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. 2024 Aug 19;14:19146. doi: 10.1038/s41598-024-68607-0

Table 3.

Zonal harmonic coefficients up to the sixth order.

The nth order zonal harmonic coefficients: [T/mn]
Coeff. Z0 Z1 Z2 Z3 Z4 Z5 Z6
Expo. 100 10-1 100 100 102 102 104
Virgin 9.372 1.997 − 4.401 8.206 0.2204 8.689 2.594
Cycle1 9.387 2.003 − 3.028 8.248 0.7946 8.495 0.1853
Cycle2 9.390 2.001 − 2.721 8.263 1.063 8.452 − 0.5120
Cycle3 9.392 2.006 − 2.543 8.272 1.241 8.425 − 0.9461
Cycle4 9.393 2.006 − 2.434 8.279 1.362 8.408 − 1.226
Cycle5 9.395 2.007 − 2.326 8.285 1.483 8.391 − 1.505
Cycle6 9.396 2.007 − 2.250 8.290 1.573 8.378 − 1.706
Cycle7 9.397 2.007 − 2.188 8.295 1.651 8.398 − 1.876
Cycle8 9.397 2.007 − 2.135 8.298 1.717 8.359 − 2.018
Cycle9 9.397 2.008 − 2.081 8.301 1.782 8.349 − 2.161
Cycle10 9.398 2.008 − 2.039 8.304 1.838 8.342 − 2.279
Cycle11 9.398 2.008 − 1.999 8.306 1.889 8.334 − 2.389
Cycle12 9.398 2.008 − 1.965 8.309 1.934 8.328 − 2.485
Cycle13 9.399 2.009 − 1.931 8.311 1.979 8.321 − 2.581
Cycle14 9.399 2.009 − 1.901 8.314 2.020 8.316 − 2.666
Cycle15 9.399 2.009 − 1.894 8.314 2.032 8.315 − 2.689
Cycle16 9.400 2.009 − 1.885 8.315 2.044 8.313 − 2.716
Final 9.400 2.009 − 1.877 8.316 2.058 8.312 − 2.742