Table 1
Orbital theory of Titan and solid Cassini state.
| j | i j |
|
Period | γ j | ε j | f rj |
| (deg) | (rad/year) | (years) | (deg) | (deg) | ||
|
|
||||||
| 1 | 0.3197 | −0.00893124 | −703.51 | 160.691 | 0.1199 | 1.38 |
| 2 | 0.0150 | −0.00192554 | −3263.07 | 102.230 | 0.0009 | 1.06 |
| 3 | 0.0129 | 0.42659824 | 14.73 | 292.867 | −0.0120 | − |
| 4 | 0.0022 | −0.21329912 | −29.46 | 222.920 | −0.0026 | 1.18 |
Notes. Columns 2 to 5: amplitudes, frequencies, periods, and phases of the orbit precession adapted from Vienne & Duriez (1995). They give the orbital precession in the equatorial plane of Saturn and used J1980 as the time origin. Here we consider the Laplace plane and J2000 time origin. The Laplace plane has a node of 184.578° and an inclination (also called tilt) of 0.6420° with respect to the equatorial plane of Saturn. Since the tilt is small, the frequency and amplitude of the orbital precession are almost the same with respect to the Laplace plane as to the equatorial plane of Saturn. The x-axis of the Laplace place is taken as the node of the Laplace plane on the equatorial plane of Saturn. The obliquity amplitudes and resonance factors (frj) of the solid Cassini state model presented in Sect. 3 are given in the last two columns.
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