  We present a realization of astronomical relativistic reference frames in the
solar system and its application to the GRAIL mission. We model the necessary
spacetime coordinate transformations for light-trip time computations and
address some practical aspects of the implementation of the resulting model. We
develop all the relevant relativistic coordinate transformations that are
needed to describe the motion of the GRAIL spacecraft and to compute all
observable quantities. We take into account major relativistic effects
contributing to the dual one-way range observable, which is derived from
one-way signal travel times between the two GRAIL spacecraft. We develop a
general relativistic model for this fundamental observable of GRAIL, accurate
to 1 $\mu$m. We develop and present a relativistic model for another key
observable of this experiment, the dual one-way range-rate, accurate to 1
$\mu$m/s. The presented formulation justifies the basic assumptions behind the
design of the GRAIL mission. It may also be used to further improve the already
impressive results of this lunar gravity recovery experiment after the mission
is complete. Finally, we present transformation rules for frequencies and
gravitational potentials and their application to GRAIL.
