Brans-Dicke corrections to the gravitational Sagnac effect - art. no. 084027

The exact formulation for the effect of the Brans-Dicke scalar field on the gravitational corrections to the Sagnac delay in the Jordan and Einstein f rames is presented. The results completely agree with the known parametrize d post Newtonian factors in the weak-field region. The calculations also re veal how the Brans-Dicke coupling parameter <(<omega>)over bar> appears in various correction terms far different types of source or observer orbits. A first-order correction of roughly 2.83 x 10(-1) fringe shift for visible light is introduced by the gravity-scalar field combination far Earth-bound equatorial orbits. It is also demonstrated that the final predictions in t he two frames do not differ. The effect of the scalar field on the geodetic and Lense-Thirring precession of a spherical gyroscope in a circular polar orbit around the Earth is also computed with an eye towards the Stanford G ravity Probe-B experiment currently in progress. The feasibility of optical and matter-wave interferometric measurements is discussed briefly.