An Analysis of the Transits of Mercury : 1677-1973

About 2400 observations of the universal times of internal contact for the transits of Mercury in the period 1677 to 1973 are compared with the ephemeris times calculated from the gravitational theories of the motions of Mercury and the Earth. The O–C differences in the times are attributed to two causes: the differences between the ephemeris and universal time scales, ∆T (arising from the non-uniformity of the Earth's rate of rotation on its axis) and errors in the values of the orbital elements in the adopted theory of Mercury's motion. In order to separate these two effects, we adopt known estimates of ∆T derived previously from observations of the Moon's motion and solve for corrections to Mercury's orbital elements and a term varying with the square of time. This last term allows for a possible correction to the value of the tidal acceleration in the lunar theory which is implicit in the derivation of the estimates of ∆T from lunar observations. By this method of analysis we find the tidal acceleration of the Moon to be $$-{26}^{\prime{}\prime}\pm{2}^{\prime{}\prime}\,\text{cy}^{-2}$$, and that the excess of the observed over the Newtonian value of the motion of Mercury's perihelion is $$+{41}^{\prime{}\prime}\cdot 9\pm{0}^{\prime{}\prime}\cdot 5\,\text{cy}^{-2}$$.