C**** ORBPAR.FOR Calculate ORBital PARameters 2002/09/11
C****
C**** Output: ECCEN = eccentricity of the Earth's orbit about the Sun
C**** OBLIQ = obliquity = latitude of Tropic of Cancer (degrees)
C**** OMEGVP = longitude of perihelion =
C**** = spatial angle from vernal equinox to perihelion
C**** with Sun as angle vertex
C****
IMPLICIT REAL*8 (A-H,M,O-Z)
PARAMETER (TWOPI=6.283185307179586477d0, PIz180=TWOPI/360.)
CHARACTER ARG*80
C****
NARGS = IARGC()
IF(NARGS.le.0) GO TO 800
C****
C**** Decode command line arguments
C****
CALL GETARG (1,ARG)
READ (ARG,*,ERR=810) IYMIN
IF(ABS(IYMIN).gt.5000000) GO TO 811
IYMAX = IYMIN
IYINC = 1000
IF(NARGS.le.1) GO TO 150
CALL GETARG (2,ARG)
READ (ARG,*,ERR=812) IYMAX
IF(NARGS.le.2) GO TO 150
CALL GETARG (3,ARG)
READ (ARG,*,ERR=813) IYINC
IF(IYINC.eq.0) IYINC = 1000
C**** Limit calculations to 1001 years
150 IF((IYINC.gt.0 .and. IYMAX.gt.IYMIN+1000*IYINC) .or.
* (IYINC.lt.0 .and. IYMAX.lt.IYMIN+1000*IYINC))
* IYMAX = IYMIN+1000*IYINC
IF(IYMAX.gt. 5000000) IYMAX = 5000000
IF(IYMAX.lt.-5000000) IYMAX = -5000000
C****
C**** Loop over years
C****
WRITE (6,920)
DO 210 IYEAR = IYMIN,IYMAX,IYINC
C**** Determine orbital parameters
YEAR = IYEAR
CALL ORBPAR (YEAR, ECCEN,OBLIQ,OMEGVP)
OBLIQ = OBLIQ /PIz180
OMEGVP = OMEGVP/PIz180
210 WRITE (6,921) IYEAR, ECCEN,OBLIQ,OMEGVP
GO TO 999
C****
800 WRITE (6,*)
*'Usage: ORBPAR Ymin(A.D.) [Ymax Yinc] 2002/09/11'
WRITE (6,*)
*' Calculate Earth''s orbital parameters for range of years'
WRITE (6,*)
*' Parameters are precise + or - 1000000 years from present'
GO TO 999
810 WRITE (0,*) 'Unable to decipher minimum year from first' //
* ' command line argument: ',TRIM(ARG)
STOP 810
811 WRITE (0,*) 'Years are limited to be between 5000000 BC and' //
* ' 5000000 AD.'
STOP 811
812 WRITE (0,*) 'Unable to decipher maximum year from second' //
* ' command line argument: ',TRIM(ARG)
STOP 812
813 WRITE (0,*) 'Unable to decipher yearly increment from third' //
* ' command line argument: ',TRIM(ARG)
STOP 813
C****
900 FORMAT ('Content-type: text/plain' /)
920 FORMAT ('Orbital Parmameters'
* // ' Long. of',
* / ' Year Eccentri Obliquity Perihel.',
* / ' (A.D.) city (degrees) (degrees)',
* / ' ------ -------- --------- --------')
921 FORMAT (I8,F11.6,F13.4,F13.3)
999 END
SUBROUTINE ORBPAR (YEAR, ECCEN,OBLIQ,OMEGVP)
C****
C**** ORBPAR calculates the three orbital parameters as a function of
C**** YEAR. The source of these calculations is: Andre L. Berger,
C**** 1978, "Long-Term Variations of Daily Insolation and Quaternary
C**** Climatic Changes", JAS, v.35, p.2362. Also useful is: Andre L.
C**** Berger, May 1978, "A Simple Algorithm to Compute Long Term
C**** Variations of Daily Insolation", published by Institut
C**** D'Astronomie de Geophysique, Universite Catholique de Louvain,
C**** Louvain-la Neuve, No. 18.
C****
C**** Tables and equations refer to the first reference (JAS). The
C**** corresponding table or equation in the second reference is
C**** enclosed in parentheses. The coefficients used in this
C**** subroutine are slightly more precise than those used in either
C**** of the references. The generated orbital parameters are precise
C**** within plus or minus 1000000 years from present.
C****
C**** Input: YEAR = years A.D. are positive, B.C. are negative
C**** Output: ECCEN = eccentricity of orbital ellipse
C**** OBLIQ = latitude of Tropic of Cancer in radians
C**** OMEGVP = longitude of perihelion =
C**** = spatial angle from vernal equinox to perihelion
C**** in radians with sun as angle vertex
C****
IMPLICIT REAL*8 (A-H,O-Z)
PARAMETER (TWOPI=6.283185307179586477d0, PIz180=TWOPI/360.d0)
REAL*8 TABLE1(3,47),TABLE4(3,19),TABLE5(3,78)
C**** Table 1 (2). Obliquity relative to mean ecliptic of date: OBLIQD
DATA TABLE1/-2462.2214466d0, 31.609974d0, 251.9025d0,
2 -857.3232075d0, 32.620504d0, 280.8325d0,
3 -629.3231835d0, 24.172203d0, 128.3057d0,
4 -414.2804924d0, 31.983787d0, 292.7252d0,
5 -311.7632587d0, 44.828336d0, 15.3747d0,
6 308.9408604d0, 30.973257d0, 263.7951d0,
7 -162.5533601d0, 43.668246d0, 308.4258d0,
8 -116.1077911d0, 32.246691d0, 240.0099d0,
9 101.1189923d0, 30.599444d0, 222.9725d0,
O -67.6856209d0, 42.681324d0, 268.7809d0,
1 24.9079067d0, 43.836462d0, 316.7998d0,
2 22.5811241d0, 47.439436d0, 319.6024d0,
3 -21.1648355d0, 63.219948d0, 143.8050d0,
4 -15.6549876d0, 64.230478d0, 172.7351d0,
5 15.3936813d0, 1.010530d0, 28.9300d0,
6 14.6660938d0, 7.437771d0, 123.5968d0,
7 -11.7273029d0, 55.782177d0, 20.2082d0,
8 10.2742696d0, .373813d0, 40.8226d0,
9 6.4914588d0, 13.218362d0, 123.4722d0,
O 5.8539148d0, 62.583231d0, 155.6977d0,
1 -5.4872205d0, 63.593761d0, 184.6277d0,
2 -5.4290191d0, 76.438310d0, 267.2772d0,
3 5.1609570d0, 45.815258d0, 55.0196d0,
4 5.0786314d0, 8.448301d0, 152.5268d0,
5 -4.0735782d0, 56.792707d0, 49.1382d0,
6 3.7227167d0, 49.747842d0, 204.6609d0,
7 3.3971932d0, 12.058272d0, 56.5233d0,
8 -2.8347004d0, 75.278220d0, 200.3284d0,
9 -2.6550721d0, 65.241008d0, 201.6651d0,
O -2.5717867d0, 64.604291d0, 213.5577d0,
1 -2.4712188d0, 1.647247d0, 17.0374d0,
2 2.4625410d0, 7.811584d0, 164.4194d0,
3 2.2464112d0, 12.207832d0, 94.5422d0,
4 -2.0755511d0, 63.856665d0, 131.9124d0,
5 -1.9713669d0, 56.155990d0, 61.0309d0,
6 -1.8813061d0, 77.448840d0, 296.2073d0,
7 -1.8468785d0, 6.801054d0, 135.4894d0,
8 1.8186742d0, 62.209418d0, 114.8750d0,
9 1.7601888d0, 20.656133d0, 247.0691d0,
O -1.5428851d0, 48.344406d0, 256.6114d0,
1 1.4738838d0, 55.145460d0, 32.1008d0,
2 -1.4593669d0, 69.000539d0, 143.6804d0,
3 1.4192259d0, 11.071350d0, 16.8784d0,
4 -1.1818980d0, 74.291298d0, 160.6835d0,
5 1.1756474d0, 11.047742d0, 27.5932d0,
6 -1.1316126d0, 0.636717d0, 348.1074d0,
7 1.0896928d0, 12.844549d0, 82.6496d0/
C**** Table 4 (1). Fundamental elements of the ecliptic: ECCEN sin(pi)
DATA TABLE4/ .01860798d0, 4.207205d0, 28.620089d0,
2 .01627522d0, 7.346091d0, 193.788772d0,
3 -.01300660d0, 17.857263d0, 308.307024d0,
4 .00988829d0, 17.220546d0, 320.199637d0,
5 -.00336700d0, 16.846733d0, 279.376984d0,
6 .00333077d0, 5.199079d0, 87.195000d0,
7 -.00235400d0, 18.231076d0, 349.129677d0,
8 .00140015d0, 26.216758d0, 128.443387d0,
9 .00100700d0, 6.359169d0, 154.143880d0,
O .00085700d0, 16.210016d0, 291.269597d0,
1 .00064990d0, 3.065181d0, 114.860583d0,
2 .00059900d0, 16.583829d0, 332.092251d0,
3 .00037800d0, 18.493980d0, 296.414411d0,
4 -.00033700d0, 6.190953d0, 145.769910d0,
5 .00027600d0, 18.867793d0, 337.237063d0,
6 .00018200d0, 17.425567d0, 152.092288d0,
7 -.00017400d0, 6.186001d0, 126.839891d0,
8 -.00012400d0, 18.417441d0, 210.667199d0,
9 .00001250d0, 0.667863d0, 72.108838d0/
C**** Table 5 (3). General precession in longitude: psi
DATA TABLE5/ 7391.0225890d0, 31.609974d0, 251.9025d0,
2 2555.1526947d0, 32.620504d0, 280.8325d0,
3 2022.7629188d0, 24.172203d0, 128.3057d0,
4 -1973.6517951d0, 0.636717d0, 348.1074d0,
5 1240.2321818d0, 31.983787d0, 292.7252d0,
6 953.8679112d0, 3.138886d0, 165.1686d0,
7 -931.7537108d0, 30.973257d0, 263.7951d0,
8 872.3795383d0, 44.828336d0, 15.3747d0,
9 606.3544732d0, 0.991874d0, 58.5749d0,
O -496.0274038d0, 0.373813d0, 40.8226d0,
1 456.9608039d0, 43.668246d0, 308.4258d0,
2 346.9462320d0, 32.246691d0, 240.0099d0,
3 -305.8412902d0, 30.599444d0, 222.9725d0,
4 249.6173246d0, 2.147012d0, 106.5937d0,
5 -199.1027200d0, 10.511172d0, 114.5182d0,
6 191.0560889d0, 42.681324d0, 268.7809d0,
7 -175.2936572d0, 13.650058d0, 279.6869d0,
8 165.9068833d0, 0.986922d0, 39.6448d0,
9 161.1285917d0, 9.874455d0, 126.4108d0,
O 139.7878093d0, 13.013341d0, 291.5795d0,
1 -133.5228399d0, 0.262904d0, 307.2848d0,
2 117.0673811d0, 0.004952d0, 18.9300d0,
3 104.6907281d0, 1.142024d0, 273.7596d0,
4 95.3227476d0, 63.219948d0, 143.8050d0,
5 86.7824524d0, 0.205021d0, 191.8927d0,
6 86.0857729d0, 2.151964d0, 125.5237d0,
7 70.5893698d0, 64.230478d0, 172.7351d0,
8 -69.9719343d0, 43.836462d0, 316.7998d0,
9 -62.5817473d0, 47.439436d0, 319.6024d0,
O 61.5450059d0, 1.384343d0, 69.7526d0,
1 -57.9364011d0, 7.437771d0, 123.5968d0,
2 57.1899832d0, 18.829299d0, 217.6432d0,
3 -57.0236109d0, 9.500642d0, 85.5882d0,
4 -54.2119253d0, 0.431696d0, 156.2147d0,
5 53.2834147d0, 1.160090d0, 66.9489d0,
6 52.1223575d0, 55.782177d0, 20.2082d0,
7 -49.0059908d0, 12.639528d0, 250.7568d0,
8 -48.3118757d0, 1.155138d0, 48.0188d0,
9 -45.4191685d0, 0.168216d0, 8.3739d0,
O -42.2357920d0, 1.647247d0, 17.0374d0,
1 -34.7971099d0, 10.884985d0, 155.3409d0,
2 34.4623613d0, 5.610937d0, 94.1709d0,
3 -33.8356643d0, 12.658184d0, 221.1120d0,
4 33.6689362d0, 1.010530d0, 28.9300d0,
5 -31.2521586d0, 1.983748d0, 117.1498d0,
6 -30.8798701d0, 14.023871d0, 320.5095d0,
7 28.4640769d0, 0.560178d0, 262.3602d0,
8 -27.1960802d0, 1.273434d0, 336.2148d0,
9 27.0860736d0, 12.021467d0, 233.0046d0,
O -26.3437456d0, 62.583231d0, 155.6977d0,
1 24.7253740d0, 63.593761d0, 184.6277d0,
2 24.6732126d0, 76.438310d0, 267.2772d0,
3 24.4272733d0, 4.280910d0, 78.9281d0,
4 24.0127327d0, 13.218362d0, 123.4722d0,
5 21.7150294d0, 17.818769d0, 188.7132d0,
6 -21.5375347d0, 8.359495d0, 180.1364d0,
7 18.1148363d0, 56.792707d0, 49.1382d0,
8 -16.9603104d0, 8.448301d0, 152.5268d0,
9 -16.1765215d0, 1.978796d0, 98.2198d0,
O 15.5567653d0, 8.863925d0, 97.4808d0,
1 15.4846529d0, 0.186365d0, 221.5376d0,
2 15.2150632d0, 8.996212d0, 168.2438d0,
3 14.5047426d0, 6.771027d0, 161.1199d0,
4 -14.3873316d0, 45.815258d0, 55.0196d0,
5 13.1351419d0, 12.002811d0, 262.6495d0,
6 12.8776311d0, 75.278220d0, 200.3284d0,
7 11.9867234d0, 65.241008d0, 201.6651d0,
8 11.9385578d0, 18.870667d0, 294.6547d0,
9 11.7030822d0, 22.009553d0, 99.8233d0,
O 11.6018181d0, 64.604291d0, 213.5577d0,
1 -11.2617293d0, 11.498094d0, 154.1631d0,
2 -10.4664199d0, 0.578834d0, 232.7153d0,
3 10.4333970d0, 9.237738d0, 138.3034d0,
4 -10.2377466d0, 49.747842d0, 204.6609d0,
5 10.1934446d0, 2.147012d0, 106.5938d0,
6 -10.1280191d0, 1.196895d0, 250.4676d0,
7 10.0289441d0, 2.133898d0, 332.3345d0,
8 -10.0034259d0, 0.173168d0, 27.3039d0/
C****
YM1950 = YEAR-1950.
C****
C**** Obliquity from Table 1 (2):
C**** OBLIQ# = 23.320556 (degrees) Equation 5.5 (15)
C**** OBLIQD = OBLIQ# + sum[A cos(ft+delta)] Equation 1 (5)
C****
SUMC = 0.
DO 110 I=1,47
ARG = PIz180*(YM1950*TABLE1(2,I)/3600.+TABLE1(3,I))
110 SUMC = SUMC + TABLE1(1,I)*COS(ARG)
OBLIQD = 23.320556d0 + SUMC/3600.
OBLIQ = OBLIQD*PIz180
C****
C**** Eccentricity from Table 4 (1):
C**** ECCEN sin(pi) = sum[M sin(gt+beta)] Equation 4 (1)
C**** ECCEN cos(pi) = sum[M cos(gt+beta)] Equation 4 (1)
C**** ECCEN = ECCEN sqrt[sin(pi)^2 + cos(pi)^2]
C****
ESINPI = 0.
ECOSPI = 0.
DO 210 I=1,19
ARG = PIz180*(YM1950*TABLE4(2,I)/3600.+TABLE4(3,I))
ESINPI = ESINPI + TABLE4(1,I)*SIN(ARG)
210 ECOSPI = ECOSPI + TABLE4(1,I)*COS(ARG)
ECCEN = SQRT(ESINPI*ESINPI+ECOSPI*ECOSPI)
C****
C**** Perihelion from Equation 4,6,7 (9) and Table 4,5 (1,3):
C**** PSI# = 50.439273 (seconds of degree) Equation 7.5 (16)
C**** ZETA = 3.392506 (degrees) Equation 7.5 (17)
C**** PSI = PSI# t + ZETA + sum[F sin(ft+delta)] Equation 7 (9)
C**** PIE = atan[ECCEN sin(pi) / ECCEN cos(pi)]
C**** OMEGVP = PIE + PSI + 3.14159 Equation 6 (4.5)
C****
PIE = ATAN2(ESINPI,ECOSPI)
FSINFD = 0.
DO 310 I=1,78
ARG = PIz180*(YM1950*TABLE5(2,I)/3600.+TABLE5(3,I))
310 FSINFD = FSINFD + TABLE5(1,I)*SIN(ARG)
PSI = PIz180*(3.392506d0+(YM1950*50.439273d0+FSINFD)/3600.)
OMEGVP = MODULO (PIE+PSI+.5*TWOPI, TWOPI)
C****
RETURN
END