Classical Solution of the Two-Body Problem If the Gravitational Constant Diminishes Inversely with the Age of the Universe

Dirac's 1938 suggestion that G varies inversely with the age t of the Universe is first modified to G = A (k + t) −1. Here A and k are to be universal constants, k being inserted to avoid infinities in the resulting exact classical solution for the orbit in the two-body problem. In the solar system variations in the two masses are negligible compared to that postulated in G if |k + t 10^10| yr. Applications to the solar system give | (k + t) ^-1| for the fractional rate of change of the osculating semi-latus rectum and |-2 (k + t) ^-1nₒsc| for the secular acceleration of the osculating mean longitude, nosc being the osculating mean motion. With Van Flandern's value for this acceleration for the Moon, one finds k + t = (1. 08) 1010 yr as the age of the Universe. The verification of such results may become fully possible only after another decade of atomic time will have permitted measurement of planetary orbits freed from the possible impurities of ephemeris time.