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    Re: Sun and Moon in the Arctic
    From: Andrés Ruiz
    Date: 2026 Feb 27, 08:04 +0100

    Date: 21 june 2025 --solstice! Height: 8m. Index error included in sights (no further correction). 

    Moon sight:
    UL of crescent Moon
    Hs 10d 50'
    UTC 05:39:02

    Sun sight (below the pole):
    LL of Sun
    Hs 15d 57'
    UTC 05:40:30
    Azimuth: near 000° true


    21/06/2025
    05:39:02 UT1

    Bap = 80.000000 º =  80º  0.0'
    Lap = -80.000000 º = -80º  0.0'

    NAUTICAL ALMANAC
    Moon
    GHA = 325.500740 º = 325º 30.0'
    Dec = 15.306206 º =  15º 18.4'
    SD = 16.3413 '
    HP = 59.9723 '

    ALTITUDE CORRECTION
    Limb: upper
    Ref: SeaHorizon
    Hs = 10.8333 º =  10º 50.0'
    ic = 0.0000 '
    heas = 8.0000 m
    T = 10.0 ºC
    P = 1010.0 hPa
    Hoi = 10.8333 º =  10º 50.0'
    dip = 0.0830 º = 5.0'
    Ha = 10.7504 º =  10º 45.0'
    R0 = 0.0828 º = 5.0'
    f = 1.00
    R = 0.0828 º = 5.0'
    OB = -0.00309740 º = -0.1858'
    HP = 0.9995 º = 59.972'
    PA = 0.97889676 º = 58.734'
    SD = -0.2724 º = -16.3'
    Aug = -0.00088911 º = -0.05'
    SDag = -16.39462922 '
    Ho = 11.3741 º =  11º 22.4'

    21/06/2025
    05:40:30 UT1

    Bap = 80.000000 º =  80º  0.0'
    Lap = -80.000000 º = -80º  0.0'

    NAUTICAL ALMANAC
    Sun
    GHA = 264.675073 º = 264º 40.5'
    Dec = 23.438322 º =  23º 26.3'
    SD = 15.7387 '
    HP = 0.1442 '

    ALTITUDE CORRECTION
    Limb: lower
    Ref: SeaHorizon
    Hs = 15.9500 º =  15º 57.0'
    ic = 0.0000 '
    heas = 8.0000 m
    T = 10.0 ºC
    P = 1010.0 hPa
    Hoi = 15.9500 º =  15º 57.0'
    dip = 0.0830 º = 5.0'
    Ha = 15.8670 º =  15º 52.0'
    R0 = 0.0570 º = 3.4'
    f = 1.00
    R = 0.0570 º = 3.4'
    OB = -0.00000677 º = -0.0004'
    HP = 0.0024 º = 0.144'
    PA = 0.00230545 º = 0.138'
    SD = 0.2623 º = 15.7'
    Aug = 0.00000301 º = 0.00'
    SDag = 15.73883665 '
    Ho = 16.0747 º =  16º  4.5'

    Vector Solution for the intersection of two Circles of Equal Altitude
    Andrés Ruiz González - Navigational Algorithms - http://sites.google.com/site/navigationalalgorithms/

    GP1 0.7949005301338428 0.5463048757497425 0.2639775178400505
    GP2 -0.08514642208582357 0.9135292936227563 0.3977616327640095
    alpha 57.56226862494698
    k1 0.0683653516937601
    k2 0.2402196166571115
    OIc 0.03388981343097536 0.25679598168174744 0.11359706278985801
    l1 0.9591678745992478
    l2 -0.9591678745992478
    GP1xGP2_unit -0.02826159472455019 -0.4012651106102638 0.9155258561452855
    I1(xyz) 0.006782199686243235 -0.1280846216131314 0.9917400523693882
    I2(xyz) 0.06099742717570748 0.6416765849766263 -0.7645459267896721
    I1(BL) 82.63070964504695 -86.96896594578148
    I2(BL) -49.86661255366185 84.56981140477252
    I1 82º 37.8' N 086º 58.1' W
    I2 49º 52.0' S 084º 34.2' E


    Least squares algorithm for n LOPs
    n iterations = 3
    82º 37.8' N 086º 58.1' W

    AstroNavigation.Fix.png

    Fair winds and following seas.
    --
    Andrés Ruiz
    Navigational Algorithms
    http://sites.google.com/site/navigationalalgorithms/

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