Determination of the Astronomical Unit by the Dynamical Method

Abstract

THE dynamical method of determining the astronomical unit is based on a relation between the astronomical unit A expressed in km and the ratio m of the mass of the Earth–Moon system to the solar mass. According to this relation m A³ equals a constant which is known with sufficient accuracy for all practical purposes. A derivation of this relation was recently given by Brouwer¹. The effects of the attraction of the Earth–Moon system on bodies in close approaches permit the determination of m and thus of A. Various authors have tried to determine the mass of the Earth–Moon system from observations of the Minor Planet (433) Eros which comes near to the Earth. The first determination of this kind was performed by Witt² and the most recent one was published by Rabe³. An independent determination of the astronomical unit became possible using radar echoes from Venus, but the radar result differs significantly from Rabe's result. Considerable effort was made by Eckstein⁴ and Marsden⁵ to reconcile the two differing values using numerical material previously published by Rabe.