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|
/* obliqui2.cpp: alternative obliquity formulae
Copyright (C) 2011, Project Pluto
This program is free software; you can redistribute it and/or
modify it under the terms of the GNU General Public License
as published by the Free Software Foundation; either version 2
of the License, or (at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
02110-1301, USA. */
/* This file contains some alternatives to the obliquity */
/* formula in 'obliquit.cpp'. That file uses a polynomial */
/* from Meeus' _Astronomical Algorithms_ with excellent */
/* accuracy between -8000 to 12000. See 'oblitest.cpp' */
/* for a comparison of these methods. */
/* Simple cubic polynomial, pretty good over -8000 to +12000: */
double iau_obliquity( const double t_cen);
/* Cubic spline interpolation within values from a file. This can */
/* give values (if you have both of two data files) from -20 Myears */
/* to +10 Myears. (I _assume_ the accuracy is really much worse */
/* than that for very distant dates!) */
double file_obliquity( const double t_cen);
/* Similar to above, but the interpolation is done from an */
/* an in-memory array. This produces identical results to the */
/* 'file' version, but covers "only" -200000 to +200000 years */
/* around J2000. */
double spline_obliquity( const double t_cen);
/* Following is a subset of the obliquity tables from...
http://cdsarc.u-strasbg.fr/viz-bin/Cat?VI/63
Orbital, precessional, and insolation quantities for the Earth from
-20 Myr to +10Myr
Laskar J., Joutel F., Boudin F.
<Astron. Astrophys. 270, 522 (1993)>
=1993A&A...270..522L
The original "prec0n.asc" table spans -20 million years to
the present; "prec0p.asc" covers the present to +10 million years,
in 1000-year increments. I just ripped out the parts from
-200000 to +200000 years; it would obviously be straightforward
enough to grab a larger slice if desired, but I really just
wanted to compare it to other precession methods. */
/* t_millennia obliquity (radians) precession (radians) */
static double obliquity_table[] = {
/* -200.*/ 0.4037885426446118, /* 0.1339510175094548D+01 */
/* -199.*/ 0.4014029192421371, /* 0.1586640230299418D+01 */
/* -198.*/ 0.3992034078913982, /* 0.1834798619105780D+01 */
/* -197.*/ 0.3972336017046813, /* 0.2083884169827716D+01 */
/* -196.*/ 0.3955302089388765, /* 0.2333775580625925D+01 */
/* -195.*/ 0.3941224026372330, /* 0.2584335247084895D+01 */
/* -194.*/ 0.3930314575491552, /* 0.2835413585419945D+01 */
/* -193.*/ 0.3922706668433547, /* 0.3086853604320969D+01 */
/* -192.*/ 0.3918455092263272, /*-0.2944689823359653D+01 */
/* -191.*/ 0.3917540257448628, /*-0.2693004353041361D+01 */
/* -190.*/ 0.3919873656059647, /*-0.2441427995120438D+01 */
/* -189.*/ 0.3925304674556337, /*-0.2190104358552203D+01 */
/* -188.*/ 0.3933628490998685, /*-0.1939165025066516D+01 */
/* -187.*/ 0.3944594774740303, /*-0.1688727305713193D+01 */
/* -186.*/ 0.3957916791023747, /*-0.1438892760683180D+01 */
/* -185.*/ 0.3973280334530701, /*-0.1189746506441763D+01 */
/* -184.*/ 0.3990351775377368, /*-0.9413572491876909D+00 */
/* -183.*/ 0.4008784516958364, /*-0.6937778773714424D+00 */
/* -182.*/ 0.4028223414939910, /*-0.4470463514946498D+00 */
/* -181.*/ 0.4048307175964914, /*-0.2011865865244649D+00 */
/* -180.*/ 0.4068669321289857, /* 0.4379094049661961D-01 */
/* -179.*/ 0.4088938770197513, /* 0.2878890063810521D+00 */
/* -178.*/ 0.4108741279688113, /* 0.5311238610633428D+00 */
/* -177.*/ 0.4127702768343329, /* 0.7735256652286102D+00 */
/* -176.*/ 0.4145454993757426, /* 0.1015138857715480D+01 */
/* -175.*/ 0.4161643322251866, /* 0.1256022158118792D+01 */
/* -174.*/ 0.4175935676318083, /* 0.1496248002593092D+01 */
/* -173.*/ 0.4188031393180127, /* 0.1735901367238320D+01 */
/* -172.*/ 0.4197668787916150, /* 0.1975078097534182D+01 */
/* -171.*/ 0.4204630645543220, /* 0.2213882978749377D+01 */
/* -170.*/ 0.4208747499001514, /* 0.2452427816684915D+01 */
/* -169.*/ 0.4209899159874482, /* 0.2690829747191581D+01 */
/* -168.*/ 0.4208015364893035, /* 0.2929209881513875D+01 */
/* -167.*/ 0.4203076489957907, /*-0.3115493044461023D+01 */
/* -166.*/ 0.4195115084470201, /*-0.2876782312112722D+01 */
/* -165.*/ 0.4184218595607502, /*-0.2637715969149654D+01 */
/* -164.*/ 0.4170533216125710, /*-0.2398166771213800D+01 */
/* -163.*/ 0.4154268406673447, /*-0.2158009132711500D+01 */
/* -162.*/ 0.4135701367057120, /*-0.1917121407365678D+01 */
/* -161.*/ 0.4115180560920585, /*-0.1675388910987818D+01 */
/* -160.*/ 0.4093127308342338, /*-0.1432707724896901D+01 */
/* -159.*/ 0.4070034429721541, /*-0.1188989238384790D+01 */
/* -158.*/ 0.4046460959615538, /*-0.9441652871637584D+00 */
/* -157.*/ 0.4023022090569454, /*-0.6981936177176215D+00 */
/* -156.*/ 0.4000373807704586, /*-0.4510632627955551D+00 */
/* -155.*/ 0.3979192169392561, /*-0.2027992750391293D+00 */
/* -154.*/ 0.3960147860987865, /* 0.4653382770597182D-01 */
/* -153.*/ 0.3943877411361167, /* 0.2968305568953047D+00 */
/* -152.*/ 0.3930953167334913, /* 0.5479454218359485D+00 */
/* -151.*/ 0.3921854591466817, /* 0.7996966590919110D+00 */
/* -150.*/ 0.3916943530459567, /* 0.1051872661915091D+01 */
/* -149.*/ 0.3916445722033650, /* 0.1304240668428315D+01 */
/* -148.*/ 0.3920440013940864, /* 0.1556556943089509D+01 */
/* -147.*/ 0.3928855727178632, /* 0.1808577500357416D+01 */
/* -146.*/ 0.3941477551512818, /* 0.2060068417978295D+01 */
/* -145.*/ 0.3957956562616347, /* 0.2310814960601550D+01 */
/* -144.*/ 0.3977825566043267, /* 0.2560629021802592D+01 */
/* -143.*/ 0.4000517042268930, /* 0.2809354705739983D+01 */
/* -142.*/ 0.4025382390810887, /* 0.3056872125620810D+01 */
/* -141.*/ 0.4051711756915037, /*-0.2980085662711740D+01 */
/* -140.*/ 0.4078754253894146, /*-0.2735190489462288D+01 */
/* -139.*/ 0.4105738697239499, /*-0.2491631059578896D+01 */
/* -138.*/ 0.4131894967981779, /*-0.2249372831172193D+01 */
/* -137.*/ 0.4156475856939623, /*-0.2008345333137299D+01 */
/* -136.*/ 0.4178778832111104, /*-0.1768445043196632D+01 */
/* -135.*/ 0.4198166786114337, /*-0.1529539067449005D+01 */
/* -134.*/ 0.4214086615292320, /*-0.1291469487555972D+01 */
/* -133.*/ 0.4226084551432352, /*-0.1054058166259334D+01 */
/* -132.*/ 0.4233817513586616, /*-0.8171117515395443D+00 */
/* -131.*/ 0.4237060279618796, /*-0.5804266192331232D+00 */
/* -130.*/ 0.4235708836825826, /*-0.3437935524084872D+00 */
/* -129.*/ 0.4229780684329310, /*-0.1070020633788405D+00 */
/* -128.*/ 0.4219412995229169, /* 0.1301556057457765D+00 */
/* -127.*/ 0.4204859361556167, /* 0.3678806518974641D+00 */
/* -126.*/ 0.4186485406083307, /* 0.6063638303525037D+00 */
/* -125.*/ 0.4164763008231587, /* 0.8457813115258453D+00 */
/* -124.*/ 0.4140262450008719, /* 0.1086290144417220D+01 */
/* -123.*/ 0.4113641602906746, /* 0.1328023335360554D+01 */
/* -122.*/ 0.4085631416116406, /* 0.1571084712331518D+01 */
/* -121.*/ 0.4057017382071585, /* 0.1815543889067492D+01 */
/* -120.*/ 0.4028617207514982, /* 0.2061431739069698D+01 */
/* -119.*/ 0.4001255439252907, /* 0.2308736824890932D+01 */
/* -118.*/ 0.3975736159817093, /* 0.2557403209189059D+01 */
/* -117.*/ 0.3952815044996214, /* 0.2807330016763336D+01 */
/* -116.*/ 0.3933172114414114, /* 0.3058373033747754D+01 */
/* -115.*/ 0.3917386497574056, /*-0.2972836786075786D+01 */
/* -114.*/ 0.3905914542285366, /*-0.2720146034601439D+01 */
/* -113.*/ 0.3899072596993416, /*-0.2466982555801384D+01 */
/* -112.*/ 0.3897025718022222, /*-0.2213604404366734D+01 */
/* -111.*/ 0.3899783282005895, /*-0.1960274307418756D+01 */
/* -110.*/ 0.3907201971292523, /*-0.1707248611547955D+01 */
/* -109.*/ 0.3918995898417922, /*-0.1454766909937642D+01 */
/* -108.*/ 0.3934752896506145, /*-0.1203043147112416D+01 */
/* -107.*/ 0.3953955416210456, /*-0.9522587721508926D+00 */
/* -106.*/ 0.3976004183670721, /*-0.7025582074115939D+00 */
/* -105.*/ 0.4000242831442562, /*-0.4540465982372720D+00 */
/* -104.*/ 0.4025982045447609, /*-0.2067895778608778D+00 */
/* -103.*/ 0.4052522231247924, /* 0.3918534428095763D-01 */
/* -102.*/ 0.4079174136831955, /* 0.2838861867762197D+00 */
/* -101.*/ 0.4105277166999889, /* 0.5273530624437238D+00 */
/* -100.*/ 0.4130215252143140, /* 0.7696542000191245D+00 */
/* -99.*/ 0.4153430129545066, /* 0.1010881644401755D+01 */
/* -98.*/ 0.4174431839835416, /* 0.1251146812766256D+01 */
/* -97.*/ 0.4192806221972361, /* 0.1490576064620303D+01 */
/* -96.*/ 0.4208219266296318, /* 0.1729306440547494D+01 */
/* -95.*/ 0.4220418369550156, /* 0.1967481721032381D+01 */
/* -94.*/ 0.4229230794241352, /* 0.2205248939363528D+01 */
/* -93.*/ 0.4234559900919690, /* 0.2442755443684477D+01 */
/* -92.*/ 0.4236379919781642, /* 0.2680146543830155D+01 */
/* -91.*/ 0.4234730095304949, /* 0.2917563707466080D+01 */
/* -90.*/ 0.4229708944563522, /*-0.3128042105826061D+01 */
/* -89.*/ 0.4221469128921307, /*-0.2890170284106579D+01 */
/* -88.*/ 0.4210213104050873, /*-0.2651883357612840D+01 */
/* -87.*/ 0.4196189369065240, /*-0.2413066758857398D+01 */
/* -86.*/ 0.4179688875872035, /*-0.2173615254686386D+01 */
/* -85.*/ 0.4161041061546177, /*-0.1933434227108985D+01 */
/* -84.*/ 0.4140609063818383, /*-0.1692441048821370D+01 */
/* -83.*/ 0.4118783947630255, /*-0.1450566433088198D+01 */
/* -82.*/ 0.4095978124589096, /*-0.1207755621150562D+01 */
/* -81.*/ 0.4072618463055355, /*-0.9639693053546469D+00 */
/* -80.*/ 0.4049139738632165, /*-0.7191842645058081D+00 */
/* -79.*/ 0.4025978980796790, /*-0.4733937834681989D+00 */
/* -78.*/ 0.4003570931142296, /*-0.2266080038682889D+00 */
/* -77.*/ 0.3982344338462959, /* 0.2114563030390704D-01 */
/* -76.*/ 0.3962718347171669, /* 0.2698217304426851D+00 */
/* -75.*/ 0.3945097978351587, /* 0.5193561560972624D+00 */
/* -74.*/ 0.3929867790632433, /* 0.7696652401874184D+00 */
/* -73.*/ 0.3917383254419973, /* 0.1020645382372826D+01 */
/* -72.*/ 0.3907960050842220, /* 0.1272173398933720D+01 */
/* -71.*/ 0.3901862188823471, /* 0.1524107953306865D+01 */
/* -70.*/ 0.3899290281566938, /* 0.1776292222399513D+01 */
/* -69.*/ 0.3900371388752039, /* 0.2028557733147899D+01 */
/* -68.*/ 0.3905151518157988, /* 0.2280729104055514D+01 */
/* -67.*/ 0.3913591343081909, /* 0.2532629307775426D+01 */
/* -66.*/ 0.3925565154137390, /* 0.2784085055099727D+01 */
/* -65.*/ 0.3940862713065346, /* 0.3034931965802242D+01 */
/* -64.*/ 0.3959193578225051, /*-0.2998166018760701D+01 */
/* -63.*/ 0.3980193556084838, /*-0.2748971294741219D+01 */
/* -62.*/ 0.4003433052031937, /*-0.2500781044963122D+01 */
/* -61.*/ 0.4028427116175390, /*-0.2253683423665604D+01 */
/* -60.*/ 0.4054646866540161, /*-0.2007741148070215D+01 */
/* -59.*/ 0.4081531789745269, /*-0.1762990665463898D+01 */
/* -58.*/ 0.4108502291362232, /*-0.1519442136418256D+01 */
/* -57.*/ 0.4134971898427233, /*-0.1277080084830247D+01 */
/* -56.*/ 0.4160358729710453, /*-0.1035864509865132D+01 */
/* -55.*/ 0.4184096177485623, /*-0.7957322502031227D+00 */
/* -54.*/ 0.4205643060684390, /*-0.5565984413329632D+00 */
/* -53.*/ 0.4224493686082863, /*-0.3183579949062421D+00 */
/* -52.*/ 0.4240188218582427, /*-0.8088712504362428D-01 */
/* -51.*/ 0.4252323523015520, /* 0.1559549810751986D+00 */
/* -50.*/ 0.4260564282353656, /* 0.3923242224756961D+00 */
/* -49.*/ 0.4264653844159292, /* 0.6283892670514071D+00 */
/* -48.*/ 0.4264424015063243, /* 0.8643288068569152D+00 */
/* -47.*/ 0.4259802982916808, /* 0.1100328405721968D+01 */
/* -46.*/ 0.4250820704900247, /* 0.1336577020609500D+01 */
/* -45.*/ 0.4237611403737662, /* 0.1573263312614944D+01 */
/* -44.*/ 0.4220413170053153, /* 0.1810571861520689D+01 */
/* -43.*/ 0.4199564972537426, /* 0.2048679360993549D+01 */
/* -42.*/ 0.4175501542075140, /* 0.2287750811440860D+01 */
/* -41.*/ 0.4148746574007646, /* 0.2527935663353095D+01 */
/* -40.*/ 0.4119904489174027, /* 0.2769363818701827D+01 */
/* -39.*/ 0.4089650667384774, /* 0.3012141393999119D+01 */
/* -38.*/ 0.4058719716751814, /*-0.3026839104828821D+01 */
/* -37.*/ 0.4027891089243749, /*-0.2781162278958302D+01 */
/* -36.*/ 0.3997971308357887, /*-0.2534006370516114D+01 */
/* -35.*/ 0.3969772310218505, /*-0.2285406257945027D+01 */
/* -34.*/ 0.3944085919953214, /*-0.2035441920990531D+01 */
/* -33.*/ 0.3921655216481440, /*-0.1784239842618717D+01 */
/* -32.*/ 0.3903144332768422, /*-0.1531972001913010D+01 */
/* -31.*/ 0.3889108902794321, /*-0.1278851994083649D+01 */
/* -30.*/ 0.3879969715113198, /*-0.1025128143225890D+01 */
/* -29.*/ 0.3875992046384497, /*-0.7710738860230836D+00 */
/* -28.*/ 0.3877272620443951, /*-0.5169761094581331D+00 */
/* -27.*/ 0.3883735287254252, /*-0.2631224259718647D+00 */
/* -26.*/ 0.3895135546374215, /*-0.9788496389462916D-02 */
/* -25.*/ 0.3911073169630848, /* 0.2427735526946539D+00 */
/* -24.*/ 0.3931011561132117, /* 0.4943447874864249D+00 */
/* -23.*/ 0.3954302174083974, /* 0.7447466718600525D+00 */
/* -22.*/ 0.3980212227039923, /* 0.9938455982557106D+00 */
/* -21.*/ 0.4007954023543951, /* 0.1241554791835688D+01 */
/* -20.*/ 0.4036714292374652, /* 0.1487833839494220D+01 */
/* -19.*/ 0.4065682103583174, /* 0.1732686237442576D+01 */
/* -18.*/ 0.4094074108960788, /* 0.1976155439034697D+01 */
/* -17.*/ 0.4121156154125473, /* 0.2218319922018747D+01 */
/* -16.*/ 0.4146260729802799, /* 0.2459287778869943D+01 */
/* -15.*/ 0.4168800222221041, /* 0.2699191262710689D+01 */
/* -14.*/ 0.4188276375966949, /* 0.2938181601266707D+01 */
/* -13.*/ 0.4204286669980098, /*-0.3106761063672589D+01 */
/* -12.*/ 0.4216528346605714, /*-0.2869090746452861D+01 */
/* -11.*/ 0.4224800633281588, /*-0.2631811387522883D+01 */
/* -10.*/ 0.4229005359258803, /*-0.2394739305292919D+01 */
/* -9.*/ 0.4229145851278091, /*-0.2157692044100071D+01 */
/* -8.*/ 0.4225323833330887, /*-0.1920491819747929D+01 */
/* -7.*/ 0.4217734121543107, /*-0.1682968842703293D+01 */
/* -6.*/ 0.4206657157453829, /*-0.1444964443881118D+01 */
/* -5.*/ 0.4192449738329285, /*-0.1206333923966576D+01 */
/* -4.*/ 0.4175534529720676, /*-0.9669490865584757D+00 */
/* -3.*/ 0.4156388971064635, /*-0.7267004768910357D+00 */
/* -2.*/ 0.4135533987884533, /*-0.4854993986755168D+00 */
/* -1.*/ 0.4113522583107795, /*-0.2432797910064849D+00 */
/* 0.*/ 0.4090928042223416, /* 0.0000000000000000D+00 */
/* 1.*/ 0.4068331306224137, /* 0.2443556166147563D+00 */
/* 2.*/ 0.4046307140843110, /* 0.4897754299502705D+00 */
/* 3.*/ 0.4025409062755741, /* 0.7362198976873164D+00 */
/* 4.*/ 0.4006153476974149, /* 0.9836218435742742D+00 */
/* 5.*/ 0.3989003972459766, /* 0.1231887910097264D+01 */
/* 6.*/ 0.3974357043804754, /* 0.1480901300404421D+01 */
/* 7.*/ 0.3962530535517125, /* 0.1730525738907529D+01 */
/* 8.*/ 0.3953755816010525, /* 0.1980610391924189D+01 */
/* 9.*/ 0.3948174158666943, /* 0.2230995352572876D+01 */
/* 10.*/ 0.3945837191886220, /* 0.2481517244187717D+01 */
/* 11.*/ 0.3946710755773147, /* 0.2732014541182347D+01 */
/* 12.*/ 0.3950681208246240, /* 0.2982332322324208D+01 */
/* 13.*/ 0.3957563212685792, /*-0.3050858992199093D+01 */
/* 14.*/ 0.3967108271244377, /*-0.2801319094117513D+01 */
/* 15.*/ 0.3979013626107844, /*-0.2552346984074016D+01 */
/* 16.*/ 0.3992931489193319, /*-0.2304037703751810D+01 */
/* 17.*/ 0.4008478755146728, /*-0.2056466181013103D+01 */
/* 18.*/ 0.4025247342047322, /*-0.1809686364813078D+01 */
/* 19.*/ 0.4042815107640464, /*-0.1563731008137131D+01 */
/* 20.*/ 0.4060756993806367, /*-0.1318612140790998D+01 */
/* 21.*/ 0.4078655781426910, /*-0.1074322220583949D+01 */
/* 22.*/ 0.4096111706400367, /*-0.8308358691276224D+00 */
/* 23.*/ 0.4112750261617907, /*-0.5881120142768895D+00 */
/* 24.*/ 0.4128227784927114, /*-0.3460962042650276D+00 */
/* 25.*/ 0.4142234836000313, /*-0.1047228497557210D+00 */
/* 26.*/ 0.4154497777284317, /* 0.1360828047621590D+00 */
/* 27.*/ 0.4164779271557997, /* 0.3764030905014157D+00 */
/* 28.*/ 0.4172878502067638, /* 0.6163267079279625D+00 */
/* 29.*/ 0.4178631787524808, /* 0.8559478113817843D+00 */
/* 30.*/ 0.4181913955356478, /* 0.1095365232926585D+01 */
/* 31.*/ 0.4182640462891083, /* 0.1334681685360392D+01 */
/* 32.*/ 0.4180769947246574, /* 0.1574002822845911D+01 */
/* 33.*/ 0.4176306740187046, /* 0.1813436102844365D+01 */
/* 34.*/ 0.4169302933654310, /* 0.2053089456292002D+01 */
/* 35.*/ 0.4159859771766924, /* 0.2293069808431037D+01 */
/* 36.*/ 0.4148128362904114, /* 0.2533481488346331D+01 */
/* 37.*/ 0.4134309829982735, /* 0.2774424528322483D+01 */
/* 38.*/ 0.4118654976707642, /* 0.3015992808388241D+01 */
/* 39.*/ 0.4101463357263359, /*-0.3024913330602498D+01 */
/* 40.*/ 0.4083081394031458, /*-0.2781848214031362D+01 */
/* 41.*/ 0.4063899027014311, /*-0.2537935297606801D+01 */
/* 42.*/ 0.4044344403646262, /*-0.2293128726410040D+01 */
/* 43.*/ 0.4024876344847781, /*-0.2047401418800972D+01 */
/* 44.*/ 0.4005974666244765, /*-0.1800747614461007D+01 */
/* 45.*/ 0.3988128743632460, /*-0.1553184987937212D+01 */
/* 46.*/ 0.3971824855115845, /*-0.1304756171319349D+01 */
/* 47.*/ 0.3957532764747999, /*-0.1055529583150466D+01 */
/* 48.*/ 0.3945691809094172, /*-0.8055994839071512D+00 */
/* 49.*/ 0.3936696568430963, /*-0.5550851576863607D+00 */
/* 50.*/ 0.3930882208334509, /*-0.3041290735837638D+00 */
/* 51.*/ 0.3928509836446831, /*-0.5289385348489109D-01 */
/* 52.*/ 0.3929752667351771, /* 0.1984420852290875D+00 */
/* 53.*/ 0.3934684241855990, /* 0.4496902076101385D+00 */
/* 54.*/ 0.3943270183092096, /* 0.7006586421142208D+00 */
/* 55.*/ 0.3955364831922726, /* 0.9511596152675641D+00 */
/* 56.*/ 0.3970713568729473, /* 0.1201016918161661D+01 */
/* 57.*/ 0.3988960831120016, /* 0.1450072733407353D+01 */
/* 58.*/ 0.4009663009430399, /* 0.1698193246750059D+01 */
/* 59.*/ 0.4032304782061602, /* 0.1945272680096612D+01 */
/* 60.*/ 0.4056317196870841, /* 0.2191235647566864D+01 */
/* 61.*/ 0.4081095941243174, /* 0.2436037979137428D+01 */
/* 62.*/ 0.4106018679176829, /* 0.2679666320375329D+01 */
/* 63.*/ 0.4130460901994423, /* 0.2922136877163754D+01 */
/* 64.*/ 0.4153810262203307, /*-0.3119691666838704D+01 */
/* 65.*/ 0.4175479702703095, /*-0.2879378977649773D+01 */
/* 66.*/ 0.4194919795713276, /*-0.2640017127489179D+01 */
/* 67.*/ 0.4211630586804311, /*-0.2401491712321727D+01 */
/* 68.*/ 0.4225172980342602, /*-0.2163669672984704D+01 */
/* 69.*/ 0.4235179414023910, /*-0.1926402025130027D+01 */
/* 70.*/ 0.4241363355894057, /*-0.1689526829649581D+01 */
/* 71.*/ 0.4243527085098502, /*-0.1452872384966725D+01 */
/* 72.*/ 0.4241567303539652, /*-0.1216260580675402D+01 */
/* 73.*/ 0.4235478334654247, /*-0.9795103282517400D+00 */
/* 74.*/ 0.4225352926410604, /*-0.7424409882597867D+00 */
/* 75.*/ 0.4211380903815376, /*-0.5048757446124233D+00 */
/* 76.*/ 0.4193846038503792, /*-0.2666449261647262D+00 */
/* 77.*/ 0.4173121478346718, /*-0.2758932863770884D-01 */
/* 78.*/ 0.4149663912585334, /* 0.2124363732195464D+00 */
/* 79.*/ 0.4124006389033184, /* 0.4535600297618344D+00 */
/* 80.*/ 0.4096749436630418, /* 0.6958881844143646D+00 */
/* 81.*/ 0.4068549978794650, /* 0.9395020389540526D+00 */
/* 82.*/ 0.4040107531129969, /* 0.1184453367540253D+01 */
/* 83.*/ 0.4012147392298109, /* 0.1430760655982383D+01 */
/* 84.*/ 0.3985400924104437, /* 0.1678405843684044D+01 */
/* 85.*/ 0.3960583480967850, /* 0.1927332094227704D+01 */
/* 86.*/ 0.3938370966381299, /* 0.2177443000786976D+01 */
/* 87.*/ 0.3919376260275518, /* 0.2428603546750192D+01 */
/* 88.*/ 0.3904126834388647, /* 0.2680643008723552D+01 */
/* 89.*/ 0.3893044789354861, /* 0.2933359833804336D+01 */
/* 90.*/ 0.3886430397161544, /*-0.3096656942093088D+01 */
/* 91.*/ 0.3884450100590401, /*-0.2843278172374169D+01 */
/* 92.*/ 0.3887129826219560, /*-0.2589937016873094D+01 */
/* 93.*/ 0.3894354340775427, /*-0.2336877740361646D+01 */
/* 94.*/ 0.3905873104924948, /*-0.2084331211489573D+01 */
/* 95.*/ 0.3921312572599651, /*-0.1832506026276891D+01 */
/* 96.*/ 0.3940194180073068, /*-0.1581581271407524D+01 */
/* 97.*/ 0.3961956531522340, /*-0.1331701442505301D+01 */
/* 98.*/ 0.3985979751817953, /*-0.1082973733897298D+01 */
/* 99.*/ 0.4011609839328693, /*-0.8354675832113583D+00 */
/* 100.*/ 0.4038181172056783, /*-0.5892160743901576D+00 */
/* 101.*/ 0.4065035990919956, /*-0.3442186450908055D+00 */
/* 102.*/ 0.4091540473916359, /*-0.1004445326578767D+00 */
/* 103.*/ 0.4117097671429156, /* 0.1421634990364562D+00 */
/* 104.*/ 0.4141157922931505, /* 0.3836854408402384D+00 */
/* 105.*/ 0.4163227383095657, /* 0.6242204527748144D+00 */
/* 106.*/ 0.4182875045720320, /* 0.8638834253217347D+00 */
/* 107.*/ 0.4199738333870426, /* 0.1102801658831977D+01 */
/* 108.*/ 0.4213527085904940, /* 0.1341111647012224D+01 */
/* 109.*/ 0.4224025705700182, /* 0.1578955992778419D+01 */
/* 110.*/ 0.4231093368122283, /* 0.1816480523027157D+01 */
/* 111.*/ 0.4234662409114051, /* 0.2053831680676985D+01 */
/* 112.*/ 0.4234735277784344, /* 0.2291154250293499D+01 */
/* 113.*/ 0.4231380586184182, /* 0.2528589424843650D+01 */
/* 114.*/ 0.4224728802038215, /* 0.2766273162342554D+01 */
/* 115.*/ 0.4214967987433137, /* 0.3004334731870390D+01 */
/* 116.*/ 0.4202339740339891, /*-0.3040289982688469D+01 */
/* 117.*/ 0.4187135224730843, /*-0.2801118693454088D+01 */
/* 118.*/ 0.4169690961382974, /*-0.2561236116718987D+01 */
/* 119.*/ 0.4150383956077978, /*-0.2320554449046042D+01 */
/* 120.*/ 0.4129625788017915, /*-0.2079000466958799D+01 */
/* 121.*/ 0.4107855450518595, /*-0.1836517300006162D+01 */
/* 122.*/ 0.4085530976060879, /*-0.1593066046199709D+01 */
/* 123.*/ 0.4063120118034033, /*-0.1348627091061239D+01 */
/* 124.*/ 0.4041090533340783, /*-0.1103201019437420D+01 */
/* 125.*/ 0.4019899966373665, /*-0.8568090556093901D+00 */
/* 126.*/ 0.3999986864808658, /*-0.6094930165136480D+00 */
/* 127.*/ 0.3981761691340588, /*-0.3613147988120235D+00 */
/* 128.*/ 0.3965598996109067, /*-0.1123554318723623D+00 */
/* 129.*/ 0.3951830158216477, /* 0.1372862858511940D+00 */
/* 130.*/ 0.3940736653411686, /* 0.3874955796921174D+00 */
/* 131.*/ 0.3932543781833389, /* 0.6381439602493516D+00 */
/* 132.*/ 0.3927414966879600, /* 0.8890919956226929D+00 */
/* 133.*/ 0.3925446941940581, /* 0.1140192602733037D+01 */
/* 134.*/ 0.3926666285652076, /* 0.1391294797751150D+01 */
/* 135.*/ 0.3931027776267974, /* 0.1642247761377218D+01 */
/* 136.*/ 0.3938414890354592, /* 0.1892905003320007D+01 */
/* 137.*/ 0.3948642513986466, /* 0.2143128379203586D+01 */
/* 138.*/ 0.3961461660713683, /* 0.2392791735432366D+01 */
/* 139.*/ 0.3976565805499599, /* 0.2641784024899493D+01 */
/* 140.*/ 0.3993598414282442, /* 0.2890011821638704D+01 */
/* 141.*/ 0.4012161366630831, /* 0.3137401232012463D+01 */
/* 142.*/ 0.4031824150415920, /*-0.2899286076932724D+01 */
/* 143.*/ 0.4052133832237458, /*-0.2653710871754694D+01 */
/* 144.*/ 0.4072625780763823, /*-0.2409067990768375D+01 */
/* 145.*/ 0.4092834927031928, /*-0.2165345514234318D+01 */
/* 146.*/ 0.4112307067195019, /*-0.1922511085716443D+01 */
/* 147.*/ 0.4130609494043810, /*-0.1680513488932353D+01 */
/* 148.*/ 0.4147340223878986, /*-0.1439284647229781D+01 */
/* 149.*/ 0.4162135327393912, /*-0.1198741832272754D+01 */
/* 150.*/ 0.4174674321213753, /*-0.9587898466278730D+00 */
/* 151.*/ 0.4184684070546409, /*-0.7193229936990948D+00 */
/* 152.*/ 0.4191941994813850, /*-0.4802267584488698D+00 */
/* 153.*/ 0.4196279409163138, /*-0.2413792580818679D+00 */
/* 154.*/ 0.4197585545731583, /*-0.2652636193900383D-02 */
/* 155.*/ 0.4195812282688133, /* 0.2360853725923978D+00 */
/* 156.*/ 0.4190979057668582, /* 0.4749695039202526D+00 */
/* 157.*/ 0.4183177053671864, /* 0.7141345356686158D+00 */
/* 158.*/ 0.4172571646732103, /* 0.9537123750222740D+00 */
/* 159.*/ 0.4159402308041304, /* 0.1193828775360574D+01 */
/* 160.*/ 0.4143979562373412, /* 0.1434599866151028D+01 */
/* 161.*/ 0.4126679061850000, /* 0.1676128692149758D+01 */
/* 162.*/ 0.4107933185158665, /* 0.1918501924043020D+01 */
/* 163.*/ 0.4088220723229434, /* 0.2161786845595691D+01 */
/* 164.*/ 0.4068055156587129, /* 0.2406028672562051D+01 */
/* 165.*/ 0.4047971840033980, /* 0.2651248240309658D+01 */
/* 166.*/ 0.4028514202965486, /* 0.2897440119852649D+01 */
/* 167.*/ 0.4010218959888728, /*-0.3138614029761584D+01 */
/* 168.*/ 0.3993600371834810, /*-0.2890604849660533D+01 */
/* 169.*/ 0.3979133805880060, /*-0.2641806793560400D+01 */
/* 170.*/ 0.3967239145739813, /*-0.2392335400132350D+01 */
/* 171.*/ 0.3958264912782198, /*-0.2142329777348108D+01 */
/* 172.*/ 0.3952474162542253, /*-0.1891948422446297D+01 */
/* 173.*/ 0.3950033255861159, /*-0.1641363809132225D+01 */
/* 174.*/ 0.3951004445907086, /*-0.1390756025786525D+01 */
/* 175.*/ 0.3955342905536659, /*-0.1140305874230724D+01 */
/* 176.*/ 0.3962898415108828, /*-0.8901879045573635D+00 */
/* 177.*/ 0.3973421523769988, /*-0.6405638574385065D+00 */
/* 178.*/ 0.3986573660100075, /*-0.3915769183297437D+00 */
/* 179.*/ 0.4001940443743395, /*-0.1433470784603047D+00 */
/* 180.*/ 0.4019047345415215, /* 0.1040322285444517D+00 */
/* 181.*/ 0.4037376835332590, /* 0.3504961644861406D+00 */
/* 182.*/ 0.4056386209691270, /* 0.5960092453166138D+00 */
/* 183.*/ 0.4075525351607142, /* 0.8405649360181059D+00 */
/* 184.*/ 0.4094253743325376, /* 0.1084184241851686D+01 */
/* 185.*/ 0.4112056102067528, /* 0.1326913485271506D+01 */
/* 186.*/ 0.4128456087605856, /* 0.1568821477773958D+01 */
/* 187.*/ 0.4143027659792556, /* 0.1809996308164642D+01 */
/* 188.*/ 0.4155403870327739, /* 0.2050541968150751D+01 */
/* 189.*/ 0.4165283143167994, /* 0.2290575014205324D+01 */
/* 190.*/ 0.4172433378940939, /* 0.2530221414702089D+01 */
/* 191.*/ 0.4176694427620714, /* 0.2769613654611978D+01 */
/* 192.*/ 0.4177979527762254, /* 0.3008888078885497D+01 */
/* 193.*/ 0.4176276164551140, /*-0.3035002935109985D+01 */
/* 194.*/ 0.4171646474152031, /*-0.2795552285742719D+01 */
/* 195.*/ 0.4164226912490700, /*-0.2555812692955428D+01 */
/* 196.*/ 0.4154226556232529, /*-0.2315658424736075D+01 */
/* 197.*/ 0.4141923256760832, /*-0.2074973789539310D+01 */
/* 198.*/ 0.4127657011969876, /*-0.1833656405749656D+01 */
/* 199.*/ 0.4111820342269412, /*-0.1591620312189744D+01 */
/* 200.*/ 0.4094846033468814, /*-0.1348798640860899D+01 */
};
// #include "watdefs.h"
// #include "lunar.h"
#define PI 3.1415926535897932384626433832795028841971693993751058209749445923
#define CVT (PI / 180.)
#define ARCSECONDS_TO_RADIANS (CVT / 3600.)
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
/* Copied from (22.2), Meeus, p. 147; he, in turn, got it
from _Astronomical Almanac_ 1984, p. S26. */
double iau_obliquity( const double t_cen)
{
const double rval =
(23. * 3600. + 26. * 60 + 21.448) * ARCSECONDS_TO_RADIANS
+ t_cen * (-46.8150 * ARCSECONDS_TO_RADIANS /* linear */
+ t_cen * (-0.00059 * ARCSECONDS_TO_RADIANS /* quad */
+ t_cen * 0.001813 * ARCSECONDS_TO_RADIANS));
return( rval);
}
double cubic_spline_interpolate_within_table( /* spline.cpp */
const double *table, const int n_entries, double x, int *err_code);
double spline_obliquity( const double t_cen)
{
const double table_start = -2000.; /* table starts at 2000 */
/* centuries before J2000 */
return( cubic_spline_interpolate_within_table(
obliquity_table,
sizeof( obliquity_table) / sizeof( double),
(t_cen - table_start) / 10., NULL));
}
/* The following does a cubic interpolation within values from Laskar
et. al. (same as in the above obliquity_table[], except that the
files cover about a time span about 75 times greater.) Note that
file_obliquity( ) is somewhat complicated by the fact that Laskar
et. al. provided data split between two files. Rather than read
from both files when in the "transition" zone at J2000 +/- one
millennium, I just stored values for the years 1000 and 3000. */
double file_obliquity( const double t_cen)
{
FILE *ifile = fopen( t_cen < 0. ? "prec0n.asc" : "prec0p.asc", "rb");
double rval = 0.;
if( ifile)
{
char buff[80];
if( fgets( buff, sizeof( buff), ifile))
{
double loc = fabs( t_cen / 10.); /* one record per millenium */
int iloc = (int)loc - 1, i, err = 0;
double array[4];
for( i = 0; i < 4; i++, iloc++)
{
const double obliquit_minus_1k = 0.4113522583107795;
const double obliquit_plus_1k = 0.4068331306224137;
if( iloc == -1)
array[i] = (t_cen < 0. ? obliquit_plus_1k : obliquit_minus_1k);
else
{
fseek( ifile, iloc * (long)strlen( buff), SEEK_SET);
if( fgets( buff, sizeof( buff), ifile))
array[i] = atof( buff + 11);
else
err = -99;
}
}
if( !err)
rval = cubic_spline_interpolate_within_table(
array, 4, loc - iloc + 4., &err);
if( err)
printf( "Interpolation: %d\n", err);
}
fclose( ifile);
}
return( rval);
}
|
