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Astron. Astrophys. 329, 329-338 (1998)

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2. Notations and constants

The notations are the same as in Bretagnon et al. (1997). The unit of time is one thousand Julian years (tjy). The following constants are taken from the numerical integration of the JPL DE403/LE403 (Standish et al., 1995) and from the IERS Standards 1996 (IERS, 1996).

Value of the astronomical unit:

[EQUATION]

Equatorial radius of the Earth:

[EQUATION]

We note [FORMULA], [FORMULA], [FORMULA] the masses of the Sun, the Earth and the Moon. From DE403/LE403 we take

[EQUATION]

From the value of the Gaussian gravitational constant [FORMULA] and from the mass of the Earth, we compute

[EQUATION]

The geopotential coefficients [FORMULA] are computed from the GEM-T3 model given by the IERS Standards 1992 (IERS, 1992). The longitude of the major axis of the equatorial ellipse corresponding to the principal moment of inertia A is computed from [FORMULA] and [FORMULA]

[EQUATION]

The constants depending of the precision of the solution, like principal moments of inertia, have slight modifications. So, to obtain the William's (1994) value of the constant of the general precession [FORMULA] /tjy, the equations of Sect. 3 must be solved to yield

[EQUATION]

We thus obtained

[EQUATION]

The dynamical ellipticity [FORMULA] is

[EQUATION]

The values of the moments of inertia A, B, C and therefore [FORMULA] are slightly different from the ones of Bretagnon et al. (1997) because of the modifications of the constants used for the masses of the Earth and the Moon and for the equatorial radius of the Earth.

The linear part of the angle [FORMULA] measuring the rotation of the Earth is

[EQUATION]

with

[EQUATION]

For the obliquity [FORMULA] we take the angle between the rotational equator J2000 and the inertial dynamical ecliptic J2000:

[EQUATION]

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© European Southern Observatory (ESO) 1998

Online publication: November 24, 1997
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