# Howell Jul07 - Solar insolation calculations using a QNial programming language adaptation of: # J. Laskar, P. Robutel, F. Joutel, M. Gastineau, A.C.M. Correia, B. Levrard 2004 # "A long term numerical solution for the insolation quantities of the Earth" # Astronomy & Astrophysics manuscript no. La-2004 May 23, 2004 # http://www.imcce.fr/fr/presentation/equipes/ASD/preprints/prep.2004/La_2004_prep.pdf # Solar constant assumed : 1368 # Latitude of calculations : 73 # Solar insolation average for each month (W/m2, roughly the 21st to 20th of first/second month): # ky BP 1 Dec-Jan 2 Jan-Feb 3 Feb-Mar 4 Mar-Apr 5 Apr-May 6 May-Jun 7 Jun-Jul 8 Jul-Aug 9 Aug-Sep 10 Sep-Oct 11 Oct-Nov 12 Nov-Dec a := -6012 0.0000000 5.6798694 67.7868528 203.4806396 393.1035652 547.5971015 533.0409398 355.3153872 163.9662757 39.2971395 0.5567048 0.0000000 -6011 0.0000000 6.2752265 67.3484644 195.7003985 374.9459089 531.8988946 535.8755865 371.0914350 175.5245377 42.9375521 0.6813850 0.0000000 -6010 0.0000000 6.7899977 67.1936028 189.1176285 357.3965169 512.5924185 533.2456887 386.5631219 190.5910948 49.3625978 1.0463824 0.0000000 -6009 0.0000000 7.2097420 67.3609311 184.2285234 342.1335318 492.3253983 525.3908141 398.8448049 207.1945398 58.2873550 1.8632920 0.0000000 -6008 0.0000000 7.4661423 67.8349002 181.2925997 330.2971209 473.3428528 513.5415487 406.1876623 223.1124337 69.1615234 3.2246855 0.0000000 -6007 0.0000000 7.5149621 68.5456094 180.3499493 322.4058262 457.3015888 499.5637053 407.8410081 236.1969722 80.9294237 5.3980029 0.0000000 -6006 0.0000000 7.3550358 69.3687447 181.2675797 318.6611899 445.5852802 485.7654059 404.3821528 244.5393267 91.7095955 8.3207438 0.0000000 -6005 0.0000000 7.0200663 70.2051871 183.8679947 318.8760163 438.4838252 473.4662585 397.0510264 247.6919432 100.1088293 11.5537926 0.0000000 -6004 0.0000000 6.5432957 70.9668368 187.8863190 322.7636521 436.0682646 463.6391234 387.3176274 245.8590419 104.9365172 14.5450503 0.0000000 -6003 0.0000000 5.9964473 71.6074081 192.9551545 329.7896382 437.9472511 456.6400348 376.4451896 239.9696246 105.8273361 16.6683615 0.0000000 -6002 0.0000000 5.4877604 72.1298963 198.7464415 339.4575856 443.6002558 452.3428476 365.1145770 231.0317123 103.0786397 17.3679795 0.0000000 -6001 0.0000000 5.1014693 72.5536047 204.7226938 350.7884086 452.0419570 450.3528953 354.0936096 220.3573743 97.6359094 16.6969792 0.0000000 -6000 0.0000000 4.8659587 72.8888276 210.3963104 363.0014698 462.7485347 450.5311520 343.7561846 208.6655620 90.1748461 14.8484616 0.0000000 -5999 0.0000000 4.7692451 73.1274261 215.2064090 374.9181501 474.6299594 452.4644877 334.6868132 197.0352395 81.8561776 12.3557011 0.0000000 -5998 0.0000000 4.8042455 73.2306728 218.6510190 385.4977511 486.8872367 456.0849904 327.3317083 186.1969702 73.4506290 9.6880615 0.0000000 -5997 0.0000000 4.9541934 73.1452635 220.3237347 393.7150716 498.7304297 461.4659695 322.3339372 176.8119018 65.5752297 7.2516956 0.0000000 -5996 0.0000000 5.2000724 72.8367375 220.0566728 398.6816731 509.1985602 468.5276610 320.2527592 169.5628696 58.8082042 5.2757333 0.0000000 -5995 0.0000000 5.4998973 72.3010166 217.9010566 399.8495052 517.3721957 477.1087429 321.5640351 165.0123907 53.5198701 3.7587631 0.0000000 -5994 0.0000000 5.8131674 71.5755417 214.1936168 397.3060308 522.6650911 486.8293991 326.3548670 163.3905946 49.8109765 2.7464805 0.0000000 -5993 0.0000000 6.0845396 70.7466349 209.4925745 391.5047881 524.3755288 496.6965419 334.4938362 165.0417691 47.9268169 2.1191181 0.0000000 -5992 0.0000000 6.2954426 69.9129156 204.4148754 383.4129227 522.4454695 505.6159964 345.3962485 169.9125194 47.8985189 1.8260828 0.0000000 -5991 0.0000000 6.4319720 69.1675164 199.5849494 374.3381255 517.5266933 512.5702935 357.8689811 177.4819672 49.6021623 1.7534385 0.0000000 -5990 0.0000000 6.4775703 68.5863144 195.4859993 365.3552325 510.3152449 516.6721991 370.6036025 187.2615575 53.0782721 1.9122751 0.0000000 -5989 0.0000000 6.4243803 68.1995146 192.4922771 357.6577431 502.3017422 517.8670169 381.9775502 197.9695320 57.9218805 2.2871513 0.0000000 -5988 0.0000000 6.2742771 67.9923162 190.6728348 351.7531467 494.5398372 516.6365158 391.0568244 208.5549664 63.7272671 2.8764275 0.0000000 -5987 0.0000000 6.0185965 67.9417354 190.1614214 348.2412997 488.1397718 513.6562154 397.0405320 217.7321408 69.8636483 3.7219228 0.0000000 -5986 0.0000000 5.6758934 67.9878892 190.7336767 346.9560546 483.5447309 509.8871955 400.0942061 224.8328535 75.6773317 4.7367153 0.0000000 -5985 0.0000000 5.2860011 68.0861734 192.3054447 347.9886282 481.2858544 506.1369083 400.3766166 229.1491793 80.3840371 5.7660341 0.0000000 -5984 0.0000000 4.9068158 68.2018482 194.5899254 350.8535572 481.1032737 502.8328216 398.5343283 230.8633211 83.6751277 6.7434316 0.0000000 -5983 0.0000000 4.5587664 68.3176180 197.3956832 355.2763774 482.8869394 500.2658847 395.0555316 230.1038558 85.2819479 7.4871116 0.0000000 -5982 0.0000000 4.2583845 68.4214646 200.3787508 360.6609303 486.2176601 498.6273884 390.6423334 227.3802699 85.2146912 7.8510151 0.0000000 -5981 0.0000000 4.0183365 68.5263938 203.3606676 366.5412877 490.5434985 497.6692211 385.6430993 223.2878722 83.8507148 7.8778799 0.0000000 -5980 0.0000000 3.8590792 68.6305543 206.0271417 372.2788797 495.3619828 497.3958520 380.5788769 218.4027505 81.4867588 7.5957738 0.0000000 -5979 0.0000000 3.7825896 68.7380039 208.2031695 377.4336007 500.2153569 497.6447327 375.7725285 213.2013346 78.5028010 7.0941767 0.0000000 -5978 0.0000000 3.7816247 68.8509790 209.7628656 381.5658832 504.5421371 498.1467032 371.5055519 208.2233578 75.3779147 6.4998002 0.0000000 -5977 0.0000000 3.8501074 68.9646077 210.6229757 384.3791963 507.9849610 498.7775747 367.9832949 203.8132500 72.4050389 5.9005867 0.0000000 -5976 0.0000000 3.9796836 69.0742534 210.7814647 385.7542070 510.3360023 499.4366034 365.3074179 200.1668127 69.7693231 5.3574186 0.0000000 -5975 0.0000000 4.1493623 69.1875981 210.3717217 385.7180543 511.3060170 499.7810114 363.4678107 197.5290167 67.7683277 4.9542502 0.0000000 -5974 0.0000000 4.3500929 69.3033919 209.5048814 384.4793675 511.0310615 499.8058376 362.3676571 195.8030990 66.3519577 4.6772395 0.0000000 -5973 0.0000000 4.5669115 69.4291774 208.3605775 382.3418514 509.6410166 499.3778750 361.7836479 194.8901604 65.5218461 4.5229330 0.0000000 -5972 0.0000000 4.7818183 69.5775181 207.1558949 379.6884940 507.3204957 498.3267356 361.4244923 194.6483174 65.2757263 4.4956200 0.0000000 -5971 0.0000000 4.9976789 69.7451321 205.9988443 376.8775494 504.5154101 496.8270886 361.0718948 194.7417864 65.3743351 4.5486846 0.0000000 -5970 0.0000000 5.2127845 69.9313624 204.9899218 374.2043653 501.5509765 494.9755079 360.5404739 194.9307540 65.6663734 4.6588265 0.0000000 -5969 0.0000000 5.4097644 70.1371825 204.2488695 371.9857401 498.7628124 492.8493511 359.6197852 194.9625388 66.0054062 4.8083367 0.0000000 -5968 0.0000000 5.5985097 70.3407879 203.6576033 370.1479569 496.3524118 490.8076257 358.4821503 194.7396807 66.2014206 4.9391238 0.0000000 -5967 0.0000000 5.7769743 70.5349917 203.2428508 368.8360608 494.5661511 489.0084085 357.0678260 194.0895796 66.1082947 5.0143632 0.0000000 -5966 0.0000000 5.9521123 70.7039362 202.8435452 367.7285179 493.1794459 487.5664023 355.7225305 193.2787274 65.8228063 5.0357629 0.0000000 -5965 0.0000000 6.1265212 70.8331370 202.3859160 366.7645566 492.2755915 486.6744745 354.5644896 192.2833524 65.2599831 4.9730047 0.0000000 -5964 0.0000000 6.3118597 70.9051678 201.6671258 365.4965316 491.4753761 486.4030287 354.0399006 191.4970439 64.6017851 4.8482667 0.0000000 -5963 0.0000000 6.4957349 70.9289375 200.7372863 363.8825193 490.5553911 486.5341258 354.1740648 191.1229296 64.0497136 4.7135906 0.0000000 -5962 0.0000000 6.6895610 70.8874185 199.4025591 361.5031191 489.1607928 487.1500715 355.3885472 191.5224446 63.7503910 4.5827097 0.0000000 -5961 0.0000000 6.8734392 70.8030220 197.8044766 358.4522283 487.0786724 487.8841038 357.5732702 192.8748715 63.9362650 4.5168650 0.0000000 -5960 0.0000000 7.0422388 70.6916137 196.0012187 354.7045679 484.0646555 488.4538684 360.7390619 195.4095263 64.8239042 4.5620189 0.0000000 -5959 0.0000000 7.1791281 70.5744641 194.1464635 350.4989364 480.1694734 488.6052302 364.6416135 199.0952372 66.4997767 4.7471984 0.0000000 -5958 0.0000000 7.2597791 70.4797575 192.4569691 346.2189409 475.5775142 488.0490438 368.8266008 203.7601611 69.0216564 5.1129025 0.0000000 -5957 0.0000000 7.2581177 70.4354621 191.1864168 342.3468264 470.6215416 486.5480374 372.7115264 209.0775788 72.3916964 5.7090435 0.0000000 -5956 0.0000000 7.1670975 70.4444848 190.4796811 339.2956506 465.8448630 484.2498180 375.8701473 214.4983233 76.3495751 6.5242303 0.0000000 -5955 0.0000000 6.9817688 70.5087647 190.5290691 337.5572460 461.8453338 481.3307566 377.8273772 219.3706805 80.5629141 7.5193063 0.0000000 -5954 0.0000000 6.6904620 70.6201643 191.4890832 337.5581157 459.1839854 478.0643093 378.1688538 223.0475787 84.6055156 8.6526234 0.0000000 -5953 0.0000000 6.3082533 70.7419538 193.2990020 339.4308943 458.3387373 475.0493257 376.9838432 225.0236562 87.8602233 9.8031055 0.0000000 -5952 0.0000000 5.8374712 70.8598082 196.0282181 343.4449652 459.6802898 472.5639930 374.1983291 224.8977921 89.8633706 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72.9517610 235.5126690 429.0318681 528.4692796 464.4316827 306.0368952 159.5943767 55.5810262 5.0519707 0.0000000 -5922 0.0000000 4.4580053 73.0603753 233.7383357 432.8033449 539.4112949 469.4651499 299.8138701 148.7178359 47.0360287 3.0773605 0.0000000 -5921 0.0000000 5.2670131 72.7472010 228.6374374 430.0674816 547.1919705 477.4196020 298.4565451 141.2410785 40.3792020 1.7946009 0.0000000 -5920 0.0000000 6.1852688 72.0074107 220.5577298 420.1862636 550.0518283 488.3300751 303.0653585 138.1446869 35.9404087 1.0555294 0.0000000 -5919 0.0000000 7.1059556 70.9731309 210.5481974 403.9924154 546.4246816 500.8875270 314.0402735 140.1546133 33.9032019 0.6728904 0.0000000 -5918 0.0000000 8.0213766 69.8449296 199.7726491 383.2361070 535.2393648 512.6609722 331.2258300 148.0345953 34.5171818 0.5557951 0.0000000 -5917 0.0000000 8.8416888 68.8720829 189.5465462 360.4586450 516.8762572 520.2124065 353.0004751 162.1589549 38.1956807 0.6361717 0.0000000 -5916 0.0000000 9.5242008 68.2778283 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318.6471407 420.2789422 444.6276870 381.9611734 257.7985608 124.5686044 24.3068222 0.0000000 -5908 0.0000000 4.6088109 71.8729911 199.3427726 334.6955652 432.2979173 443.7957665 370.4327789 246.5099730 120.2580054 25.1151372 -0.0005855 -5907 0.0000000 3.7427535 71.8113121 209.0186740 353.8309175 448.2521334 445.6001120 358.6340376 232.4646993 111.7702869 23.3905076 -0.0005768 -5906 0.0000000 3.1722763 71.7478868 218.6822890 374.8536008 467.0352157 449.3566708 346.7849749 216.8066852 100.4790167 19.7052888 0.0000000 -5905 0.0000000 2.8598874 71.7454264 227.5447329 396.3591770 487.5274198 454.4588540 335.1605288 200.4999312 87.7617370 15.0916426 0.0000000 -5904 0.0000000 2.7438258 71.7818542 234.8034858 416.7648046 508.6598505 460.5811288 324.2749702 184.4233673 74.8120142 10.4624021 0.0000000 -5903 0.0000000 2.8061596 71.7510347 239.4452568 433.9996274 529.2911062 468.0265846 315.1390815 169.6152605 62.6132671 6.5869103 0.0000000 -5902 0.0000000 3.0045790 71.5334669 240.9007850 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