  We present a theoretical foundation for relativistic astronomical
measurements in curved space-time. In particular, we discuss a new iterative
approach for describing the dynamics of an astronomical N-body system. To do
this, we generalize the Fock-Chandrasekhar method of the weak-field and
slow-motion approximation (WFSMA) and develop a theory of relativistic
reference frames (RF) for a gravitationally bounded many-extended-body problem.
In any proper RF constructed in the immediate vicinity of an arbitrary body,
the N-body solutions of the gravitational field equations are presented as a
sum of the Riemann-flat inertial space-time, the gravitational field generated
by the body itself, the unperturbed solutions for each body in the system
transformed to the coordinates of this proper RF, and the gravitational
interaction term. We develop the basic concept of a general theory of the
celestial RFs applicable to a wide class of metric theories of gravity with an
arbitrary model of matter distribution. We apply the proposed method to general
relativity. Bodies are described using a perfect fluid model; as such, they
possess any number of internal mass and current multipole moments which
explicitly characterize their internal structure. The obtained relativistic
equations of motion contain an explicit information about the coupling of the
bodies proper multiple moments to the surrounding gravitational field. We
further generalize the proposed method and include two Eddington parameters
$(\gamma,\beta)$. This generalized approach was used to derive the relativistic
equations of satellite motion in the vicinity of the extended bodies. We
discuss the possible future implementation of the proposed formalism in
software codes developed for solar-system orbit determination.
