  Our present relativistic part of the geodetic VLBI model for Earthbound
antennas is a consensus model which is considered as a standard for processing
high-precision VLBI observations. It was created as a compromise between a
variety of relativistic VLBI models proposed by different authors as documented
in the IERS Conventions 2010. The accuracy of the consensus model is in the
picosecond range for the group delay but this is not sufficient for current
geodetic pur- poses. This paper provides a fully documented derivation of a new
relativistic model having an accuracy substantially higher than one picosecond
and based upon a well accepted formalism of relativistic celestial mechanics,
astrometry and geodesy. Our new model fully confirms the consensus model at the
picosecond level and in several respects goes to a great extent beyond it. More
specifically, terms related to the acceleration of the geocenter are considered
and kept in the model, the gravitational time-delay due to a massive body
(planet, Sun, etc.) with arbitrary mass and spin-multipole moments is derived
taking into account the motion of the body, and a new formalism for the
time-delay problem of radio sources located at finite distance from VLBI
stations is presented. Thus, the paper presents a substantially elaborated
theoretical justification of the consensus model and its significant extension
that allows researchers to make concrete estimates of the magnitude of residual
terms of this model for any conceivable configuration of the source of light,
massive bodies, and VLBI stations. The largest terms in the relativistic time
delay which can affect the current VLBI observations are from the quadrupole
and the angular momentum of the gravitating bodies that are known from the
literature. These terms should be included in the new geodetic VLBI model for
improving its consistency.
