St-Petersburg, ITA RAS, Russia
The problem of constructing the long-term numerical ephemeris of the Sun, major planets and Moon is based essentially on the high-precision numerical solution of the Solar System major bodies motion problem in the post-newtonian approximation and high-precision polynomial representation of data. Some experience of using a compiler, providing a representation of real numbers with 16 decimal figures, permits to formulate the following simple rules, promoting an effective solution of the formulated problem and in particular, the construction of the AE95 ephemeris.
1) It is preferable to use convenient variables, especially for the numerical integration. When constructing the AE95 ephemeris the rectangular coordinates for the orbital motion ( barycentric for the Sun and major planets and geocentric for the Moon) and Rodriges-Hamilton parameters for the rotational motion were used.
2) It is preferable to apply a high-precision numerical integration method taking into account the astronomical features of the problem to be solved. The AE95 ephemeris is constructed with the one-step predictor-corrector method of the numerical integration based on the almost-uniform approximation of the differential equation right-hand sides by Chebyshev polynomial series expansions. This method is developed especially for solving the problem of the Solar System major body motions. A high-precision numerical integration of the equations of the motion is carried out with the 8-day constant step-size and 24-th degree of the approximating polynomial. A comparison of the numerical integration results with the DE200/LE200 ephemeris data has discovered discrepancies in the radius vector values of the Sun, major planets and Moon, not exceeding 20mm ( 80 mm for Uranus, Neptune and Pluto) over the 1960-2010 years interval.
3) One have to use advantages of the Chebyshev polynomial approximation for achieving almost-uniform approximation of data. Because of performing the numerical integration with a constant step-size, the errors of the polynomial approximation of the AE95 ephemeris do not depend on the time-distance of an approximation interval from the initial point of the AE95 ephemeris.
On the base of the model of the numerical ephemeris of the Sun, major planets and Moon AE94 the reduction of optical observational data for the Sun and major planets and the radar ranging data for the inner planets (1960-1991) is carried out, including the calculation of the (O-C) residuals, the composition and solution of the normal system of conditional equations and determination of the following corrections: for the major planets orbital elements, the FK5 catalog's equinox and equator, the adopted radii of the inner planets, as well as the calculation of the initial conditions of the motions.
As a result of the reduction of 37730 optical observations data for the Sun, Mercury, Venus and Mars and radar ranging data for the inner planets, spanning 1960-1991 years interval, the ephemeris AE95 has been constructed in the form of Chebyshev's polynomials for the time interval 1960-2010 years.