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epv.f
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SUBROUTINE sla_EPV ( DATE, PH, VH, PB, VB )
*+
* - - - -
* E P V
* - - - -
*
* Earth position and velocity, heliocentric and barycentric, with
* respect to the Barycentric Celestial Reference System.
*
* Given:
* DATE d date, TDB Modified Julian Date (Note 1)
*
* Returned:
* PH d(3) heliocentric Earth position (AU)
* VH d(3) heliocentric Earth velocity (AU,AU/day)
* PB d(3) barycentric Earth position (AU)
* VB d(3) barycentric Earth velocity (AU/day)
*
* Notes:
*
* 1) The date is TDB as an MJD (=JD-2400000.5). TT can be used instead
* of TDB in most applications.
*
* 2) On return, the arrays PH, VH, PV, PB contain the following:
*
* PH(1) x }
* PH(2) y } heliocentric position, AU
* PH(3) z }
*
* VH(1) xdot }
* VH(2) ydot } heliocentric velocity, AU/d
* VH(3) zdot }
*
* PB(1) x }
* PB(2) y } barycentric position, AU
* PB(3) z }
*
* VB(1) xdot }
* VB(2) ydot } barycentric velocity, AU/d
* VB(3) zdot }
*
* The vectors are with respect to the Barycentric Celestial
* Reference System (BCRS); velocities are in AU per TDB day.
*
* 3) The routine is a SIMPLIFIED SOLUTION from the planetary theory
* VSOP2000 (X. Moisson, P. Bretagnon, 2001, Celes. Mechanics &
* Dyn. Astron., 80, 3/4, 205-213) and is an adaptation of original
* Fortran code supplied by P. Bretagnon (private comm., 2000).
*
* 4) Comparisons over the time span 1900-2100 with this simplified
* solution and the JPL DE405 ephemeris give the following results:
*
* RMS max
* Heliocentric:
* position error 3.7 11.2 km
* velocity error 1.4 5.0 mm/s
*
* Barycentric:
* position error 4.6 13.4 km
* velocity error 1.4 4.9 mm/s
*
* The results deteriorate outside this time span.
*
* 5) The routine sla_EVP is faster but less accurate. The present
* routine targets the case where high accuracy is more important
* than CPU time, yet the extra complication of reading a pre-
* computed ephemeris is not justified.
*
* Last revision: 7 April 2005
*
* Copyright P.T.Wallace. All rights reserved.
*
*
* License:
* 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 (see SLA_CONDITIONS); if not, write to the
* Free Software Foundation, Inc., 59 Temple Place, Suite 330,
* Boston, MA 02111-1307 USA
*
*-----------------------------------------------------------------------
IMPLICIT NONE
DOUBLE PRECISION DATE, PH(3), VH(3), PB(3), VB(3)
DOUBLE PRECISION T, T2, XYZ, XYZD, A, B, C, CT, P, CP,
: HP(3), HV(3), BP(3), BV(3), X, Y, Z
INTEGER I, J, K
* Days per Julian year
DOUBLE PRECISION DJY
PARAMETER ( DJY = 365.25D0 )
* Reference epoch (J2000), MJD
DOUBLE PRECISION DJM0
PARAMETER ( DJM0 = 51544.5D0 )
*
* Matrix elements for orienting the analytical model to DE405/ICRF.
*
* The corresponding Euler angles are:
*
* d ' "
* 1st rotation - 23 26 21.4091 about the x-axis (obliquity)
* 2nd rotation + 0.0475 about the z-axis (RA offset)
*
* These were obtained empirically, by comparisons with DE405 over
* 1900-2100.
*
DOUBLE PRECISION AM12, AM13, AM21, AM22, AM23, AM32, AM33
PARAMETER ( AM12 = +0.000000211284D0,
: AM13 = -0.000000091603D0,
: AM21 = -0.000000230286D0,
: AM22 = +0.917482137087D0,
: AM23 = -0.397776982902D0,
: AM32 = +0.397776982902D0,
: AM33 = +0.917482137087D0 )
* ----------------------
* Ephemeris Coefficients
* ----------------------
*
* The coefficients are stored in arrays of dimension (3,n,3). There
* are separate sets of arrays for (i) the Sun to Earth vector and
* (ii) the Solar-System barycenter to Sun vector. Each of these two
* sets contains separate arrays for the terms (n in number) in each
* power of time (in Julian years since J2000): T^0, T^1 and T^2.
* Within each array, all the Cartesian x-components, elements (i,j,1),
* appear first, followed by all the y-components, elements (i,j,2) and
* finally all the z-components, elements (i,j,3). At the lowest level
* are groups of three coefficients. The first coefficient in each
* group, element (1,j,k), is the amplitude of the term, the second,
* element (2,j,k), is the phase and the third, element (3,j,k), is the
* frequency.
*
* The naming scheme is such that a block
*
* DOUBLE PRECISION bn(3,Mbn,3)
*
* applies to body b and time exponent n:
*
* . b can be either E (Earth with respect to Sun) or S (Sun with
* respect to Solar-System Barycenter)
*
* . n can be 0, 1 or 2, for T^0, T^1 or T^2
*
* For example, array E2(3,ME2,3) contains the coefficients for
* the T^2 terms for the Sun-to-Earth vector.
*
* There is no requirement for the X, Y and Z models for a particular
* block to use the same number of coefficients. The number actually
* used is parameterized, the number of terms being used called NbnX,
* NbnY, and NbnZ respectively. The parameter Mbn is the biggest of
* the three, and defines the array size. Unused elements are not
* initialized and are never accessed.
*
INTEGER NE0(3), NE0X, NE0Y, NE0Z, ME0,
: NE1(3), NE1X, NE1Y, NE1Z, ME1,
: NE2(3), NE2X, NE2Y, NE2Z, ME2,
: NS0(3), NS0X, NS0Y, NS0Z, MS0,
: NS1(3), NS1X, NS1Y, NS1Z, MS1,
: NS2(3), NS2X, NS2Y, NS2Z, MS2
PARAMETER ( NE0X = 501, NE0Y = 501, NE0Z = 137, ME0 = NE0X,
: NE1X = 79, NE1Y = 80, NE1Z = 12, ME1 = NE1Y,
: NE2X = 5, NE2Y = 5, NE2Z = 3, ME2 = NE2X,
: NS0X = 212, NS0Y = 213, NS0Z = 69, MS0 = NS0Y,
: NS1X = 50, NS1Y = 50, NS1Z = 14, MS1 = NS1X,
: NS2X = 9, NS2Y = 9, NS2Z = 2, MS2 = NS2X )
DOUBLE PRECISION E0(3,ME0,3), E1(3,ME1,3), E2(3,ME2,3),
: S0(3,MS0,3), S1(3,MS1,3), S2(3,MS2,3)
DATA NE0 / NE0X, NE0Y, NE0Z /
DATA NE1 / NE1X, NE1Y, NE1Z /
DATA NE2 / NE2X, NE2Y, NE2Z /
DATA NS0 / NS0X, NS0Y, NS0Z /
DATA NS1 / NS1X, NS1Y, NS1Z /
DATA NS2 / NS2X, NS2Y, NS2Z /
* Sun-to-Earth, T^0, X
DATA ((E0(I,J,1),I=1,3),J= 1, 10) /
: 0.9998292878132D+00, 0.1753485171504D+01, 0.6283075850446D+01,
: 0.8352579567414D-02, 0.1710344404582D+01, 0.1256615170089D+02,
: 0.5611445335148D-02, 0.0000000000000D+00, 0.0000000000000D+00,
: 0.1046664295572D-03, 0.1667225416770D+01, 0.1884922755134D+02,
: 0.3110842534677D-04, 0.6687513390251D+00, 0.8399684731857D+02,
: 0.2552413503550D-04, 0.5830637358413D+00, 0.5296909721118D+00,
: 0.2137207845781D-04, 0.1092330954011D+01, 0.1577343543434D+01,
: 0.1680240182951D-04, 0.4955366134987D+00, 0.6279552690824D+01,
: 0.1679012370795D-04, 0.6153014091901D+01, 0.6286599010068D+01,
: 0.1445526946777D-04, 0.3472744100492D+01, 0.2352866153506D+01 /
DATA ((E0(I,J,1),I=1,3),J= 11, 20) /
: 0.1091038246184D-04, 0.3689845786119D+01, 0.5223693906222D+01,
: 0.9344399733932D-05, 0.6073934645672D+01, 0.1203646072878D+02,
: 0.8993182910652D-05, 0.3175705249069D+01, 0.1021328554739D+02,
: 0.5665546034116D-05, 0.2152484672246D+01, 0.1059381944224D+01,
: 0.6844146703035D-05, 0.1306964099750D+01, 0.5753384878334D+01,
: 0.7346610905565D-05, 0.4354980070466D+01, 0.3981490189893D+00,
: 0.6815396474414D-05, 0.2218229211267D+01, 0.4705732307012D+01,
: 0.6112787253053D-05, 0.5384788425458D+01, 0.6812766822558D+01,
: 0.4518120711239D-05, 0.6087604012291D+01, 0.5884926831456D+01,
: 0.4521963430706D-05, 0.1279424524906D+01, 0.6256777527156D+01 /
DATA ((E0(I,J,1),I=1,3),J= 21, 30) /
: 0.4497426764085D-05, 0.5369129144266D+01, 0.6309374173736D+01,
: 0.4062190566959D-05, 0.5436473303367D+00, 0.6681224869435D+01,
: 0.5412193480192D-05, 0.7867838528395D+00, 0.7755226100720D+00,
: 0.5469839049386D-05, 0.1461440311134D+01, 0.1414349524433D+02,
: 0.5205264083477D-05, 0.4432944696116D+01, 0.7860419393880D+01,
: 0.2149759935455D-05, 0.4502237496846D+01, 0.1150676975667D+02,
: 0.2279109618501D-05, 0.1239441308815D+01, 0.7058598460518D+01,
: 0.2259282939683D-05, 0.3272430985331D+01, 0.4694002934110D+01,
: 0.2558950271319D-05, 0.2265471086404D+01, 0.1216800268190D+02,
: 0.2561581447555D-05, 0.1454740653245D+01, 0.7099330490126D+00 /
DATA ((E0(I,J,1),I=1,3),J= 31, 40) /
: 0.1781441115440D-05, 0.2962068630206D+01, 0.7962980379786D+00,
: 0.1612005874644D-05, 0.1473255041006D+01, 0.5486777812467D+01,
: 0.1818630667105D-05, 0.3743903293447D+00, 0.6283008715021D+01,
: 0.1818601377529D-05, 0.6274174354554D+01, 0.6283142985870D+01,
: 0.1554475925257D-05, 0.1624110906816D+01, 0.2513230340178D+02,
: 0.2090948029241D-05, 0.5852052276256D+01, 0.1179062909082D+02,
: 0.2000176345460D-05, 0.4072093298513D+01, 0.1778984560711D+02,
: 0.1289535917759D-05, 0.5217019331069D+01, 0.7079373888424D+01,
: 0.1281135307881D-05, 0.4802054538934D+01, 0.3738761453707D+01,
: 0.1518229005692D-05, 0.8691914742502D+00, 0.2132990797783D+00 /
DATA ((E0(I,J,1),I=1,3),J= 41, 50) /
: 0.9450128579027D-06, 0.4601859529950D+01, 0.1097707878456D+02,
: 0.7781119494996D-06, 0.1844352816694D+01, 0.8827390247185D+01,
: 0.7733407759912D-06, 0.3582790154750D+01, 0.5507553240374D+01,
: 0.7350644318120D-06, 0.2695277788230D+01, 0.1589072916335D+01,
: 0.6535928827023D-06, 0.3651327986142D+01, 0.1176985366291D+02,
: 0.6324624183656D-06, 0.2241302375862D+01, 0.6262300422539D+01,
: 0.6298565300557D-06, 0.4407122406081D+01, 0.6303851278352D+01,
: 0.8587037089179D-06, 0.3024307223119D+01, 0.1672837615881D+03,
: 0.8299954491035D-06, 0.6192539428237D+01, 0.3340612434717D+01,
: 0.6311263503401D-06, 0.2014758795416D+01, 0.7113454667900D-02 /
DATA ((E0(I,J,1),I=1,3),J= 51, 60) /
: 0.6005646745452D-06, 0.3399500503397D+01, 0.4136910472696D+01,
: 0.7917715109929D-06, 0.2493386877837D+01, 0.6069776770667D+01,
: 0.7556958099685D-06, 0.4159491740143D+01, 0.6496374930224D+01,
: 0.6773228244949D-06, 0.4034162934230D+01, 0.9437762937313D+01,
: 0.5370708577847D-06, 0.1562219163734D+01, 0.1194447056968D+01,
: 0.5710804266203D-06, 0.2662730803386D+01, 0.6282095334605D+01,
: 0.5709824583726D-06, 0.3985828430833D+01, 0.6284056366286D+01,
: 0.5143950896447D-06, 0.1308144688689D+01, 0.6290189305114D+01,
: 0.5088010604546D-06, 0.5352817214804D+01, 0.6275962395778D+01,
: 0.4960369085172D-06, 0.2644267922349D+01, 0.6127655567643D+01 /
DATA ((E0(I,J,1),I=1,3),J= 61, 70) /
: 0.4803137891183D-06, 0.4008844192080D+01, 0.6438496133249D+01,
: 0.5731747768225D-06, 0.3794550174597D+01, 0.3154687086868D+01,
: 0.4735947960579D-06, 0.6107118308982D+01, 0.3128388763578D+01,
: 0.4808348796625D-06, 0.4771458618163D+01, 0.8018209333619D+00,
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: 0.1074569126382D-08, 0.1720485636868D+01, 0.8397383534231D+02 /
DATA ((E0(I,J,1),I=1,3),J=471,480) /
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: 0.7217398104321D-09, 0.1597772562175D+01, 0.2457074661053D+03 /
DATA ((E0(I,J,1),I=1,3),J=481,490) /
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: 0.5604061331253D-09, 0.1638816006247D+01, 0.8433466158131D+02,
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: 0.4771358267658D-09, 0.5308027211629D+01, 0.1805255418145D+03 /
DATA ((E0(I,J,1),I=1,3),J=491,500) /
: 0.3943451445989D-09, 0.2195145341074D+01, 0.2568537517081D+03,
: 0.3952109120244D-09, 0.5081189491586D+01, 0.2449975330562D+03,
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DATA ((E0(I,J,1),I=1,3),J=501,NE0X) /
: 0.9015823460025D-10, 0.3807792942715D+01, 0.4171445043968D+03 /
* Sun-to-Earth, T^1, X
DATA ((E1(I,J,1),I=1,3),J= 1, 10) /
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: 0.4866923261539D-09, 0.5213203771824D+01, 0.7755226100720D+00 /
DATA ((E1(I,J,1),I=1,3),J= 11, 20) /
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: 0.4610675141648D-09, 0.1837249181372D-01, 0.7860419393880D+01,
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: 0.2875473577986D-09, 0.5916256610193D+01, 0.2513230340178D+02,
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: 0.2751248215916D-09, 0.5502088574662D+01, 0.6438496133249D+01,
: 0.2481432881127D-09, 0.2921989846637D+01, 0.5486777812467D+01 /
DATA ((E1(I,J,1),I=1,3),J= 21, 30) /
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: 0.2015522342591D-09, 0.5979395259740D+01, 0.6290189305114D+01,
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: 0.1209868266342D-09, 0.4150425791727D+01, 0.4694002934110D+01 /
DATA ((E1(I,J,1),I=1,3),J= 31, 40) /
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: 0.1047261388602D-09, 0.4229590090227D+01, 0.6282095334605D+01,
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: 0.9590900593873D-10, 0.1894393939924D+01, 0.4136910472696D+01,
: 0.9146249188071D-10, 0.2010647519562D+01, 0.6496374930224D+01,
: 0.8545274480290D-10, 0.5529846956226D-01, 0.1194447056968D+01,
: 0.8224377881194D-10, 0.1254304102174D+01, 0.1589072916335D+01,
: 0.6183529510410D-10, 0.3360862168815D+01, 0.8827390247185D+01,
: 0.6259255147141D-10, 0.4755628243179D+01, 0.8429241228195D+01 /
DATA ((E1(I,J,1),I=1,3),J= 41, 50) /
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: 0.7328259466314D-10, 0.4927699613906D+00, 0.4535059491685D+01,
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: 0.4598076850751D-10, 0.6023631226459D+01, 0.6525804586632D+01 /
DATA ((E1(I,J,1),I=1,3),J= 51, 60) /
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: 0.4325493872224D-10, 0.1330845906564D+01, 0.7632943190217D+01,
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: 0.5257043167676D-10, 0.6195089830590D+01, 0.8031092209206D+01,
: 0.5076613989393D-10, 0.2305124132918D+01, 0.7477522907414D+01,
: 0.3342169352778D-10, 0.5415998155071D+01, 0.1097707878456D+02,
: 0.3545881983591D-10, 0.3727160564574D+01, 0.4164311961999D+01,
: 0.3364063738599D-10, 0.2901121049204D+00, 0.1137170464392D+02 /
DATA ((E1(I,J,1),I=1,3),J= 61, 70) /
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: 0.4307412268687D-10, 0.4938909587445D+01, 0.1592596075957D+01,
: 0.3405769115435D-10, 0.2408890766511D+01, 0.3128388763578D+01,
: 0.3001926198480D-10, 0.4862239006386D+01, 0.1748016358760D+01,
: 0.2778264787325D-10, 0.5241168661353D+01, 0.7342457794669D+01,
: 0.2676159480666D-10, 0.3423593942199D+01, 0.2146165377750D+01,
: 0.2954273399939D-10, 0.1881721265406D+01, 0.5368044267797D+00,
: 0.3309362888795D-10, 0.1931525677349D+01, 0.8018209333619D+00,
: 0.2810283608438D-10, 0.2414659495050D+01, 0.5225775174439D+00,
: 0.3378045637764D-10, 0.4238019163430D+01, 0.1554202828031D+00 /
DATA ((E1(I,J,1),I=1,3),J= 71,NE1X) /
: 0.2558134979840D-10, 0.1828225235805D+01, 0.5230807360890D+01,
: 0.2273755578447D-10, 0.5858184283998D+01, 0.7084896783808D+01,
: 0.2294176037690D-10, 0.4514589779057D+01, 0.1726015463500D+02,
: 0.2533506099435D-10, 0.2355717851551D+01, 0.5216580451554D+01,
: 0.2716685375812D-10, 0.2221003625100D+01, 0.8635942003952D+01,
: 0.2419043435198D-10, 0.5955704951635D+01, 0.4690479774488D+01,
: 0.2521232544812D-10, 0.1395676848521D+01, 0.5481254917084D+01,
: 0.2630195021491D-10, 0.5727468918743D+01, 0.2629832328990D-01,
: 0.2548395840944D-10, 0.2628351859400D-03, 0.1349867339771D+01 /
* Sun-to-Earth, T^2, X
DATA ((E2(I,J,1),I=1,3),J= 1,NE2X) /
: -0.4143818297913D-10, 0.0000000000000D+00, 0.0000000000000D+00,
: 0.2171497694435D-10, 0.4398225628264D+01, 0.1256615170089D+02,
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: 0.9256833552682D-12, 0.4191264694361D+01, 0.1884922755134D+02,
: 0.1022049384115D-12, 0.5381133195658D+01, 0.8399684731857D+02 /
* Sun-to-Earth, T^0, Y
DATA ((E0(I,J,2),I=1,3),J= 1, 10) /
: 0.9998921098898D+00, 0.1826583913846D+00, 0.6283075850446D+01,
: -0.2442700893735D-01, 0.0000000000000D+00, 0.0000000000000D+00,
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: 0.1046697300177D-03, 0.9641423109763D-01, 0.1884922755134D+02,
: 0.3110841876663D-04, 0.5381140401712D+01, 0.8399684731857D+02,
: 0.2570269094593D-04, 0.5301016407128D+01, 0.5296909721118D+00,
: 0.2147389623610D-04, 0.2662510869850D+01, 0.1577343543434D+01,
: 0.1680344384050D-04, 0.5207904119704D+01, 0.6279552690824D+01,
: 0.1679117312193D-04, 0.4582187486968D+01, 0.6286599010068D+01,
: 0.1440512068440D-04, 0.1900688517726D+01, 0.2352866153506D+01 /
DATA ((E0(I,J,2),I=1,3),J= 11, 20) /
: 0.1135139664999D-04, 0.5273108538556D+01, 0.5223693906222D+01,
: 0.9345482571018D-05, 0.4503047687738D+01, 0.1203646072878D+02,
: 0.9007418719568D-05, 0.1605621059637D+01, 0.1021328554739D+02,
: 0.5671536712314D-05, 0.5812849070861D+00, 0.1059381944224D+01,
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: 0.6814275881697D-05, 0.6472990145974D+00, 0.4705732307012D+01,
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: 0.4522249141926D-05, 0.5991783029224D+01, 0.6256777527156D+01 /
DATA ((E0(I,J,2),I=1,3),J= 21, 30) /
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: 0.5514927480180D-05, 0.3961257833388D+01, 0.5507553240374D+01,
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: 0.2278386100876D-05, 0.4845456398785D+01, 0.4694002934110D+01,
: 0.2559088003308D-05, 0.6945321117311D+00, 0.1216800268190D+02 /
DATA ((E0(I,J,2),I=1,3),J= 31, 40) /
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: 0.1792755796387D-05, 0.1400122509632D+01, 0.7962980379786D+00,
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: 0.2000617940427D-05, 0.2501426281450D+01, 0.1778984560711D+02,
: 0.1289731195580D-05, 0.3646340599536D+01, 0.7079373888424D+01,
: 0.1282657998934D-05, 0.3232864804902D+01, 0.3738761453707D+01 /
DATA ((E0(I,J,2),I=1,3),J= 41, 50) /
: 0.1528915968658D-05, 0.5581433416669D+01, 0.2132990797783D+00,
: 0.1187304098432D-05, 0.5453576453694D+01, 0.9437762937313D+01,
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: 0.8068948788113D-06, 0.9224087798609D+00, 0.6069776770667D+01 /
DATA ((E0(I,J,2),I=1,3),J= 51, 60) /
: 0.8353786011661D-06, 0.4631707184895D+01, 0.3340612434717D+01,
: 0.6009324532132D-06, 0.1829498827726D+01, 0.4136910472696D+01,
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: 0.4960654697891D-06, 0.1073450946756D+01, 0.6127655567643D+01 /
DATA ((E0(I,J,2),I=1,3),J= 61, 70) /
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: 0.6109911263665D-06, 0.5343356157914D+01, 0.3154687086868D+01,
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: 0.3950929600897D-06, 0.3359394184254D+01, 0.5481254917084D+01 /
DATA ((E0(I,J,2),I=1,3),J= 71, 80) /
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: 0.4215241688886D-06, 0.2065368800993D+01, 0.1726015463500D+02,
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DATA ((E0(I,J,2),I=1,3),J= 81, 90) /
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DATA ((E0(I,J,2),I=1,3),J= 91,100) /
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DATA ((E0(I,J,2),I=1,3),J=101,110) /
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DATA ((E0(I,J,2),I=1,3),J=111,120) /
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DATA ((E0(I,J,2),I=1,3),J=121,130) /
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DATA ((E0(I,J,2),I=1,3),J=131,140) /
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DATA ((E0(I,J,2),I=1,3),J=141,150) /
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