New orbital elements for Moon and planets

Abstract

The results of a simultaneous solution for the orbital elements of Moon and planets are given and their derivation is discussed. A modern Cowell integrator is used for orbit computations, and least-squares fits are made to some 40000 optical observations taken since 1913. The model includes relativistic terms, the leading zonal harmonics of Earth and Moon, the precession of the lunar equator, and the tidal couple between Earth and Moon. The tidal term in the Moon's mean longitude is found to be −19″±4″ per century squared. The solution also yields an extrapolation of the atomic time scale back to 1912.5. At that time, the difference between atomic and ephemeris time is about 6±2 s. Lunar declinations observed by the Washington transit circles, after receiving limb corrections and thus with respect to the center of Watts' reference sphere, are smaller than computed values by 0″.33±0″.01. It is found that solar oblateness cannot quite be determined with optical data covering about 50 yr, butJ2 is unlikely to be much larger than 10−5. The advance of Mercury's perihelion is verified to within our resolution of 2″ per century to match that predicted by Einstein.