Advances of the Perigees of Earth-Satellites Predicted by General Relativity

J. J. Gilvarry has suggested1 the possibility of checking the advance of perihelion predicted by the general theory of relativity by observations on the motion of minor planets of high eccentricity. Examination of the orbital elements of the minor planets leads Gilvarry to the conclusions that while Icarus (1566) provides the most favorable test object by a wide margin, and while an observational check on the advance of perihelion for this particular asteroid is possible, . . decades of astronomical observation may be necessary to measure the perihelion advance with sufficient precision. Since the statement just quoted seems amply justified and since additional checks on what is probably the least ambiguous of the crucial tests so far proposed for the theory of relativity are needed,2 one is led to look for test objects providing peri-primary advances of greater magnitude than those predicted for Icarus. Since the advance, v (in radians per century), is inversely proportional to (1 e2)a5/2, where e and a are, respectively, the eccentricity and the semi-major axis of the test object's orbit, it is natural to think of utilizing planetary satellites moving at mean distances quite small in comparison with the semi-major axes of the orbits of planets ; and, indeed, De Sitter chose our moon as a test object as long ago as 1916.3 Although he was primarily concerned with determining the modifications of the moon's orbit resulting from the combined attraction of the earth and the sun under Einstein's new law of gravitation, it was found that the modification imposed by Einstein's law on the gravitational field of the earth alone resulted in an advance of the lunar perigee of O'/O6 per century,4 an amount far too small to be detected. It is our purpose to point out that while the advance of the lunar perigee is too small to provide an observational check on the validity of general relativity, the same would not be true of the perigeal advances of satellites moving about the earth at