Energy-dependent metric for gravitation from clock-rate experiments

We carry out a detailed analysis of the data on the comparison of clock rates between a flying dock and a clock at ground, performed by Alley and co-workers at the end of 1970's. The fit to such data is in favor of an energy-dependent metric for gravitation, whose time coefficient is at variance with the standard Einsteinian one in the weak-field approximation. By exploiting the formalism of a deformed Minkowski space-time, with metric coefficients dependent on the energy, we show that a possible lower limit on the propagation speed of gravitational effects is about 10(10)c, in agreement with a recent analysis by Van Flandern based on the acceleration of binary systems.