Table 2
Linear and power-law fits for the time evolution of the parameters (Fig. 10) of the skew Gaussian mixture model (Eq. (19)) for the fundamental frequencies of the Solar System.
| μ0 (′′ yr−1) | a (′′ yr−1)2 | b | α0 | μ1 (′′ yr−1) |  (′′ yr−1)2 |
A1 | |
|---|---|---|---|---|---|---|---|
| g1 | 5.759 + 0.006 T | 3.37 × 10−2 | 0.52 | − 2.25 − 0.50 T | |||
| g2 | 7.448 − 0.004 T | 4.17 × 10−4 | 0.70 | 1.38 + 0.21 T | |||
| g3 | 17.269 + 0.002 T | 6.63 × 10−3 | 0.43 | ||||
| g4 | 417.896 + 0.005 T | 46.88 × 10−3 | 0.41 | 17.6755 | 0.0034 | 0.110 − 0.012 T | |
| s1 | − 5.652 − 0.032 T | 2.68 × 10−2 | 0.83 | 1.12 + 0.16 T | |||
| s2 | − 6.709 + 0.030 T | 1.20 × 10−1 | 0.76 | 4 − 2.94 − 1.23 T | |||
| s3 | − 18.773 + 0.009 T | 2.86 × 10−2 | 0.56 | − 3.40 − 0.08 T | − 18.5256 | 0.0028 | 0.023 |
| s4 | − 17.707 + 0.013 T | 1.19 × 10−2 | 0.68 | − 1.73 − 0.28 T | |||
| g5 | 4.257454 − 2.1 × 10−6 T | 4.63 × 10−10 | 0.88 | ||||
| g6 | 2.824523 − 1.4 × 10−4 T | 1.40 × 10−6 | 0.84 | ||||
| g7 | 3.087957 − 1.2 × 10−6 T | 4.80 × 10−10 | 1.11 | ||||
| g8 | 6.730237 | 9.89 × 10−11 | 1.49 | ||||
| s6 | − 2.634787 + 1.5 × 10−5 T | 1.21 × 10−8 | 0.85 | ||||
| s7 | − 2.992527 | 8.31 × 10−10 | 1.39 | ||||
| s8 | − 6.917366 | 42.93 × 10−11 | 1.47 | ||||
Notes. Column 1 contains the considered secular frequencies. In Col. 2, we show the linear fits of μ0 that represent the center of the distribution.The power-law fit of 
has the form
(Eq. (20)), where T = t∕(1 Gyr) and a and b are given in Cols. 3 and 4, respectively. Linear fits of the skewness parameter α0 are given inCol. 5. The last three columns show linear fits of the secondary mode of g4 and s3 (Eq. (19)). The parameter 
is fitted from 200 Myr to 5 Gyr in the past, while all the others are fitted from 500 Myr.
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