Post-Newtonian Covariant Formulation for Gravity Determination by Differential Chronometry

Following Synge's idea, a Post-Newtonian Covariant Formulation to estimate orders of magnitude in the design of experiments for the measurement by differential chronometry of the curvature of an observer world-line (g) and the curvature of space-time (R-ijkm) is discussed. The local geometric model considered corresponds to local Fermi coordinates associated to an observer O and Fermi transported tetrads, and by using Synge's world-function the measurement formulation for the relative distance in terms of the O-proper time s(1), corresponding to the instant at which an electromagnetic signal is emitted from O, and the O-proper time s(2) at which the signal is received by O after a trip-time to complete a circuit is presented.