00: 1.12)

==> GHA-Aries-E2000-Y1800-2199-M02.log <==
----------------------------------------
Quantiles: q(0.25: 0.13, 0.50: 0.26, 0.70: 0.39, 0.80: 0.48, 0.90: 0.61, 0.95: 0.72, 0.99: 0.87, 1.00: 1.16)

==> GHA-Aries-E2000-Y1800-2199-M03.log <==
----------------------------------------
Quantiles: q(0.25: 0.13, 0.50: 0.28, 0.70: 0.41, 0.80: 0.50, 0.90: 0.62, 0.95: 0.72, 0.99: 0.87, 1.00: 1.12)

==> GHA-Aries-E2000-Y1800-2199-M04.log <==
----------------------------------------
Quantiles: q(0.25: 0.12, 0.50: 0.27, 0.70: 0.41, 0.80: 0.50, 0.90: 0.61, 0.95: 0.70, 0.99: 0.86, 1.00: 1.16)

==> GHA-Aries-E2000-Y1800-2199-M05.log <==
----------------------------------------
Quantiles: q(0.25: 0.13, 0.50: 0.27, 0.70: 0.41, 0.80: 0.49, 0.90: 0.62, 0.95: 0.72, 0.99: 0.89, 1.00: 1.17)

==> GHA-Aries-E2000-Y1800-2199-M06.log <==
----------------------------------------
Quantiles: q(0.25: 0.13, 0.50: 0.27, 0.70: 0.41, 0.80: 0.50, 0.90: 0.62, 0.95: 0.73, 0.99: 0.91, 1.00: 1.18)

==> GHA-Aries-E2000-Y1800-2199-M07.log <==
----------------------------------------
Quantiles: q(0.25: 0.13, 0.50: 0.28, 0.70: 0.41, 0.80: 0.51, 0.90: 0.64, 0.95: 0.74, 0.99: 0.93, 1.00: 1.22)

==> GHA-Aries-E2000-Y1800-2199-M08.log <==
----------------------------------------
Quantiles: q(0.25: 0.13, 0.50: 0.28, 0.70: 0.41, 0.80: 0.50, 0.90: 0.62, 0.95: 0.72, 0.99: 0.90, 1.00: 1.26)

==> GHA-Aries-E2000-Y1800-2199-M09.log <==
----------------------------------------
Quantiles: q(0.25: 0.13, 0.50: 0.28, 0.70: 0.41, 0.80: 0.49, 0.90: 0.61, 0.95: 0.72, 0.99: 0.88, 1.00: 1.15)

==> GHA-Aries-E2000-Y1800-2199-M10.log <==
----------------------------------------
Quantiles: q(0.25: 0.13, 0.50: 0.28, 0.70: 0.41, 0.80: 0.50, 0.90: 0.61, 0.95: 0.70, 0.99: 0.86, 1.00: 1.09)

==> GHA-Aries-E2000-Y1800-2199-M11.log <==
----------------------------------------
Quantiles: q(0.25: 0.13, 0.50: 0.27, 0.70: 0.40, 0.80: 0.49, 0.90: 0.61, 0.95: 0.72, 0.99: 0.88, 1.00: 1.14)

==> GHA-Aries-E2000-Y1800-2199-M12.log <==
----------------------------------------
Quantiles: q(0.25: 0.13, 0.50: 0.27, 0.70: 0.40, 0.80: 0.49, 0.90: 0.61, 0.95: 0.71, 0.99: 0.87, 1.00: 1.14)

Some example:

Sight time: 1855/01/15 18:31:34
Star: Rigel

GHA Aries:
(a) correction for year 1855:
    113:45:48 + 00:07:00 = 113:52:48
(b) increment for hours:
    113:52:48 + 270:44:21 = 384:37:09 = 24:37:09
(b) increment for minutes:
    24:37:09 + 7:46:16 = 32:23:25
(c) increment for seconds:
    32:23:25 + 0:08:31 = 32:31:56

Rigel's SHA:
(a) correction for years (y=-145):
    -(10 * 10 + 10 * 4 + 5) = -(-4329 - 1732 - 216) = -6277 = -(3600 + 2677) = -(-1deg 44min 37sec) = 1:44:37
(b) non-linear correction for 1855:
    +9"
(c) total correction: 1:44:37 + 0:00:09 = 1:44:46
(d) 281:21:32 + 1:44:37 = 283:06:09

Rigel's dec:
(a) correction for years (y=-145):
    -(10 * 10 + 10 * 4 + 5) = -(395 + 158 + 20) = -573
(b) non-linear correction for 1855:
    -11
(c) total correction: -573 - 11 = -584 = -0:09:44
(d) -8:12:39 - 0:09:44 = -8:22:23 = 8:22:23 S

Data returned by Skyfield:
(a) SHA: 283:06:18
(b) dec: -8:22:22

Our tabular method errors were: -9 arcsec for SHA and +1 arcsec for dec.

Sun's GHA:
(a) corrections for years:
    a0 = -391.0
    a1 = +1.8
    correction = -391.0 + 15 * 1.8 = -391.0 + 27.0 = -364.0 = -6.1'
    GHA for 2000/01/15: 177 44.4
    GHA for 1855/01/15 00:00:00: 177:44.4 + (-0:06.1) = 177:38.3

Sun's dec:
(a) corrections for years:
    a0 = -26.0
    a1 = +5.4
    orrection = -26.0 + 15 * 5.4 = -26 + 81 = 55 = +0.9'
    dec for 2000/01/15: -21:17.1
    dec for 1855/01/15 00:00:00: -21:17.1 + 0:00.9 = -21:16.2

Data returned by Skyfield:
(a) GHA: 177:38.4
(b) dec: -21:16.1

Our tabular method errors were: -0.1' for SHA and +0.1' for dec.

The file I attached does not contain data for Sun. The readable form is still under development.

Best reragds,
Rafal

File:
LongTermAlmanac_ROrlik-sample.pdf

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