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

## 6. Description of the SMART97 solution

In the construction of the solutions, all the angles are reckoned positively in positive rotation and the obliquity is the one of the equator about the ecliptic J2000.

In the final form of the SMART97 solution, we take up the usual conventions: and are reckoned in the negative direction and and are the obliquities of the ecliptic J2000 and of the ecliptic of date respectively about the equator.

Moreover, we have added the precession to the mean longitudes of the planets in order to have the same frequencies and the same periods as in the other solutions. Thus, the mean longitudes of the planets are reckoned from the equinox of date. We give hereafter the value of the 12 angles of the SMART97 solution: The linear parts of the angles are computed from Simon et al. (1994). The differences result from the modification of the tidal model in the lunar theory and of the new inertial ecliptic and dynamical equinox defined by DE403/LE403.

### 6.1. List of the variables of the solution

The solution of the Euler equations gives the analytical expressions of the angles , , and fixing the Earth with respect to the ecliptic and equinox J2000 in the dynamical reference frame. As in Bretagnon et al (1997), from these 3 angles we have determined the analytical solutions of , , and , and consequently of the sidereal time ST ( ), fixing the Earth with respect to the ecliptic and equinox of date.

### 6.2. Dynamical and kinematical reference frames

From the 7 quantities , , , , , , and ST defined in the dynamical system, we have computed the corresponding 7 quantities in the kinematical system with the Brumberg's (1996) formulas. These formulas use the 3 rotations of geodesic precession-nutation.

### 6.3. Axis of figure, axis of rotation, axis of angular momentum

The solution of the equations (6) gives the variations of the axis of figure. In order to compare SMART97 with other solutions we have determined, for the quantities and in the dynamical system, the differences between the axis of figure and the axis of rotation and between the axis of figure and the axis of angular momentum.

### 6.4. Presentation of the files of the SMART97 solution

The SMART97 solution is displayed in the form of 18 files. 14 files correspond to the variables linked up with the axis of figure in the dynamical system and in the kinematical system. There are also 2 files giving the difference between the axis of figure and the axis of rotation and 2 files giving the difference between the axis of figure and the axis of angular momentum for the variables and expressed in the dynamical system.

In each file, the solution for a variable x is represented in two forms: and with The coefficients , , are in as/tjyk ; t is counted in tjy from J2000. The angles , D, F, l, are given in (13).

Each record contains: with The quantities , , , , , are defined by the formulas (14), (15), (16).

In the files of SMART97, we have only kept the terms with an amplitude greater than 0.01 as (longitude) and 0.004 as (obliquity) over the time span 1900-2100. This truncation involves an uncertainty of about 1 as that we have to add to the residuals of Tables 2 and 3 obtained with the complete series. We give in Table 5 the number of terms and the accuracy for different levels of truncation. Table 5. Number of terms of the series and .

In the form (15) of the SMART97 solutions, the substitution of time in the 4929 terms of , for example, uses 0.0055 second of computer.

The 18 files of SMART97 solutions are available in electronic form given in: ftp cdsarc.u-strasbg.fr (or) ftp 130.79.128.5 username : anonymous password : (type your e-mail address here) ftp cd pub/A+A/ this volume number this page number or ftp bdl.fr (or) ftp 193.48.190.1 username : anonymous password : (type your e-mail address here) ftp cd pub/ephem/ref_frame/smart97    © European Southern Observatory (ESO) 1998

Online publication: November 24, 1997 