Local gravitational physics of the Hubble expansion
  We study physical consequences of the Hubble expansion of FLRW manifold on
measurement of space, time and light propagation in the local inertial frame.
We analyse the solar system radar ranging and Doppler tracking experiments, and
time synchronization. FLRW manifold is covered by global coordinates (t,y^i),
where t is the cosmic time coinciding with the proper time of the Hubble
observers. We introduce local inertial coordinates x^a=(x^0,x^i) in the
vicinity of a world line of a Hubble observer with the help of a special
conformal transformation. The local inertial metric is Minkowski flat and is
materialized by the congruence of time-like geodesics of static observers being
at rest with respect to the local spatial coordinates x^i. We consider geodesic
motion of test particles and notice that the local coordinate time x^0=x^0(t)
taken as a parameter along the world line of particle, is a function of the
Hubble's observer time t. This function changes smoothly from x^0=t for a
particle at rest (observer's clock), to x^0=t+1/2 Ht^2 for photons, where H is
the Hubble constant. Thus, motion of a test particle is non-uniform when its
world line is parametrized by time t. NASA JPL Orbit Determination Program
presumes that motion of light (after the Shapiro delay is excluded) is uniform
with respect to the time t but it does not comply with the non-uniform motion
of light on cosmological manifold. For this reason, the motion of light in the
solar system analysed with the Orbit Determination Program appears as having a
systematic blue shift of frequency, of radio waves circulating in the
Earth-spacecraft radio link. The magnitude of the anomalous blue shift of
frequency is proportional to the Hubble constant H that may open an access to
the measurement of this fundamental cosmological parameter in the solar system
radiowave experiments.
