Function frhling(jahr As Integer) As Double





jr = (jahr - 2000) / 1000

jdef = 2451623.80984 + 365242.37404 * jr + 0.05169 * jr ^ 2 - 0.00411 * jr ^ 3 - 0.00057 * jr ^ 4

jdes = 2451716.56767 + 365241.62603 * jr + 0.00325 * jr * jr + 0.00888 * jr ^ 3 - 0.0003 * jr ^ 4

jdeh = 2451810.21715 + 365242.01767 * jr - 0.11575 * jr ^ 2 + 0.00337 * jr ^ 3 + 0.00078 * jr ^ 4

jdew = 2451900.05952 + 365242.74049 * jr - 0.06223 * jr ^ 2 - 0.00823 * jr ^ 3 + 0.00032 * jr ^ 4

tf = (jdef - 2451545) / 36525
ts = (jdes - 2451545) / 36525
th = (jdeh - 2451545) / 36525
tw = (jdew - 2451545) / 36525

wf = 35999.373 * tf - 2.47
ws = 35999.373 * ts - 2.47
wh = 35999.373 * th - 2.47
ww = 35999.373 * tw - 2.47

lf = 1 + 0.0334 * Cos(wf * 3.14159265358979 / 180) + 0.0007 * Cos(2 * wf * 3.14159265358979 / 180)

ls = 1 + 0.0334 * Cos(ws * 3.14159265358979 / 180) + 0.0007 * Cos(2 * ws * 3.14159265358979 / 180)

lh = 1 + 0.0334 * Cos(wh * 3.14159265358979 / 180) + 0.0007 * Cos(2 * wh * 3.14159265358979 / 180)

lw = 1 + 0.0334 * Cos(ww * 3.14159265358979 / 180) + 0.0007 * Cos(2 * ww * 3.14159265358979 / 180)



sf1 = 485 * Cos((324.96 + 1934.136 * tf) * 3.14159265358979 / 180) + 203 * Cos((337.23 + 32964.467 * tf) * 3.14159265358979 / 180) + 199 * Cos((342.08 + 20.186 * tf) * 3.14159265358979 / 180) + 182 * Cos((27.85 + 445267.112 * tf) * 3.14159265358979 / 180) + 156 * Cos((73.14 + 45036.886 * tf) * 3.14159265358979 / 180) + 136 * Cos((171.52 + 22518.443 * tf) * 3.14159265358979 / 180) + 77 * Cos((222.54 + 65928.934 * tf) * 3.14159265358979 / 180) + 74 * Cos((296.72 + 3034.906 * tf) * 3.14159265358979 / 180) + 70 * Cos((243.58 + 9037.513 * tf) * 3.14159265358979 / 180) + 58 * Cos((119.81 + 33718.147 * tf) * 3.14159265358979 / 180) + 52 * Cos((297.17 + 150.678 * tf) * 3.14159265358979 / 180) + 50 * Cos((21.02 + 2281.226) * 3.14159265358979 / 180)

sf2 = 45 * Cos((247.54 + 29929.562 * tf) * 3.14159265358979 / 180) + 44 * Cos((325.15 + 31555.956 * tf) * 3.14159265358979 / 180) + 29 * Cos((60.93 + 4443.417 * tf) * 3.14159265358979 / 180) + 18 * Cos((155.12 + 67555.328 * tf) * 3.14159265358979 / 180) + 17 * Cos((288.79 + 4562.452 * tf) * 3.14159265358979 / 180) + 16 * Cos((198.04 + 62894.029 * tf) * 3.14159265358979 / 180) + 14 * Cos((199.76 + 31436.921 * tf) * 3.14159265358979 / 180) + 12 * Cos((95.39 + 14577.848 * tf) * 3.14159265358979 / 180) + 12 * Cos((287.11 + 31931.756 * tf) * 3.14159265358979 / 180) + 12 * Cos((320.81 + 34777.259 * tf) * 3.14159265358979 / 180) + 9 * Cos((227.73 + 1222.114 * tf) * 3.14159265358979 / 180) + 8 * Cos((15.45 + 16859.074 * tf) * 3.14159265358979 / 180)

sf = sf1 + sf2


ss1 = 485 * Cos((324.96 + 1934.136 * ts) * 3.14159265358979 / 180) + 203 * Cos((337.23 + 32964.467 * ts) * 3.14159265358979 / 180) + 199 * Cos((342.08 + 20.186 * ts) * 3.14159265358979 / 180) + 182 * Cos((27.85 + 445267.112 * ts) * 3.14159265358979 / 180) + 156 * Cos((73.14 + 45036.886 * ts) * 3.14159265358979 / 180) + 136 * Cos((171.52 + 22518.443 * ts) * 3.14159265358979 / 180) + 77 * Cos((222.54 + 65928.934 * ts) * 3.14159265358979 / 180) + 74 * Cos((296.72 + 3034.906 * ts) * 3.14159265358979 / 180) + 70 * Cos((243.58 + 9037.513 * ts) * 3.14159265358979 / 180) + 58 * Cos((119.81 + 33718.147 * ts) * 3.14159265358979 / 180) + 52 * Cos((297.17 + 150.678 * ts) * 3.14159265358979 / 180) + 50 * Cos((21.02 + 2281.226) * 3.14159265358979 / 180)

ss2 = 45 * Cos((247.54 + 29929.562 * ts) * 3.14159265358979 / 180) + 44 * Cos((325.15 + 31555.956 * ts) * 3.14159265358979 / 180) + 29 * Cos((60.93 + 4443.417 * ts) * 3.14159265358979 / 180) + 18 * Cos((155.12 + 67555.328 * ts) * 3.14159265358979 / 180) + 17 * Cos((288.79 + 4562.452 * ts) * 3.14159265358979 / 180) + 16 * Cos((198.04 + 62894.029 * ts) * 3.14159265358979 / 180) + 14 * Cos((199.76 + 31436.921 * ts) * 3.14159265358979 / 180) + 12 * Cos((95.39 + 14577.848 * ts) * 3.14159265358979 / 180) + 12 * Cos((287.11 + 31931.756 * ts) * 3.14159265358979 / 180) + 12 * Cos((320.81 + 34777.259 * ts) * 3.14159265358979 / 180) + 9 * Cos((227.73 + 1222.114 * ts) * 3.14159265358979 / 180) + 8 * Cos((15.45 + 16859.074 * ts) * 3.14159265358979 / 180)

ss = ss1 + ss2


sh1 = 485 * Cos((324.96 + 1934.136 * th) * 3.14159265358979 / 180) + 203 * Cos((337.23 + 32964.467 * th) * 3.14159265358979 / 180) + 199 * Cos((342.08 + 20.186 * th) * 3.14159265358979 / 180) + 182 * Cos((27.85 + 445267.112 * th) * 3.14159265358979 / 180) + 156 * Cos((73.14 + 45036.886 * th) * 3.14159265358979 / 180) + 136 * Cos((171.52 + 22518.443 * th) * 3.14159265358979 / 180) + 77 * Cos((222.54 + 65928.934 * th) * 3.14159265358979 / 180) + 74 * Cos((296.72 + 3034.906 * th) * 3.14159265358979 / 180) + 70 * Cos((243.58 + 9037.513 * th) * 3.14159265358979 / 180) + 58 * Cos((119.81 + 33718.147 * th) * 3.14159265358979 / 180) + 52 * Cos((297.17 + 150.678 * th) * 3.14159265358979 / 180) + 50 * Cos((21.02 + 2281.226) * 3.14159265358979 / 180)

sh2 = 45 * Cos((247.54 + 29929.562 * th) * 3.14159265358979 / 180) + 44 * Cos((325.15 + 31555.956 * th) * 3.14159265358979 / 180) + 29 * Cos((60.93 + 4443.417 * th) * 3.14159265358979 / 180) + 18 * Cos((155.12 + 67555.328 * th) * 3.14159265358979 / 180) + 17 * Cos((288.79 + 4562.452 * th) * 3.14159265358979 / 180) + 16 * Cos((198.04 + 62894.029 * th) * 3.14159265358979 / 180) + 14 * Cos((199.76 + 31436.921 * th) * 3.14159265358979 / 180) + 12 * Cos((95.39 + 14577.848 * th) * 3.14159265358979 / 180) + 12 * Cos((287.11 + 31931.756 * th) * 3.14159265358979 / 180) + 12 * Cos((320.81 + 34777.259 * th) * 3.14159265358979 / 180) + 9 * Cos((227.73 + 1222.114 * th) * 3.14159265358979 / 180) + 8 * Cos((15.45 + 16859.074 * th) * 3.14159265358979 / 180)

sh = sh1 + sh2


sw1 = 485 * Cos((324.96 + 1934.136 * tw) * 3.14159265358979 / 180) + 203 * Cos((337.23 + 32964.467 * tw) * 3.14159265358979 / 180) + 199 * Cos((342.08 + 20.186 * tw) * 3.14159265358979 / 180) + 182 * Cos((27.85 + 445267.112 * tw) * 3.14159265358979 / 180) + 156 * Cos((73.14 + 45036.886 * tw) * 3.14159265358979 / 180) + 136 * Cos((171.52 + 22518.443 * tw) * 3.14159265358979 / 180) + 77 * Cos((222.54 + 65928.934 * tw) * 3.14159265358979 / 180) + 74 * Cos((296.72 + 3034.906 * tw) * 3.14159265358979 / 180) + 70 * Cos((243.58 + 9037.513 * tw) * 3.14159265358979 / 180) + 58 * Cos((119.81 + 33718.147 * tw) * 3.14159265358979 / 180) + 52 * Cos((297.17 + 150.678 * tw) * 3.14159265358979 / 180) + 50 * Cos((21.02 + 2281.226) * 3.14159265358979 / 180)

sw2 = 45 * Cos((247.54 + 29929.562 * tw) * 3.14159265358979 / 180) + 44 * Cos((325.15 + 31555.956 * tw) * 3.14159265358979 / 180) + 29 * Cos((60.93 + 4443.417 * tw) * 3.14159265358979 / 180) + 18 * Cos((155.12 + 67555.328 * tw) * 3.14159265358979 / 180) + 17 * Cos((288.79 + 4562.452 * tw) * 3.14159265358979 / 180) + 16 * Cos((198.04 + 62894.029 * tw) * 3.14159265358979 / 180) + 14 * Cos((199.76 + 31436.921 * tw) * 3.14159265358979 / 180) + 12 * Cos((95.39 + 14577.848 * tw) * 3.14159265358979 / 180) + 12 * Cos((287.11 + 31931.756 * tw) * 3.14159265358979 / 180) + 12 * Cos((320.81 + 34777.259 * tw) * 3.14159265358979 / 180) + 9 * Cos((227.73 + 1222.114 * tw) * 3.14159265358979 / 180) + 8 * Cos((15.45 + 16859.074 * tw) * 3.14159265358979 / 180)

sw = sw1 + sw2





jdef = jdef + 0.00001 * sf / lf - 1 / (60 * 24)

jdes = jdes + 0.00001 * ss / ls - 1 / (60 * 24)

jdeh = jdeh + 0.00001 * sh / lh - 1 / (60 * 24)

jdew = jdew + 0.00001 * sw / lw - 1 / (60 * 24)


frhling = jdef




End Function



Function sommer(jahr As Integer) As Double





jr = (jahr - 2000) / 1000

jdef = 2451623.80984 + 365242.37404 * jr + 0.05169 * jr ^ 2 - 0.00411 * jr ^ 3 - 0.00057 * jr ^ 4

jdes = 2451716.56767 + 365241.62603 * jr + 0.00325 * jr * jr + 0.00888 * jr ^ 3 - 0.0003 * jr ^ 4

jdeh = 2451810.21715 + 365242.01767 * jr - 0.11575 * jr ^ 2 + 0.00337 * jr ^ 3 + 0.00078 * jr ^ 4

 jdew = 2451900.05952 + 365242.74049 * jr - 0.06223 * jr ^ 2 - 0.00823 * jr ^ 3 + 0.00032 * jr ^ 4

tf = (jdef - 2451545) / 36525
ts = (jdes - 2451545) / 36525
th = (jdeh - 2451545) / 36525
tw = (jdew - 2451545) / 36525

wf = 35999.373 * tf - 2.47
ws = 35999.373 * ts - 2.47
wh = 35999.373 * th - 2.47
ww = 35999.373 * tw - 2.47

lf = 1 + 0.0334 * Cos(wf * 3.14159265358979 / 180) + 0.0007 * Cos(2 * wf * 3.14159265358979 / 180)

ls = 1 + 0.0334 * Cos(ws * 3.14159265358979 / 180) + 0.0007 * Cos(2 * ws * 3.14159265358979 / 180)

lh = 1 + 0.0334 * Cos(wh * 3.14159265358979 / 180) + 0.0007 * Cos(2 * wh * 3.14159265358979 / 180)

lw = 1 + 0.0334 * Cos(ww * 3.14159265358979 / 180) + 0.0007 * Cos(2 * ww * 3.14159265358979 / 180)



sf1 = 485 * Cos((324.96 + 1934.136 * tf) * 3.14159265358979 / 180) + 203 * Cos((337.23 + 32964.467 * tf) * 3.14159265358979 / 180) + 199 * Cos((342.08 + 20.186 * tf) * 3.14159265358979 / 180) + 182 * Cos((27.85 + 445267.112 * tf) * 3.14159265358979 / 180) + 156 * Cos((73.14 + 45036.886 * tf) * 3.14159265358979 / 180) + 136 * Cos((171.52 + 22518.443 * tf) * 3.14159265358979 / 180) + 77 * Cos((222.54 + 65928.934 * tf) * 3.14159265358979 / 180) + 74 * Cos((296.72 + 3034.906 * tf) * 3.14159265358979 / 180) + 70 * Cos((243.58 + 9037.513 * tf) * 3.14159265358979 / 180) + 58 * Cos((119.81 + 33718.147 * tf) * 3.14159265358979 / 180) + 52 * Cos((297.17 + 150.678 * tf) * 3.14159265358979 / 180) + 50 * Cos((21.02 + 2281.226) * 3.14159265358979 / 180)

sf2 = 45 * Cos((247.54 + 29929.562 * tf) * 3.14159265358979 / 180) + 44 * Cos((325.15 + 31555.956 * tf) * 3.14159265358979 / 180) + 29 * Cos((60.93 + 4443.417 * tf) * 3.14159265358979 / 180) + 18 * Cos((155.12 + 67555.328 * tf) * 3.14159265358979 / 180) + 17 * Cos((288.79 + 4562.452 * tf) * 3.14159265358979 / 180) + 16 * Cos((198.04 + 62894.029 * tf) * 3.14159265358979 / 180) + 14 * Cos((199.76 + 31436.921 * tf) * 3.14159265358979 / 180) + 12 * Cos((95.39 + 14577.848 * tf) * 3.14159265358979 / 180) + 12 * Cos((287.11 + 31931.756 * tf) * 3.14159265358979 / 180) + 12 * Cos((320.81 + 34777.259 * tf) * 3.14159265358979 / 180) + 9 * Cos((227.73 + 1222.114 * tf) * 3.14159265358979 / 180) + 8 * Cos((15.45 + 16859.074 * tf) * 3.14159265358979 / 180)

sf = sf1 + sf2


ss1 = 485 * Cos((324.96 + 1934.136 * ts) * 3.14159265358979 / 180) + 203 * Cos((337.23 + 32964.467 * ts) * 3.14159265358979 / 180) + 199 * Cos((342.08 + 20.186 * ts) * 3.14159265358979 / 180) + 182 * Cos((27.85 + 445267.112 * ts) * 3.14159265358979 / 180) + 156 * Cos((73.14 + 45036.886 * ts) * 3.14159265358979 / 180) + 136 * Cos((171.52 + 22518.443 * ts) * 3.14159265358979 / 180) + 77 * Cos((222.54 + 65928.934 * ts) * 3.14159265358979 / 180) + 74 * Cos((296.72 + 3034.906 * ts) * 3.14159265358979 / 180) + 70 * Cos((243.58 + 9037.513 * ts) * 3.14159265358979 / 180) + 58 * Cos((119.81 + 33718.147 * ts) * 3.14159265358979 / 180) + 52 * Cos((297.17 + 150.678 * ts) * 3.14159265358979 / 180) + 50 * Cos((21.02 + 2281.226) * 3.14159265358979 / 180)

ss2 = 45 * Cos((247.54 + 29929.562 * ts) * 3.14159265358979 / 180) + 44 * Cos((325.15 + 31555.956 * ts) * 3.14159265358979 / 180) + 29 * Cos((60.93 + 4443.417 * ts) * 3.14159265358979 / 180) + 18 * Cos((155.12 + 67555.328 * ts) * 3.14159265358979 / 180) + 17 * Cos((288.79 + 4562.452 * ts) * 3.14159265358979 / 180) + 16 * Cos((198.04 + 62894.029 * ts) * 3.14159265358979 / 180) + 14 * Cos((199.76 + 31436.921 * ts) * 3.14159265358979 / 180) + 12 * Cos((95.39 + 14577.848 * ts) * 3.14159265358979 / 180) + 12 * Cos((287.11 + 31931.756 * ts) * 3.14159265358979 / 180) + 12 * Cos((320.81 + 34777.259 * ts) * 3.14159265358979 / 180) + 9 * Cos((227.73 + 1222.114 * ts) * 3.14159265358979 / 180) + 8 * Cos((15.45 + 16859.074 * ts) * 3.14159265358979 / 180)

ss = ss1 + ss2


sh1 = 485 * Cos((324.96 + 1934.136 * th) * 3.14159265358979 / 180) + 203 * Cos((337.23 + 32964.467 * th) * 3.14159265358979 / 180) + 199 * Cos((342.08 + 20.186 * th) * 3.14159265358979 / 180) + 182 * Cos((27.85 + 445267.112 * th) * 3.14159265358979 / 180) + 156 * Cos((73.14 + 45036.886 * th) * 3.14159265358979 / 180) + 136 * Cos((171.52 + 22518.443 * th) * 3.14159265358979 / 180) + 77 * Cos((222.54 + 65928.934 * th) * 3.14159265358979 / 180) + 74 * Cos((296.72 + 3034.906 * th) * 3.14159265358979 / 180) + 70 * Cos((243.58 + 9037.513 * th) * 3.14159265358979 / 180) + 58 * Cos((119.81 + 33718.147 * th) * 3.14159265358979 / 180) + 52 * Cos((297.17 + 150.678 * th) * 3.14159265358979 / 180) + 50 * Cos((21.02 + 2281.226) * 3.14159265358979 / 180)

sh2 = 45 * Cos((247.54 + 29929.562 * th) * 3.14159265358979 / 180) + 44 * Cos((325.15 + 31555.956 * th) * 3.14159265358979 / 180) + 29 * Cos((60.93 + 4443.417 * th) * 3.14159265358979 / 180) + 18 * Cos((155.12 + 67555.328 * th) * 3.14159265358979 / 180) + 17 * Cos((288.79 + 4562.452 * th) * 3.14159265358979 / 180) + 16 * Cos((198.04 + 62894.029 * th) * 3.14159265358979 / 180) + 14 * Cos((199.76 + 31436.921 * th) * 3.14159265358979 / 180) + 12 * Cos((95.39 + 14577.848 * th) * 3.14159265358979 / 180) + 12 * Cos((287.11 + 31931.756 * th) * 3.14159265358979 / 180) + 12 * Cos((320.81 + 34777.259 * th) * 3.14159265358979 / 180) + 9 * Cos((227.73 + 1222.114 * th) * 3.14159265358979 / 180) + 8 * Cos((15.45 + 16859.074 * th) * 3.14159265358979 / 180)

sh = sh1 + sh2


sw1 = 485 * Cos((324.96 + 1934.136 * tw) * 3.14159265358979 / 180) + 203 * Cos((337.23 + 32964.467 * tw) * 3.14159265358979 / 180) + 199 * Cos((342.08 + 20.186 * tw) * 3.14159265358979 / 180) + 182 * Cos((27.85 + 445267.112 * tw) * 3.14159265358979 / 180) + 156 * Cos((73.14 + 45036.886 * tw) * 3.14159265358979 / 180) + 136 * Cos((171.52 + 22518.443 * tw) * 3.14159265358979 / 180) + 77 * Cos((222.54 + 65928.934 * tw) * 3.14159265358979 / 180) + 74 * Cos((296.72 + 3034.906 * tw) * 3.14159265358979 / 180) + 70 * Cos((243.58 + 9037.513 * tw) * 3.14159265358979 / 180) + 58 * Cos((119.81 + 33718.147 * tw) * 3.14159265358979 / 180) + 52 * Cos((297.17 + 150.678 * tw) * 3.14159265358979 / 180) + 50 * Cos((21.02 + 2281.226) * 3.14159265358979 / 180)

sw2 = 45 * Cos((247.54 + 29929.562 * tw) * 3.14159265358979 / 180) + 44 * Cos((325.15 + 31555.956 * tw) * 3.14159265358979 / 180) + 29 * Cos((60.93 + 4443.417 * tw) * 3.14159265358979 / 180) + 18 * Cos((155.12 + 67555.328 * tw) * 3.14159265358979 / 180) + 17 * Cos((288.79 + 4562.452 * tw) * 3.14159265358979 / 180) + 16 * Cos((198.04 + 62894.029 * tw) * 3.14159265358979 / 180) + 14 * Cos((199.76 + 31436.921 * tw) * 3.14159265358979 / 180) + 12 * Cos((95.39 + 14577.848 * tw) * 3.14159265358979 / 180) + 12 * Cos((287.11 + 31931.756 * tw) * 3.14159265358979 / 180) + 12 * Cos((320.81 + 34777.259 * tw) * 3.14159265358979 / 180) + 9 * Cos((227.73 + 1222.114 * tw) * 3.14159265358979 / 180) + 8 * Cos((15.45 + 16859.074 * tw) * 3.14159265358979 / 180)

sw = sw1 + sw2






jdef = jdef + 0.00001 * sf / lf - 1 / (60 * 24)

jdes = jdes + 0.00001 * ss / ls - 1 / (60 * 24)

jdeh = jdeh + 0.00001 * sh / lh - 1 / (60 * 24)

jdew = jdew + 0.00001 * sw / lw - 1 / (60 * 24)


sommer = jdes




End Function


Function herbst(jahr As Integer) As Double




jr = (jahr - 2000) / 1000

jdef = 2451623.80984 + 365242.37404 * jr + 0.05169 * jr ^ 2 - 0.00411 * jr ^ 3 - 0.00057 * jr ^ 4

jdes = 2451716.56767 + 365241.62603 * jr + 0.00325 * jr * jr + 0.00888 * jr ^ 3 - 0.0003 * jr ^ 4

jdeh = 2451810.21715 + 365242.01767 * jr - 0.11575 * jr ^ 2 + 0.00337 * jr ^ 3 + 0.00078 * jr ^ 4

 jdew = 2451900.05952 + 365242.74049 * jr - 0.06223 * jr ^ 2 - 0.00823 * jr ^ 3 + 0.00032 * jr ^ 4

tf = (jdef - 2451545) / 36525
ts = (jdes - 2451545) / 36525
th = (jdeh - 2451545) / 36525
tw = (jdew - 2451545) / 36525

wf = 35999.373 * tf - 2.47
ws = 35999.373 * ts - 2.47
wh = 35999.373 * th - 2.47
ww = 35999.373 * tw - 2.47

lf = 1 + 0.0334 * Cos(wf * 3.14159265358979 / 180) + 0.0007 * Cos(2 * wf * 3.14159265358979 / 180)

ls = 1 + 0.0334 * Cos(ws * 3.14159265358979 / 180) + 0.0007 * Cos(2 * ws * 3.14159265358979 / 180)

lh = 1 + 0.0334 * Cos(wh * 3.14159265358979 / 180) + 0.0007 * Cos(2 * wh * 3.14159265358979 / 180)

lw = 1 + 0.0334 * Cos(ww * 3.14159265358979 / 180) + 0.0007 * Cos(2 * ww * 3.14159265358979 / 180)



sf1 = 485 * Cos((324.96 + 1934.136 * tf) * 3.14159265358979 / 180) + 203 * Cos((337.23 + 32964.467 * tf) * 3.14159265358979 / 180) + 199 * Cos((342.08 + 20.186 * tf) * 3.14159265358979 / 180) + 182 * Cos((27.85 + 445267.112 * tf) * 3.14159265358979 / 180) + 156 * Cos((73.14 + 45036.886 * tf) * 3.14159265358979 / 180) + 136 * Cos((171.52 + 22518.443 * tf) * 3.14159265358979 / 180) + 77 * Cos((222.54 + 65928.934 * tf) * 3.14159265358979 / 180) + 74 * Cos((296.72 + 3034.906 * tf) * 3.14159265358979 / 180) + 70 * Cos((243.58 + 9037.513 * tf) * 3.14159265358979 / 180) + 58 * Cos((119.81 + 33718.147 * tf) * 3.14159265358979 / 180) + 52 * Cos((297.17 + 150.678 * tf) * 3.14159265358979 / 180) + 50 * Cos((21.02 + 2281.226) * 3.14159265358979 / 180)

sf2 = 45 * Cos((247.54 + 29929.562 * tf) * 3.14159265358979 / 180) + 44 * Cos((325.15 + 31555.956 * tf) * 3.14159265358979 / 180) + 29 * Cos((60.93 + 4443.417 * tf) * 3.14159265358979 / 180) + 18 * Cos((155.12 + 67555.328 * tf) * 3.14159265358979 / 180) + 17 * Cos((288.79 + 4562.452 * tf) * 3.14159265358979 / 180) + 16 * Cos((198.04 + 62894.029 * tf) * 3.14159265358979 / 180) + 14 * Cos((199.76 + 31436.921 * tf) * 3.14159265358979 / 180) + 12 * Cos((95.39 + 14577.848 * tf) * 3.14159265358979 / 180) + 12 * Cos((287.11 + 31931.756 * tf) * 3.14159265358979 / 180) + 12 * Cos((320.81 + 34777.259 * tf) * 3.14159265358979 / 180) + 9 * Cos((227.73 + 1222.114 * tf) * 3.14159265358979 / 180) + 8 * Cos((15.45 + 16859.074 * tf) * 3.14159265358979 / 180)

sf = sf1 + sf2


ss1 = 485 * Cos((324.96 + 1934.136 * ts) * 3.14159265358979 / 180) + 203 * Cos((337.23 + 32964.467 * ts) * 3.14159265358979 / 180) + 199 * Cos((342.08 + 20.186 * ts) * 3.14159265358979 / 180) + 182 * Cos((27.85 + 445267.112 * ts) * 3.14159265358979 / 180) + 156 * Cos((73.14 + 45036.886 * ts) * 3.14159265358979 / 180) + 136 * Cos((171.52 + 22518.443 * ts) * 3.14159265358979 / 180) + 77 * Cos((222.54 + 65928.934 * ts) * 3.14159265358979 / 180) + 74 * Cos((296.72 + 3034.906 * ts) * 3.14159265358979 / 180) + 70 * Cos((243.58 + 9037.513 * ts) * 3.14159265358979 / 180) + 58 * Cos((119.81 + 33718.147 * ts) * 3.14159265358979 / 180) + 52 * Cos((297.17 + 150.678 * ts) * 3.14159265358979 / 180) + 50 * Cos((21.02 + 2281.226) * 3.14159265358979 / 180)

ss2 = 45 * Cos((247.54 + 29929.562 * ts) * 3.14159265358979 / 180) + 44 * Cos((325.15 + 31555.956 * ts) * 3.14159265358979 / 180) + 29 * Cos((60.93 + 4443.417 * ts) * 3.14159265358979 / 180) + 18 * Cos((155.12 + 67555.328 * ts) * 3.14159265358979 / 180) + 17 * Cos((288.79 + 4562.452 * ts) * 3.14159265358979 / 180) + 16 * Cos((198.04 + 62894.029 * ts) * 3.14159265358979 / 180) + 14 * Cos((199.76 + 31436.921 * ts) * 3.14159265358979 / 180) + 12 * Cos((95.39 + 14577.848 * ts) * 3.14159265358979 / 180) + 12 * Cos((287.11 + 31931.756 * ts) * 3.14159265358979 / 180) + 12 * Cos((320.81 + 34777.259 * ts) * 3.14159265358979 / 180) + 9 * Cos((227.73 + 1222.114 * ts) * 3.14159265358979 / 180) + 8 * Cos((15.45 + 16859.074 * ts) * 3.14159265358979 / 180)

ss = ss1 + ss2


sh1 = 485 * Cos((324.96 + 1934.136 * th) * 3.14159265358979 / 180) + 203 * Cos((337.23 + 32964.467 * th) * 3.14159265358979 / 180) + 199 * Cos((342.08 + 20.186 * th) * 3.14159265358979 / 180) + 182 * Cos((27.85 + 445267.112 * th) * 3.14159265358979 / 180) + 156 * Cos((73.14 + 45036.886 * th) * 3.14159265358979 / 180) + 136 * Cos((171.52 + 22518.443 * th) * 3.14159265358979 / 180) + 77 * Cos((222.54 + 65928.934 * th) * 3.14159265358979 / 180) + 74 * Cos((296.72 + 3034.906 * th) * 3.14159265358979 / 180) + 70 * Cos((243.58 + 9037.513 * th) * 3.14159265358979 / 180) + 58 * Cos((119.81 + 33718.147 * th) * 3.14159265358979 / 180) + 52 * Cos((297.17 + 150.678 * th) * 3.14159265358979 / 180) + 50 * Cos((21.02 + 2281.226) * 3.14159265358979 / 180)

sh2 = 45 * Cos((247.54 + 29929.562 * th) * 3.14159265358979 / 180) + 44 * Cos((325.15 + 31555.956 * th) * 3.14159265358979 / 180) + 29 * Cos((60.93 + 4443.417 * th) * 3.14159265358979 / 180) + 18 * Cos((155.12 + 67555.328 * th) * 3.14159265358979 / 180) + 17 * Cos((288.79 + 4562.452 * th) * 3.14159265358979 / 180) + 16 * Cos((198.04 + 62894.029 * th) * 3.14159265358979 / 180) + 14 * Cos((199.76 + 31436.921 * th) * 3.14159265358979 / 180) + 12 * Cos((95.39 + 14577.848 * th) * 3.14159265358979 / 180) + 12 * Cos((287.11 + 31931.756 * th) * 3.14159265358979 / 180) + 12 * Cos((320.81 + 34777.259 * th) * 3.14159265358979 / 180) + 9 * Cos((227.73 + 1222.114 * th) * 3.14159265358979 / 180) + 8 * Cos((15.45 + 16859.074 * th) * 3.14159265358979 / 180)

sh = sh1 + sh2


sw1 = 485 * Cos((324.96 + 1934.136 * tw) * 3.14159265358979 / 180) + 203 * Cos((337.23 + 32964.467 * tw) * 3.14159265358979 / 180) + 199 * Cos((342.08 + 20.186 * tw) * 3.14159265358979 / 180) + 182 * Cos((27.85 + 445267.112 * tw) * 3.14159265358979 / 180) + 156 * Cos((73.14 + 45036.886 * tw) * 3.14159265358979 / 180) + 136 * Cos((171.52 + 22518.443 * tw) * 3.14159265358979 / 180) + 77 * Cos((222.54 + 65928.934 * tw) * 3.14159265358979 / 180) + 74 * Cos((296.72 + 3034.906 * tw) * 3.14159265358979 / 180) + 70 * Cos((243.58 + 9037.513 * tw) * 3.14159265358979 / 180) + 58 * Cos((119.81 + 33718.147 * tw) * 3.14159265358979 / 180) + 52 * Cos((297.17 + 150.678 * tw) * 3.14159265358979 / 180) + 50 * Cos((21.02 + 2281.226) * 3.14159265358979 / 180)

sw2 = 45 * Cos((247.54 + 29929.562 * tw) * 3.14159265358979 / 180) + 44 * Cos((325.15 + 31555.956 * tw) * 3.14159265358979 / 180) + 29 * Cos((60.93 + 4443.417 * tw) * 3.14159265358979 / 180) + 18 * Cos((155.12 + 67555.328 * tw) * 3.14159265358979 / 180) + 17 * Cos((288.79 + 4562.452 * tw) * 3.14159265358979 / 180) + 16 * Cos((198.04 + 62894.029 * tw) * 3.14159265358979 / 180) + 14 * Cos((199.76 + 31436.921 * tw) * 3.14159265358979 / 180) + 12 * Cos((95.39 + 14577.848 * tw) * 3.14159265358979 / 180) + 12 * Cos((287.11 + 31931.756 * tw) * 3.14159265358979 / 180) + 12 * Cos((320.81 + 34777.259 * tw) * 3.14159265358979 / 180) + 9 * Cos((227.73 + 1222.114 * tw) * 3.14159265358979 / 180) + 8 * Cos((15.45 + 16859.074 * tw) * 3.14159265358979 / 180)

sw = sw1 + sw2





jdef = jdef + 0.00001 * sf / lf - 1 / (60 * 24)

jdes = jdes + 0.00001 * ss / ls - 1 / (60 * 24)

jdeh = jdeh + 0.00001 * sh / lh - 1 / (60 * 24)

jdew = jdew + 0.00001 * sw / lw - 1 / (60 * 24)


herbst = jdeh




End Function



Function winter(jahr As Integer) As Double




jr = (jahr - 2000) / 1000

jdef = 2451623.80984 + 365242.37404 * jr + 0.05169 * jr ^ 2 - 0.00411 * jr ^ 3 - 0.00057 * jr ^ 4

jdes = 2451716.56767 + 365241.62603 * jr + 0.00325 * jr * jr + 0.00888 * jr ^ 3 - 0.0003 * jr ^ 4

jdeh = 2451810.21715 + 365242.01767 * jr - 0.11575 * jr ^ 2 + 0.00337 * jr ^ 3 + 0.00078 * jr ^ 4

 jdew = 2451900.05952 + 365242.74049 * jr - 0.06223 * jr ^ 2 - 0.00823 * jr ^ 3 + 0.00032 * jr ^ 4

tf = (jdef - 2451545) / 36525
ts = (jdes - 2451545) / 36525
th = (jdeh - 2451545) / 36525
tw = (jdew - 2451545) / 36525

wf = 35999.373 * tf - 2.47
ws = 35999.373 * ts - 2.47
wh = 35999.373 * th - 2.47
ww = 35999.373 * tw - 2.47

lf = 1 + 0.0334 * Cos(wf * 3.14159265358979 / 180) + 0.0007 * Cos(2 * wf * 3.14159265358979 / 180)

ls = 1 + 0.0334 * Cos(ws * 3.14159265358979 / 180) + 0.0007 * Cos(2 * ws * 3.14159265358979 / 180)

lh = 1 + 0.0334 * Cos(wh * 3.14159265358979 / 180) + 0.0007 * Cos(2 * wh * 3.14159265358979 / 180)

lw = 1 + 0.0334 * Cos(ww * 3.14159265358979 / 180) + 0.0007 * Cos(2 * ww * 3.14159265358979 / 180)



sf1 = 485 * Cos((324.96 + 1934.136 * tf) * 3.14159265358979 / 180) + 203 * Cos((337.23 + 32964.467 * tf) * 3.14159265358979 / 180) + 199 * Cos((342.08 + 20.186 * tf) * 3.14159265358979 / 180) + 182 * Cos((27.85 + 445267.112 * tf) * 3.14159265358979 / 180) + 156 * Cos((73.14 + 45036.886 * tf) * 3.14159265358979 / 180) + 136 * Cos((171.52 + 22518.443 * tf) * 3.14159265358979 / 180) + 77 * Cos((222.54 + 65928.934 * tf) * 3.14159265358979 / 180) + 74 * Cos((296.72 + 3034.906 * tf) * 3.14159265358979 / 180) + 70 * Cos((243.58 + 9037.513 * tf) * 3.14159265358979 / 180) + 58 * Cos((119.81 + 33718.147 * tf) * 3.14159265358979 / 180) + 52 * Cos((297.17 + 150.678 * tf) * 3.14159265358979 / 180) + 50 * Cos((21.02 + 2281.226) * 3.14159265358979 / 180)

sf2 = 45 * Cos((247.54 + 29929.562 * tf) * 3.14159265358979 / 180) + 44 * Cos((325.15 + 31555.956 * tf) * 3.14159265358979 / 180) + 29 * Cos((60.93 + 4443.417 * tf) * 3.14159265358979 / 180) + 18 * Cos((155.12 + 67555.328 * tf) * 3.14159265358979 / 180) + 17 * Cos((288.79 + 4562.452 * tf) * 3.14159265358979 / 180) + 16 * Cos((198.04 + 62894.029 * tf) * 3.14159265358979 / 180) + 14 * Cos((199.76 + 31436.921 * tf) * 3.14159265358979 / 180) + 12 * Cos((95.39 + 14577.848 * tf) * 3.14159265358979 / 180) + 12 * Cos((287.11 + 31931.756 * tf) * 3.14159265358979 / 180) + 12 * Cos((320.81 + 34777.259 * tf) * 3.14159265358979 / 180) + 9 * Cos((227.73 + 1222.114 * tf) * 3.14159265358979 / 180) + 8 * Cos((15.45 + 16859.074 * tf) * 3.14159265358979 / 180)

sf = sf1 + sf2


ss1 = 485 * Cos((324.96 + 1934.136 * ts) * 3.14159265358979 / 180) + 203 * Cos((337.23 + 32964.467 * ts) * 3.14159265358979 / 180) + 199 * Cos((342.08 + 20.186 * ts) * 3.14159265358979 / 180) + 182 * Cos((27.85 + 445267.112 * ts) * 3.14159265358979 / 180) + 156 * Cos((73.14 + 45036.886 * ts) * 3.14159265358979 / 180) + 136 * Cos((171.52 + 22518.443 * ts) * 3.14159265358979 / 180) + 77 * Cos((222.54 + 65928.934 * ts) * 3.14159265358979 / 180) + 74 * Cos((296.72 + 3034.906 * ts) * 3.14159265358979 / 180) + 70 * Cos((243.58 + 9037.513 * ts) * 3.14159265358979 / 180) + 58 * Cos((119.81 + 33718.147 * ts) * 3.14159265358979 / 180) + 52 * Cos((297.17 + 150.678 * ts) * 3.14159265358979 / 180) + 50 * Cos((21.02 + 2281.226) * 3.14159265358979 / 180)

ss2 = 45 * Cos((247.54 + 29929.562 * ts) * 3.14159265358979 / 180) + 44 * Cos((325.15 + 31555.956 * ts) * 3.14159265358979 / 180) + 29 * Cos((60.93 + 4443.417 * ts) * 3.14159265358979 / 180) + 18 * Cos((155.12 + 67555.328 * ts) * 3.14159265358979 / 180) + 17 * Cos((288.79 + 4562.452 * ts) * 3.14159265358979 / 180) + 16 * Cos((198.04 + 62894.029 * ts) * 3.14159265358979 / 180) + 14 * Cos((199.76 + 31436.921 * ts) * 3.14159265358979 / 180) + 12 * Cos((95.39 + 14577.848 * ts) * 3.14159265358979 / 180) + 12 * Cos((287.11 + 31931.756 * ts) * 3.14159265358979 / 180) + 12 * Cos((320.81 + 34777.259 * ts) * 3.14159265358979 / 180) + 9 * Cos((227.73 + 1222.114 * ts) * 3.14159265358979 / 180) + 8 * Cos((15.45 + 16859.074 * ts) * 3.14159265358979 / 180)

ss = ss1 + ss2


sh1 = 485 * Cos((324.96 + 1934.136 * th) * 3.14159265358979 / 180) + 203 * Cos((337.23 + 32964.467 * th) * 3.14159265358979 / 180) + 199 * Cos((342.08 + 20.186 * th) * 3.14159265358979 / 180) + 182 * Cos((27.85 + 445267.112 * th) * 3.14159265358979 / 180) + 156 * Cos((73.14 + 45036.886 * th) * 3.14159265358979 / 180) + 136 * Cos((171.52 + 22518.443 * th) * 3.14159265358979 / 180) + 77 * Cos((222.54 + 65928.934 * th) * 3.14159265358979 / 180) + 74 * Cos((296.72 + 3034.906 * th) * 3.14159265358979 / 180) + 70 * Cos((243.58 + 9037.513 * th) * 3.14159265358979 / 180) + 58 * Cos((119.81 + 33718.147 * th) * 3.14159265358979 / 180) + 52 * Cos((297.17 + 150.678 * th) * 3.14159265358979 / 180) + 50 * Cos((21.02 + 2281.226) * 3.14159265358979 / 180)

sh2 = 45 * Cos((247.54 + 29929.562 * th) * 3.14159265358979 / 180) + 44 * Cos((325.15 + 31555.956 * th) * 3.14159265358979 / 180) + 29 * Cos((60.93 + 4443.417 * th) * 3.14159265358979 / 180) + 18 * Cos((155.12 + 67555.328 * th) * 3.14159265358979 / 180) + 17 * Cos((288.79 + 4562.452 * th) * 3.14159265358979 / 180) + 16 * Cos((198.04 + 62894.029 * th) * 3.14159265358979 / 180) + 14 * Cos((199.76 + 31436.921 * th) * 3.14159265358979 / 180) + 12 * Cos((95.39 + 14577.848 * th) * 3.14159265358979 / 180) + 12 * Cos((287.11 + 31931.756 * th) * 3.14159265358979 / 180) + 12 * Cos((320.81 + 34777.259 * th) * 3.14159265358979 / 180) + 9 * Cos((227.73 + 1222.114 * th) * 3.14159265358979 / 180) + 8 * Cos((15.45 + 16859.074 * th) * 3.14159265358979 / 180)

sh = sh1 + sh2


sw1 = 485 * Cos((324.96 + 1934.136 * tw) * 3.14159265358979 / 180) + 203 * Cos((337.23 + 32964.467 * tw) * 3.14159265358979 / 180) + 199 * Cos((342.08 + 20.186 * tw) * 3.14159265358979 / 180) + 182 * Cos((27.85 + 445267.112 * tw) * 3.14159265358979 / 180) + 156 * Cos((73.14 + 45036.886 * tw) * 3.14159265358979 / 180) + 136 * Cos((171.52 + 22518.443 * tw) * 3.14159265358979 / 180) + 77 * Cos((222.54 + 65928.934 * tw) * 3.14159265358979 / 180) + 74 * Cos((296.72 + 3034.906 * tw) * 3.14159265358979 / 180) + 70 * Cos((243.58 + 9037.513 * tw) * 3.14159265358979 / 180) + 58 * Cos((119.81 + 33718.147 * tw) * 3.14159265358979 / 180) + 52 * Cos((297.17 + 150.678 * tw) * 3.14159265358979 / 180) + 50 * Cos((21.02 + 2281.226) * 3.14159265358979 / 180)

sw2 = 45 * Cos((247.54 + 29929.562 * tw) * 3.14159265358979 / 180) + 44 * Cos((325.15 + 31555.956 * tw) * 3.14159265358979 / 180) + 29 * Cos((60.93 + 4443.417 * tw) * 3.14159265358979 / 180) + 18 * Cos((155.12 + 67555.328 * tw) * 3.14159265358979 / 180) + 17 * Cos((288.79 + 4562.452 * tw) * 3.14159265358979 / 180) + 16 * Cos((198.04 + 62894.029 * tw) * 3.14159265358979 / 180) + 14 * Cos((199.76 + 31436.921 * tw) * 3.14159265358979 / 180) + 12 * Cos((95.39 + 14577.848 * tw) * 3.14159265358979 / 180) + 12 * Cos((287.11 + 31931.756 * tw) * 3.14159265358979 / 180) + 12 * Cos((320.81 + 34777.259 * tw) * 3.14159265358979 / 180) + 9 * Cos((227.73 + 1222.114 * tw) * 3.14159265358979 / 180) + 8 * Cos((15.45 + 16859.074 * tw) * 3.14159265358979 / 180)

sw = sw1 + sw2





jdef = jdef + 0.00001 * sf / lf - 1 / (60 * 24)

jdes = jdes + 0.00001 * ss / ls - 1 / (60 * 24)

jdeh = jdeh + 0.00001 * sh / lh - 1 / (60 * 24)

jdew = jdew + 0.00001 * sw / lw - 1 / (60 * 24)


winter = jdew




End Function



