R1i2dZddlmZmZmZmZmZmZmZddl m Z m Z m Z m Z mZddlmZe dz ZedZedZed Zed Zed Zed Zed ZedZedZedZedZ d!dZdZdZdZ dZ!egdjD\Z#Z$ d!dZ%dZ&edjDdddddf\Z'Z(Z)Z*Z+d"dZ,dZ-dZ.dZ/d Z0y)#z%Routines that compute Earth nutation.)arraycosdotfmodsinouterzeros)ASEC2RADASEC360DEG2RADtauT0)load_bundled_npygcAz nutation.npzke0_tke1 lunisolar_longitude_coefficients lunisolar_obliquity_coefficientsnals_tnapl_tnutation_coefficients_longitudenutation_coefficients_obliquityse0_t_0se0_t_1cdt|j|||\}}|tz}|tz}||fS)zCReturn the IAU 2000A angles delta-psi and delta-epsilon in radians.)iau2000att_TENTH_USEC_2_RAD)tfundamental_argument_termslunisolar_termsplanetary_termsd_psid_epss X/home/cursorai/projects/iching/venv/lib/python3.12/site-packages/skyfield/nutationlib.pyiau2000a_radiansr&s@ADD"LE5 E E %<r'c 0t|}t|}t|}t|}t|}t|}t|| |z| |zf||z||z|z||zz||z|z||zz f||z||z|z||zz ||z|z||zzffS)aGenerate the nutation rotation matrix, given three nutation parameters. The input angles can be simple floats. Or, they can be arrays of the same length, in which case the output matrix will have an extra dimension of that same length providing *n* rotation matrices. )rrr) mean_obliquity_radianstrue_obliquity_radians psi_radianscobmsobmcobtsobtcpsispsis r%build_nutation_matrixr5,s % &D % &D % &D % &D { D { D 4%$,%$, $;$;%t 3$;%t 35$;$;%t 3$;%t 35 6 77r'c^|tz dz }d|zdz |zdz|zdz |zdz |zdz}|S)aeReturn the mean obliquity of the ecliptic in arcseconds. The caller need only supply a single argument: `jd_tdb` - TDB time as a Julian date float, or NumPy array of floats The formulae used to compute the mean obliquity are based on equations 37 and 39 from: Capitaine et al. (2003), _Astronomy and Astrophysics_ 412, 567-586. @gߧLggg+eS>gb/oi`?g6q'?g? ?kG@g#~֙@)r)jd_tdbrepsilons r%mean_obliquityr:Gsw "A #q(!"'() !'()  ()) () ),5 5G Nr'c|tz dz }t|dd}t|dk(rdnd|df}ddd d d |zz|zz|zz|zztzd |zd ztzz|d<ddddd|zz|zz|zz|zztzd|zd ztzz|d<ddddd|zz|zz|zz|zztzd|zd ztzz|d<ddddd |zz|zz|zz|zztzd!|zd ztzz|d"<d#d$d%d&d'|zz|zz|zz|zztzd(|zd ztzz|d)<d*d+|zz|d,<d-d.|zz|d/<d0d1|zz|d2<d3d4|zz|d5<d6d7|zz|d8<d9d:|zz|d;<d<d?d@|zz|dA<dBdC|zz|z|dD<|tz}t j |}tt|z}|tt|zz }||z}tj |}|tj t|z }|tj t|z }|tz}|S)EaCompute the complementary terms of the equation of the equinoxes. This routine takes a single argument: `jd_tt` - Terrestrial Time: Julian date float, or NumPy array of floats The formulae used are from: Capitaine, N., Wallace, P.T., and McCarthy, D.D. (2003). _Astron. & Astrophys._ 406, p. 1135-1149. Table 3. _IERS Conventions (2010)_, Chapter 5, p. 60, Table 5.2e. (Table 5.2e presented in the printed publication is a truncated series. The full series, which is used here, is available on the IERS Conventions Center website in file tab5.2e.txt.) ftp://tai.bipm.org/iers/conv2010/chapter5/ r7shape)r>rKAgJ{o&%A穤N@?@rmo?Qb 0g@g?g13AgHP %3Aݵ|гfLg!?XLgX@r 縏~Ag%d{A窂QI)g@g(%\0Ag%50A$~{B{?~\gP@˿yAg h",*yOe@!?RĖ0#g~E@3a@Nwh @>@0R6?u@L]@Q t@{"|/?~X |J@ Co?YuT5@ gVM@l%˼@ gj_?@gL@ &z?箶&> )rgetattrr r rrrse1_0rse1_1rrrr)jd_ttrr<faac_termss r%-equation_of_the_equinoxes_complimentary_termsrsds* wA E7B 'E  u"eAh 8B ! !! %- - C3& 'BqE ! !! %- - a#$ %BqE ! !! %- - C3& 'BqE ! !! %- - C3& 'BqE ! !! %- - a#$ %BqEOa//BFOa//BF^a//BF^a//BFma//BFma//BrF|a//BrF|a//BrF}q00A 5BrF#IB  Ac!fnG us1v~G qLG " A w{{3q6""G w{{3q6""G xG Nr'))gTϻ-@gXD@)gR@gbgj@)gF[ ?gx@)g;:@gÇ`[@)g6쮢u@gL@)rTrU)rWrX)rZr[)r]r^)r`ra)rcrd)gJL@rf)gCH@g\lo@)rirjc|tz dz }t||}|}td|j|j}t |}t |} t|td|df} | t|td|df|zz } | t| td|dfz } t| td|df} | t| td|df|zz } | t|td|dfz } |s| | fSt|dddk(r|tztz}n+tt|jtzj}|dxx|zcc<|}td|j|j}t |}t |} | t|td|dfz } | t| td|dfz } | t|td|dfz } | t| td|dfz } | | fS) aCompute Earth nutation based on the IAU 2000A nutation model. ``jd_tt`` - Terrestrial Time: Julian date float, or NumPy array of floats Returns a tuple ``(delta_psi, delta_epsilon)`` measured in tenths of a micro-arcsecond. Each value is either a float, or a NumPy array with the same dimensions as the input argument. Supply smaller integer values for ``fundamental_argument_terms``, ``lunisolar_terms``, and ``planetary_terms`` to trade off accuraccy for speed. r7Nrr rJr<r=)rfundamental_argumentsrrTrrrrrlanomaly_coefficientanomaly_constantrrrr) ror r!r"rrqcutoffargsargcargdpsidepss r%rrs&" wA a!;1gc|jS)z4Deprecated: this is now a method on the Time object.)N)rs r%compute_nutationrys 33Jr'c|j\}}|j}||z}t|j}|t |z|z}|t z |t z |t z dz |t z |t z fS)zADeprecated: these are now computed separately on the Time object.g.@)_nutation_angles_radians_mean_obliquity_radiansrsrrr r )rr#r$mean_obtrue_obrreq_eqs r% earth_tiltr}sz--LE5''GoG;ADDAG CL 7 *E g w0%(2BT2I H eh. 00r')rVr)rV)1__doc__numpyrrrrrrr constantsr r r rr functionsrr_arraysrrrrrrrrrrr&r*r5r:rsrwryrxrr)rrrrrrvrmrnrrr=r'r%rs@+:::::'sN > * en#*+M#N #*+M#N    ")*K"L")*K"L )  ) GJ%(76:gR)./): q;&%>CF ?B$ !$ q1T%S#sC(@  0r'