A farside-type rocket experiment for the measurement of the gravitational time effect

Abstract

The earth's mass causes a gravitational effect on clock rates whose maximum fractional amount is so that clocks on earth are slow. The effect comes from the Schwarzschild line element of general relativity [Landau and Lijshitz, 1951], which gives the proper time rate in terms of the position and velocity relative to the massive body Comparison of a clock in a satellite of circular orbit with an earth clock [Singer, 1956; Hoffmann, 1957] should show a fractional change in rate of where h is the height of the orbit from the center of earth. This is mostly a second-order doppler effect for h < (3/2)RE. To gain the greatest gravitational effect with the greatest economy of rocket energy, a vertically fired rocket may be considered.