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Table 2.
Selected inequalities and their periods from the VSOP2013 theory.
| Inequality | Period (yr) | kJ | kN | Pk (au) (J) | Pk (au) (N) | kJ | kN | Pk (rad) (J) | Pk (rad) (N) |
|---|---|---|---|---|---|---|---|---|---|
| (1, 0, 0, 0) | 11.86 | 17 | 43 | 2.1 × 10−5 | 4.9 × 10−5 | 17 | 10 | 1.8 × 10−5 | 4.7 × 10−5 |
| (1, 0, 0, −1) | 12.78 | 123 | 1 | 2.0 × 10−7 | 1.5 × 10−1 | 117 | 2 | 1.8 × 10−7 | 4.4 × 10−3 |
| (1, −1, 0, 0) | 19.86 | 6 | 23 | 2.1 × 10−4 | 2.5 × 10−4 | 4 | 153 | 2.4 × 10−4 | 1.1 × 10−7 |
| (0, 1, 0, −1) | 35.87 | 2641 | 2 | 1.2 × 10−10 | 3.6 × 10−2 | 573 | 3 | 2.6 × 10−9 | 9.3 × 10−4 |
| (1, −3, 0, 0) | 57.01 | 12 | 236 | 5.5 × 10−5 | 1.1 × 10−6 | 10 | 404 | 5.0 × 10−5 | 9.7 × 10−9 |
| (1, −2, 0, 0) | 60.95 | 2 | 75 | 3.2 × 10−4 | 1.3 × 10−5 | 2 | 281 | 6.2 × 10−4 | 2.4 × 10−8 |
| (0, 1, −2, 0) | 98.58 | 510 | 359 | 5.3 × 10−9 | 3.6 × 10−7 | 428 | 242 | 5.4 × 10−9 | 3.6 × 10−8 |
| (1, −3, 2, 0) | 159.65 | 130 | 2381 | 1.7 × 10−7 | 2.7 × 10−9 | 67 | 1033 | 7.7 × 10−7 | 7.6 × 10−10 |
| (0, 0, 1, −1) | 171.44 | 8616 | 5 | 5.2 × 10−12 | 4.6 × 10−3 | 475 | 6 | 4.0 × 10−9 | 1.6 × 10−4 |
| (0, 0, 2, −3) | 178.70 | 17636 | 13 | 6.4 × 10−13 | 5.1 × 10−4 | 876 | 9 | 8.7 × 10−10 | 4.7 × 10−5 |
| (1, −3, 0, 2) | 185.12 | 299 | 156 | 2.0 × 10−8 | 2.7 × 10−6 | 152 | 104 | 7.9 × 10−8 | 2.7 × 10−7 |
| (2, −6, 0, 5) | 211.22 | 1906 | 1020 | 2.6 × 10−10 | 2.5 × 10−8 | 753 | 652 | 1.3 × 10−9 | 2.7 × 10−9 |
| (1, −4, 5, −2) | 242.94 | 1356 | 2494 | 5.6 × 10−10 | 2.3 × 10−9 | 531 | 3840 | 3.0 × 10−9 | 2.1 × 10−11 |
| (4, −10, −1, 2) | 493.08 | 1042 | 4585 | 1.0 × 10−9 | 4.3 × 10−10 | 313 | 2331 | 1.2 × 10−8 | 8.6 × 10−11 |
| (0, 1, −2, −2) | 501.44 | 1223 | 341 | 7.0 × 10−10 | 4.1 × 10−7 | 329 | 263 | 1.1 × 10−8 | 3.0 × 10−8 |
| (0, 1, −5, 4) | 777.88 | 879 | 141 | 1.5 × 10−9 | 3.4 × 10−6 | 227 | 71 | 2.7 × 10−8 | 9.2 × 10−7 |
| (2, −5, −1, 2) | 1116.17 | 282 | 734 | 2.2 × 10−8 | 5.4 × 10−8 | 75 | 297 | 6.3 × 10−7 | 2.1 × 10−8 |
| (1, −3, 0, 3) | 1498.63 | 327 | 193 | 1.7 × 10−8 | 1.8 × 10−6 | 74 | 76 | 6.3 × 10−7 | 7.6 × 10−7 |
| (2, −6, 3, 0) | 1597.80 | 72 | 1185 | 1.3 × 10−6 | 1.7 × 10−8 | 13 | 379 | 4.6 × 10−5 | 1.1 × 10−8 |
| (4, −11, 3, 0) | 1975.15 | 109 | 1412 | 3.4 × 10−7 | 1.0 × 10−8 | 16 | 445 | 2.1 × 10−5 | 7.2 × 10−9 |
| (0, 0, 2, −4) | 2116.57 | 2289 | 11 | 1.7 × 10−10 | 6.9 × 10−4 | 260 | 4 | 1.8 × 10−8 | 4.2 × 10−4 |
| (1, −3, 1, 1) | 2319.94 | 995 | 590 | 1.1 × 10−9 | 1.0 × 10−7 | 163 | 202 | 6.4 × 10−8 | 6.2 × 10−8 |
| (2, −6, 4, −2) | 2566.51 | 178 | 208 | 6.5 × 10−8 | 1.5 × 10−6 | 33 | 60 | 3.8 × 10−6 | 1.2 × 10−6 |
| (0, 0, 1, −2) | 4233.14 | 619 | 3 | 3.3 × 10−9 | 8.3 × 10−3 | 78 | 1 | 5.9 × 10−7 | 1.0 × 10−2 |
Notes. The order and the Pk amplitude for the semi-major axis and for the longitude of Jupiter and Neptune, respectively, are detailed.
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