Table 2.
Convergence au sens des astronomes for the ten systems.
| System | H2 | H4 | H6 | H8 | H10 | H12 | H12/H2 | Relative error |
|---|---|---|---|---|---|---|---|---|
| HD 11506 | 9.47e−06 | 1.66e−05 | 6.31e−06 | 7.15e−06 | 2.46e−06 | 4.73e−07 | 𝒪(10−2) | 1.62e−04 |
| HD 12661 | 3.76e−05 | 7.24e−05 | 7.33e−05 | 3.96e−05 | 9.69e−06 | 9.25e−07 | 𝒪(10−2) | 1.42e−04 |
| HD 134987 | 4.42e−07 | 2.61e−08 | 1.53e−09 | 1.90e−10 | 1.09e−11 | 1.62e−12 | 𝒪(10−6) | 1.10e−05 |
| HD 142 | 4.27e−06 | 1.67e−06 | 1.40e−07 | 1.93e−08 | 1.58e−09 | 5.53e−10 | 𝒪(10−4) | 1.34e−04 |
| HD 154857 | 2.67e−05 | 2.23e−07 | 1.20e−07 | 7.54e−08 | 1.36e−08 | 2.10e−09 | 𝒪(10−4) | 9.33e−05 |
| HD 164922 | 1.24e−07 | 9.67e−09 | 4.53e−10 | 2.99e−11 | 5.95e−13 | 1.41e−13 | 𝒪(10−6) | 1.03e−05 |
| HD 169830 | 7.01e−06 | 2.40e−05 | 6.51e−09 | 7.36e−06 | 2.75e−06 | 6.26e−07 | 𝒪(10−1) | 1.46e−04 |
| HD 207832 | 9.15e−07 | 6.85e−07 | 2.08e−07 | 1.79e−07 | 4.94e−08 | 6.47e−09 | 𝒪(10−2) | 5.28e−05 |
| HD 4732 | 6.22e−06 | 1.35e−06 | 7.42e−08 | 8.36e−08 | 1.48e−08 | 1.44e−09 | 𝒪(10−4) | 7.58e−05 |
| HD 74156 | 2.93e−05 | 1.65e−05 | 4.68e−06 | 5.36e−05 | 3.24e−05 | 1.62e−05 | 𝒪(10−1) | 1.01e−04 |
Notes. The value Hj corresponds to the sum of all the terms of the Hamiltonian given by Eq. (5) of order j in eccentricities and inclinations. The last column gives the relative error between the secular Hamiltonian computed by numerical quadrature and the expansion of Eq. (5). The values are computed for the initial condition (imut, i) = (50 ° ,50 ° ).
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