Table D.1
Comparison between analytical and numerical solutions for the changes in central instants.
| Mutual | Change in tc | Relative | |
|---|---|---|---|
| approx. | analytical (s) | numerical (s) | error (–) |
| 1 | 2.17458 | 2.17455 | 7.84 × 10−6 |
| 2 | 36.7842 | 36.7824 | 4.85 × 10−5 |
| 3 | 73.9007 | 73.8972 | 4.76 × 10−5 |
| 4 | 94.9994 | 94.9951 | 4.56 × 10−5 |
| 5 | 111.043 | 111.038 | 4.74 × 10−5 |
| 6 | 132.098 | 132.092 | 4.55 × 10−5 |
| 7 | 169.169 | 169.161 | 4.55 × 10−5 |
| 8 | 203.983 | 203.974 | 4.58 × 10−5 |
| 9 | 206.006 | 206.198 | 9.30 × 10−4 |
| 10 | 241.156 | 241.145 | 4.53 × 10−5 |
| 11 | 261.643 | 261.631 | 4.35 × 10−5 |
| 12 | 278.322 | 278.309 | 4.51 × 10−5 |
| 13 | 298.557 | 298.544 | 4.21 × 10−5 |
| 14 | 335.416 | 335.403 | 4.04 × 10−5 |
| 15 | 371.133 | 371.117 | 4.27 × 10−5 |
| 16 | 372.219 | 372.205 | 3.84 × 10−5 |
| 17 | 408.219 | 408.202 | 4.23 × 10−5 |
| 18 | 445.273 | 445.254 | 4.21 × 10−5 |
| 19 | 464.009 | 463.996 | 2.82 × 10−5 |
| 20 | 482.288 | 482.267 | 4.21 × 10−5 |
Notes. This table compares the analytical and numerical solutions for the changes in central instants after applying a small variation (0.001%) in the initial states of Io, Europa and the Earth. Analytical approximations of the changes are derived from the central instants partials provided in Sect. 2.3. Results are here only reported for the 20 first mutual approximations detected in 2020 (although verification was conducted over 200 observations).
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