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Table 4:

Quasi-periodic decomposition of the resonant angle $\theta _{\rm b} = 2 \lambda _{\rm b} - 3 \lambda _{\rm c} + \omega _{\rm b} $ for an integration over 100 kyr of the orbital solution in Table 2.
Combination $\nu_i$ Ai $\phi_i$
$n_{\rm b}$ $n_{\rm c}$ g1 g2 $l_\theta$ (deg/yr) (deg) (deg)
0 0 0 0 1 19.8207 68.444 -144.426
0 0 -1 1 0 0.8698 13.400 136.931
0 0 1 -1 1 18.9509 8.606 168.643
0 0 -1 1 1 20.6905 8.094 82.505
0 0 -2 2 0 1.7396 2.165 -176.138
0 0 -2 2 1 21.5603 0.622 -50.564
0 0 0 0 3 59.4621 0.540 -73.279
1 -1 0 0 -1 172.5756 0.506 7.504
1 -1 0 0 0 192.3963 0.501 -46.923
0 0 -3 3 0 2.6093 0.416 -129.207
0 0 2 -2 1 18.0811 0.420 121.712
1 -1 0 0 1 212.2170 0.416 78.651
0 1 -1 0 0 384.7926 0.451 176.155
1 -1 0 0 -2 152.7549 0.424 -118.070
0 1 -1 0 -1 364.9719 0.341 50.581
0 1 -1 0 1 404.6133 0.274 121.729
0 0 1 -1 3 58.5923 0.212 -120.210
1 -1 0 0 2 232.0377 0.201 24.225
0 0 -1 1 3 60.3319 0.211 153.652
1 0 -1 0 -1 557.3682 0.182 -86.342
We have $\theta_{\rm b} = \sum_{i=1}^N A_i \cos(\nu_i~ t + \phi_i)$, where the amplitude and phases Ai, $\phi_i$ are given in degree, and the frequencies $\nu_i$ in degree/year. We only give the first 20 terms, ordered by decreasing amplitude. All terms are identified as integer combinations of the fundamental frequencies given in Table 3. The fact that we are able to express all the main frequencies of $ \theta _{\rm b} $ in terms of exact combinations of the fundamental frequencies g1, g2 and $l_\theta$ is a signature of a very regular motion.

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