  The Galactic Center star cluster, known as S-stars, is a perfect source of
relativistic phenomena observations. The stars are located in the strong field
of relativistic compact object Sgr A* and are moving with very high velocities
at pericenters of their orbits. In this work we consider motion of several
S-stars by using the Parameterized Post-Newtonian (PPN) formalism of General
Relativity (GR) and Post-Newtonian (PN) equations of motion of the Feynman's
quantum-field gravity theory, where the positive energy density of the gravity
field can be measured via the relativistic pericenter shift. The PPN parameters
$\beta$ and $\gamma$ are constrained using the S-stars data. The positive value
of the $T_g^{00}$ component of the gravity energy-momentum tensor is confirmed
for condition of S-stars motion.
