...
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L0_i = A_i * cos (B_i + C_i * JME) |
where:
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\[ \begin{array}{|c|c|c|} \hline A_i, & B_i, & C_i=\\ \[ \left( \begin{array}{ccc}hline 175347046.0 & 0 & 0\\ 3341656.0 & 4.6692568 & 6283.07585\\ 34894.0 & 4.6261 & 12566.1517\\ 3497.0 & 2.7441 & 5753.3849\\ 3418.0 & 2.8289 & 3.5231\\ 3136.0 & 3.6277 & 77713.7715\\ 2676.0 & 4.4181 & 7860.4194\\ 2343.0 & 6.1352 & 3930.2097\\ 1324.0 & 0.7425 & 11506.7698\\ 1273.0 & 2.0371 & 529.691\\ 1199.0 & 1.1096 & 1577.3435\\ 990 & 5.233 & 5884.927\\ 902 & 2.045 & 26.298\\ 857 & 3.508 & 398.149\\ 780 & 1.179 & 5223.694\\ 753 & 2.533 & 5507.553\\ 505 & 4.583 & 18849.228\\ 492 & 4.205 & 775.523\\ 357 & 2.92 & 0.067\\ 317 & 5.849 & 11790.629\\ 284 & 1.899 & 796.298\\ 271 & 0.315 & 10977.079\\ 243 & 0.345 & 5486.778\\ 206 & 4.806 & 2544.314\\ 205 & 1.869 & 5573.143\\ 202 & 2.458 & 6069.777\\ 156 & 0.833 & 213.299\\ 132 & 3.411 & 2942.463\\ 126 & 1.083 & 20.775\\ 115 & 0.645 & 0.98\\ 103 & 0.636 & 4694.003\\ 102 & 0.976 & 15720.839\\ 102 & 4.267 & 7.114\\ 99 & 6.21 & 2146.17\\ 98 & 0.68 & 155.42\\ 86 & 5.98 & 161000.69\\ 85 & 1.3 & 6275.96\\ 85 & 3.67 & 71430.7\\ 80 & 1.81 & 17260.15\\ 79 & 3.04 & 12036.46\\ 75 & 1.76 & 5088.63\\ 74 & 3.5 & 3154.69\\ 74 & 4.68 & 801.82\\ 70 & 0.83 & 9437.76\\ 62 & 3.98 & 8827.39\\ 61 & 1.82 & 7084.9\\ 57 & 2.78 & 6286.6\\ 56 & 4.39 & 14143.5\\ 56 & 3.47 & 6279.55\\ 52 & 0.19 & 12139.55\\ 52 & 1.33 & 1748.02\\ 51 & 0.28 & 5856.48\\ 49 & 0.49 & 1194.45\\ 41 & 5.37 & 8429.24\\ 41 & 2.4 & 19651.05\\ 39 & 6.17 & 10447.39\\ 37 & 6.04 & 10213.29\\ 37 & 2.57 & 1059.38\\ 36 & 1.71 & 2352.87\\ 36 & 1.78 & 6812.77\\ 33 & 0.59 & 17789.85\\ 30 & 0.44 & 83996.85\\ 30 & 2.74 & 1349.87\\ 25 & 3.16 & 4690.48 \end\ \hline \end{array} \right)\] |
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L0 = \sum_{i=0}^{n} L0_i |
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L1_i = A_i * cos (B_i + C_i * JME) |
where:
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L1\[ = \sum_{i=0}^{n} L0_i |
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L2_i =begin{array}{|c|c|c|} \hline A_i *& cos (B_i +& C_i\\ * JME) |
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L2 = \sum_{i=0}^{n} L0_i |
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L3_i = A_i * cos (B_i + C_i * JME) |
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L3 = \sum_{i=0}^{n} L0_i |
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L4_i = A_i * cos (B_i + C_i * JME) |
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L4 = \sum_{i=0}^{n} L0_i |
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L5_i = A_i * cos (B_i + C_i * JME) |
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L5 = \sum_{i=0}^{n} L0_i |
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L = \frac{(L0 + L1*JME + L2*JME^2 + L3*JME^3 + L4*JME^4 + L5*JME^5)}{10^8} |
Calculate Earth heliocentric latitude (B):
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B0_i = A_i * cos (B_i + C_i * JME) |
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B0 = \sum_{i=0}^{n} L0_i |
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B1_i = A_i * cos (B_i + C_i * JME) |
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B1 = \sum_{i=0}^{n} L0_i |
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B = \frac{(B0 + B1*JME)}{10^8} |
Calculate the Earth radius vector (R) in astronomical units (AU):
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R0_i = A_i * cos (B_i + C_i * JME) |
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R0 = \sum_{i=0}^{n} L0_i |
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R1_i = A_i * cos (B_i + C_i * JME) |
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R1 = \sum_{i=0}^{n} L0_i |
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R2_i = A_i * cos (B_i + C_i * JME) |
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R2 = \sum_{i=0}^{n} L0_i |
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R3_i = A_i * cos (B_i + C_i * JME) |
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R3 = \sum_{i=0}^{n} L0_i |
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R4_i = A_i * cos (B_i + C_i * JME) |
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R4 = \sum_{i=0}^{n} L0_i |
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R = \frac{(R0 + R1*JME + R2*JME^2 + R3*JME^3 + R4*JME^4)}{10^8} |
Caculate the geocentric longitude and latitude (Θ and ß)
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\theta = L + 180 |
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\beta = -B |
...
\hline
628331966747.0 & 0 & 0\\
206059.0 & 2.678235 & 6283.07585\\
4303.0 & 2.6351 & 12566.1517\\
425.0 & 1.59 & 3.523\\
119.0 & 5.796 & 26.298\\
109.0 & 2.966 & 1577.344\\
93 & 2.59 & 18849.23\\
72 & 1.14 & 529.69\\
68 & 1.87 & 398.15\\
67 & 4.41 & 5507.55\\
59 & 2.89 & 5223.69\\
56 & 2.17 & 155.42\\
45 & 0.4 & 796.3\\
36 & 0.47 & 775.52\\
29 & 2.65 & 7.11\\
21 & 5.34 & 0.98\\
19 & 1.85 & 5486.78\\
19 & 4.97 & 213.3\\
17 & 2.99 & 6275.96\\
16 & 0.03 & 2544.31\\
16 & 1.43 & 2146.17\\
15 & 1.21 & 10977.08\\
12 & 2.83 & 1748.02\\
12 & 3.26 & 5088.63\\
12 & 5.27 & 1194.45\\
12 & 2.08 & 4694\\
11 & 0.77 & 553.57\\
10 & 1.3 & 6286.6\\
10 & 4.24 & 1349.87\\
9 & 2.7 & 242.73\\
9 & 5.64 & 951.72\\
8 & 5.3 & 2352.87\\
6 & 2.65 & 9437.76\\
6 & 4.67 & 4690.48\\
\hline
\end{array} \] |
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|---|---|---|---|---|
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--uriencoded--L1 = \sum_%7Bi=0%7D%5e%7Bn%7D L1_i |
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L2_i = A_i * cos (B_i + C_i * JME) |
where:
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\[ \begin{array}{|c|c|c|}
\hline
A_i & B_i & C_i\\
\hline
52919.0 & 0 & 0\\
8720.0 & 1.0721 & 6283.0758\\
309.0 & 0.867 & 12566.152\\
27 & 0.05 & 3.52\\
16 & 5.19 & 26.3\\
16 & 3.68 & 155.42\\
10 & 0.76 & 18849.23\\
9 & 2.06 & 77713.77\\
7 & 0.83 & 775.52\\
5 & 4.66 & 1577.34\\
4 & 1.03 & 7.11\\
4 & 3.44 & 5573.14\\
3 & 5.14 & 796.3\\
3 & 6.05 & 5507.55\\
3 & 1.19 & 242.73\\
3 & 6.12 & 529.69\\
3 & 0.31 & 398.15\\
3 & 2.28 & 553.57\\
2 & 4.38 & 5223.69\\
2 & 3.75 & 0.98\\
\hline
\end{array} \] |
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|---|---|---|---|---|
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--uriencoded--L2 = \sum_%7Bi=0%7D%5e%7Bn%7D L2_i |
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L3_i = A_i * cos (B_i + C_i * JME) |
where:
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\[
\begin{array}{|c|c|c|}
\hline
A_i & B_i & C_i\\
\hline
289.0 & 5.844 & 6283.076\\
35 & 0 & 0\\
17 & 5.49 & 12566.15\\
3 & 5.2 & 155.42\\
1 & 4.72 & 3.52\\
1 & 5.3 & 18849.23\\
1 & 5.97 & 242.73\\
\hline
\end{array} \] |
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--uriencoded--L3 = \sum_%7Bi=0%7D%5e%7Bn%7D L3_i |
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L4_i = A_i * cos (B_i + C_i * JME) |
where:
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\[
\begin{array}{|c|c|c|}
\hline
A_i & B_i & C_i\\
\hline
114.0 & 3.142 & 0\\
8 & 4.13 & 6283.08\\
1 & 3.84 & 12566.15\\
\hline
\end{array} \] |
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--uriencoded--L4 = \sum_%7Bi=0%7D%5e%7Bn%7D L4_i |
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L5_i = A_i * cos (B_i + C_i * JME) |
where:
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\[
\begin{array}{|c|c|c|}
\hline
A_i & B_i & C_i\\
\hline
1 & 3.14 & 0\\
\hline
\end{array} \] |
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--uriencoded--L5 = \sum_%7Bi=0%7D%5e%7Bn%7D L5_i |
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L = \frac{(L0 + L1*JME + L2*JME^2 + L3*JME^3 + L4*JME^4 + L5*JME^5)}{10^8} |
Calculate Earth heliocentric latitude (B):
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B0_i = A_i * cos (B_i + C_i * JME) |
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|---|---|---|---|---|
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--uriencoded--B0 = \sum_%7Bi=0%7D%5e%7Bn%7D B0_i |
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B1_i = A_i * cos (B_i + C_i * JME) |
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--uriencoded--B1 = \sum_%7Bi=0%7D%5e%7Bn%7DB1_i |
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B = \frac{(B0 + B1*JME)}{10^8} |
Calculate the Earth radius vector (R) in astronomical units (AU):
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R0_i = A_i * cos (B_i + C_i * JME) |
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|---|---|---|---|---|
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--uriencoded--R0 = \sum_%7Bi=0%7D%5e%7Bn%7D R0_i |
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R1_i = A_i * cos (B_i + C_i * JME) |
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|---|---|---|---|---|
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--uriencoded--R1 = \sum_%7Bi=0%7D%5e%7Bn%7DR1_i |
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R2_i = A_i * cos (B_i + C_i * JME) |
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|---|---|---|---|---|
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--uriencoded--R2 = \sum_%7Bi=0%7D%5e%7Bn%7D R2_i |
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R3_i = A_i * cos (B_i + C_i * JME) |
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--uriencoded--R3 = \sum_%7Bi=0%7D%5e%7Bn%7D R3_i |
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R4_i = A_i * cos (B_i + C_i * JME) |
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--uriencoded--R4 = \sum_%7Bi=0%7D%5e%7Bn%7D R4_i |
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R = \frac{(R0 + R1*JME + R2*JME^2 + R3*JME^3 + R4*JME^4)}{10^8} |
Caculate the geocentric longitude and latitude (Θ and ß)
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\theta = L + 180 |
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\beta = -B |
Calculate the nutation in longitude and obliquity (Δψ and Δε)
...
Calculate the topocentric sun right ascension (α′)
Calculate the topocentric local hour angle (H′)
Calculate the topocentric zenith angle (Θ)
...
)
Calculate the topocentric local hour angle (H′)
Calculate the topocentric zenith angle (Θ)
Calculate the topocentric azimuth angle (Φ)
Calculate the angular separation
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\cos \Theta = \sin \delta_1 \sin \delta_2 + \cos \delta_1 \cos \delta_2 \cos (\alpha_1 - \alpha_2) |