Post-Newtonian Covariant Formulation for Gravity Determination by Differential Chronometry

Abstract

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 (Rijkm) 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 s1, corresponding to the instant at which an electromagnetic signal is emitted from O, and the O-proper time s2 at which the signal is received by O after a trip-time to complete a circuit is presented.