All Tables

Table 1: Main constants used in La2004. IAU76 refers to the resolutions of the International Astronmical Union of 1976, IERS1992, and IERS2000, refers to the IERS conventions (McCarthy 1992; McCarthy & Petit 2004).
Table 2: Maximum difference between La2004 and DE406 over the whole time interval of DE406 (-5000 yr to +1000 yr with origin at J2000); Col. 1: -100 to + 100 yr; Col. 2:-1000 to + 1000 yr; Col. 3: -5000 to +1000 yr. EMB is the Earth-Moon barycenter.
Table 3: Main secular frequencies g_i and s_i of La2004 determined over 20 Ma for the four inner planets, and over 50 Ma for the 5 outer planets (in arcsec yr^-1). $\Delta _{100}$ and $\Delta _{250}$ are the observed variations of the frequencies over respectively 100 and 250 Myr. In the last column, the period of the secular term are given.
Table 4: Frequency decomposition of $z=e\exp {i}\varpi$ for the Earth on the time interval [-15,+5] Myr (Eq. (25)).
Table 5: Frequency decomposition of $\zeta=\sin i/2 \exp {i}\Omega$ for the Earth on the time interval [-15,+5] Myr (Eq. (26)).
Table 6: Frequency decomposition of the eccentricity of the Earth on the time interval [-15,+5] Myr. For all computations, the data of Table 4 should be preferred. Here, $e = e_0 +\sum_{k=1}^{20} b'_k~\cos(\mu'_k~ t + \varphi_k)$ with e₀=0.0275579. For each term, in the first column is the corresponding combination of frequencies where g_i are the fundamental frequencies (Table 3), and $\mu _j$ the frequencies of the terms in z from Table 4.
Table 7: Approximation for the obliquity of the Earth, following Eq. (33). This expression is not strictly quasiperiodic, because of the presence of the dissipative term p₁ in the evolution of the precesion frequency (33).
Table 8: Main sources of uncertainty in the orbital solution (from Laskar 1999). For each limiting factor, an analytical estimate of the time of validity of the solution $T_{\rm V}$ is given (in Myr), taking into account the exponential growth of the error.
Table 9: Variants of the La2004 solutions. The nominal solution La2004 is obtained for a stepsize $\tau =5 \times 10^{-3}$ , and a Solar oblateness $J_2^{\rm S}=2.0 \times 10^{-7}$ . The other solutions, with different setting have been computed to test the stability of the nominal solution. In the last column $\gamma$ is the tidal dissipation factor.