A relativistic theory of motion of the inner planets

Abstract

The theory of the motion of Mercury,Venus, Earth and Mars is constructed by numerical integration. The theory takes into account relativistic corrections in the frame of Schwarzschild 1 s space-time metrics. The constants of the theory are determined by discussion of the Soviet and American radar observations of Mercury, Venus and Mars f position astrometric observations of these planets (and the Sun) and observations of the Soviet artificial satellites of Venus. Apart from the planet elements the value AU and corrections to the adopted radii of Mercury, Venus and Mars are determined* Statistics of residuals is given and accuracy of the theory is estimated. The theory presented is an ephemeris base for deep space experiments. These theories are atributed to classical ones. To describe the planets motion they make use of the approximate analytical methods of motion equations integration. The classical theories accuracy evaluation based on the treatment of the results of long-time optical observa tions of the planets and the Sun has shown that they enable us to calculate the planets coordinates with 63 J. Kovalevsky and V. A. Brumberg (eds.) t Relativity in Celestial Mechanics and Astrometry, 63-68.

High-Precision Ephemerides of Planets—EPM and Determination of Some Astronomical Constants

“…American groups worked at the California (JPL) (Standish et al , 1976;Newhall et al , 1983) and the Massachusetts (Ash et al , 1967) Institutes of Technology. Russian high-precision numerical ephemerides of planets (Akim et al , 1986) were created as a result of research carried out at the Institute of Applied Mathematics (Akim and Stepanianz, 1977), the Institute of Radio Engineering and Electronics, the Space Flight Control Center (Kislik et al , 1980), and the Institute of Theoretical Astronomy, where Glebova (1984), Eroshkin et al (1992), and a group led by Krasinsky (Krasinsky et al 1981(Krasinsky et al , 1982 developed independent theories. This work was continued at the Institute of Applied Astronomy, where a series of EPM ( E phemerides of P lanets and the M oon) ephemerides was produced.…”