General Relativistic Red Shift and the Artificial Satellite

Singer's formula for the general relativistic red shift on an earth satellite is modified to take account of the diurnal rotation of the earth and the lack of spherical symmetry of its gravitational field. It is shown that the Singer rates of the earth and satellite clocks need slight modifications, but that these modifications tend to cancel each other except at large distances from the earth, so that when one uses a mean radius of the earth in Singer's formula the formula is adequate for present purposes.