R1idZddlmZmZmZmZmZmZmZm Z m Z m Z m Z m Z mZmZddlmZmZmZmZmZmZmZmZmZddlmZeez Zddez z ZeezZdZddZ d Z!d Z"dd Z#d Z$d Z%y)z2Formulae for specific earth behaviors and effects.)absarcsinarccosarctan2arrayclipcosminimumpisinsqrttanwhere zeros_like) AU_MANGVELDAY_SDEG2RADERAD"IERS_2010_INVERSE_EARTH_FLATTENINGRAD2DEGT0tau)dots?ct|}t|}t|}dt||z||ztzzz }t|z}t |z|z} t |z|z} dt z|z|z} t| } t| } | |z}|| z}|| z}t|||| |zzf}ttzt| ||fz}||fS)zDDeprecated conversion from lat,lon,t -> GCRS; neglects polar motion.rg.@) rr r r one_minus_flattening_squaredearth_radius_aurrrr)latitude longitude elevationgastzerosinphicosphicsachashstloclsinstcosstacacsstaccstposvels U/home/cursorai/projects/iching/venv/lib/python3.12/site-packages/skyfield/earthlib.pyterrar4s d D ]F ]F d6F?F?%AABC CA$q(A A  )C A  )CG^d "Y .F KE KE vB JE JE tcFl23 4C 5.55&%!67 7C 8Oc|\}}}t||z||zz}t||dtz|zz tz tztz }t||}t t z } dtz } d| z| | zz } d} d} | |krL| dz } dtd| t|dzzz z } t|| | z| zt|zz|}| |krL|t|z | | zz t z}|||fS)zDDeprecated conversion from GCRS -> lat,lon,t; neglects polar motion.rg@rr) r rrr rrrrr r )xyz_aur# iterationsxyzRlonlatafe2iC elevation_ms r3 reverse_terrarF,s GAq! QqS1Q3YA 1a=2<$. . 3s :R ?C !Q-C t A 00A Q1B A A j. Q $sR3s8s?334 4a!a%"*s3x//3 j.CLAE)T1K [  r5c,tt||}tt||}ttt|z d}t |z }t||||zz }t |dd}t|}||z tz}t |z |z } || fS)a(Determine the angle of an object above or below the Earth's limb. Given an object's GCRS `position_au` |xyz| vector and the position of an `observer_au` as a vector in the same coordinate system, return a tuple that provides `(limb_ang, nadir_ang)`: limb_angle Angle of observed object above (+) or below (-) limb in degrees. nadir_angle Nadir angle of observed object as a fraction of apparent radius of limb: <1.0 means below the limb, =1.0 means on the limb, and >1.0 means above the limb. r) r rrr rr rrr) position_au observer_audisobjdisobsapradzdlimcoszdzdobj limb_angle nadir_angles r3compute_limb_anglerS@s"${K0 1F ${K0 1F 7?V3S9 :E JE k *fvo >E c "E 5ME%-7*J:&K { ""r5ct|j|j}|jtz |jzdz }dd|zdz |zdz |zdz|zdz|zz}|dz |d zzd zS) zCCompute Greenwich Mean Sidereal Time (GMST) in hours at time ``t``.g@g5&\R?g^cg%@i>gw$>gd3,C?g(@g^@g8@)earth_rotation_anglewhole ut1_fractionr tdb_fraction)tthetasts r3 sidereal_timer\ms !!.. 9E 2 &'1A 1 $#$ % #$ % $% %  $%  %%B L54< '4 //r5cHdd|tz |zzz}|dz|dzz|zdzS)zReturn the value of the Earth Rotation Angle (theta) for a UT1 date. Uses the expression from the note to IAU Resolution B1.8 of 2000. Returns a fraction between 0.0 and 1.0 whole rotations. gr'̄ ?gU擛mf?r)r)jd_ut1 fraction_ut1ths r3rUrUs: .&2+ 2LM MB Hv| #l 2c 99r5cdt|d|dzz ztzz }|d|z|dzz z}td|k|dkz|dS) zGiven an observed altitude, return how much the image is refracted. Zero refraction is returned both for objects very near the zenith, as well as for objects more than one degree below the horizon. go'?g= ףp=@g@gQ?gq@rHgyV@)rrr) alt_degrees temperature_C pressure_mbarrds r3 refractionrhs^ 3 dkC.?&@@GKLLA TM !]U%: ;3 GGr5cv|} |}|t|||z}t||z jdk}|r |S7)zEGiven an unrefracted `alt` determine where it will appear in the sky.giUMu>)rhrmax)rcrdrealtalt1 convergeds r3refractrnsM C JsM=IId O'')V3   J r5N))rb)&__doc__numpyrrrrrrr r r r r rrr constantsrrrrrrrrr functionsrrone_minus_flatteningrr4rFrSr\rUrhrnr5r3rvs8CCCCNNN+S#EEE36JJ<!(*#Z0(: H r5