RDAN97: An analytical development of rigid Earth nutation series using the torque approach

New series of rigid Earth nutations for the angular momemtum axis, the rotation axis and the figure axis, named RDAN97, are computed using the torque approach. Besides the classical J(2) terms coming from the Moan and the Sun, we also consider several additional effects: terms coming from J(3) and J(4) in the case of the Moon, direct and indirect planetary effects, lunar inequality, J(2)-tilt, planetary-tilt, effects of the precession and nutations on the nutations, secular variations of the amplitudes, effects due to the triaxiality of the Earth, new additional out-of-phase terms coming from second order effect and relativistic effects. Finally, we obtain rigid Earth nutation series of 1529 terms in longitude and 984 terms in obliquity with a truncation level of 0.1 mu as (microarcsecond) and 8 significant digits. The value of the dynamical flattening used in this theory is H-D = (C - A)/C = 0.0032737674, computed from the initial value p(a) = 50." 2877/yr for the precession rate. These new rigid Earth nutation series are then compared with the most recent models (Hartmann et al., 1998; Souchay and Kinoshita, 1996, 1997; Bretagnon et al., 1997, 1998. We also compute a benchmark series (RDNN97) from the numerical ephemerides DE403/LE403 (Standish et al., 1995) in order to test our model. The comparison between our model (RDAN97) and the benchmark series (RDNN97) shows a maximum difference, in the time domain, of 69 mu as in longitude and 29 mu as in obliquity In the frequency domain, the maximum differences are 6 mu as in longitude and 4 mu as in obliquity which is below the level of precision of the most recent observations (0.2 mas in time domain (temporal resolution of 1 day) and 0.02 mas in frequency domain).