A system of astronomical constants in the relativistic framework

The relation between the units and readings of time and space coordinates of terrestrial and barycentric reference frames is discussed from the viewpoint of general relativity. Attention is paid to the unit of space coordinates since the International Astronomical Union (IAU) regulates only the unit of time in the above two frames. Two definitions of unit of length are examined and their effects on the numerical expression of coordinate transformation, equations of planetary motions, and those for light propagation time are discussed. A clear conflict is found between the IAU (1976) recommendation on the definition of the time-scales in different frames of reference and the statement that all constants in the IAU (1976) new system of astronomical constants are defined in terms of the Internationsl System of units (SI units). One of the above two definitions is proposed to resolve this conflict by the least alteration to current procedures for analysing the recent astrometric observations such as the radar/laser rangings, the range and range-rate, and the very long baseline interferometric observations. Also, an interpretation of numerical values in the IAU (1976) new system of astronomical constants is presented. It is stressed that the definition proposed in this paper requires that a formula slightly different from that in current use be employed in the numerical transformation of readings of coordinates between the terrestrial and barycentric reference frames.