It has been found possible to obtain a solution which satisfies both the dynamical and radar investigations without doing any great injustice to any of the observations. It is deduced that the astronomical unit is determined more satisfactorily from the radar bounces off Venus rather than by dynamical methods alone. Some comments are also given concerning the masses of Mercury, Venus and Mars.

While Marsden's solution C leaves residuals with the relatively small [vv] of 13.73, it should be realized that this representation of the observations of Eros does not satisfy the fundamental principle of the least squares method, in so far as the associated value of [vv] is not a minimum with respect to small arbitrary deviations from solution C. As a matter of fact, there is an infinite number of “solutions” with [vv] between the 13.73 of Marsden's solution C and the 8.66 of his solution A, each of these being associated with a certain arbitrarily prescribed value of the mass of Mars and with a related mass of Earth + Moon. Of this infinite series of solutions, only solution A is a least squares solution in the true sense, with a minimum value of [vv]. This can be seen and verified as follows.

The availability of accurate values of the coefficients J2, J4, … in the Earth's potential and radar determinations of the distances Earth-Moon and Earth-Venus provides relations among astronomical constants different in form from those used in previous efforts to construct a consistent system of astronomical constants. Some of the important relations have gained in simplicity.

The purpose and principles of construction of a system of astronomical constants are described. The relationships between the constants are considered; all constants are defined precisely and a clear distinction between fundamental and derived constants is made. The system thus developed differs in some respects from the current system. The practical steps required to implement the formal adoption of such a new system are discussed.

The authors give the main relations between fundamental and derived constants in analytical and numerical forms. Then, they enumerate and comment results of determinations of parameters of the figure and gravity field of the Earth, solar parallax, constant of lunar equation, the masses of planets, the constants of aberration, of nutation and of precession and give an extensive list of references.

Cette séance publique s'est tenue au grand amphithéâtre de l'Institut d'Astrophysique, le lundi 27 mai 1963 à 10 h 30 m sous la présidence de M. Clemence.

Première Résolution. — En raison, d'une part, du manque de cohérence et des insuffisances de l'actuel système de constantes astronomiques, d'autre part des progrès que les récentes observations ont apportés à la connaissance de ces constantes, nous recommandons que les éphémérides nationales et internationales soient fondées sur un système de constantes astronomiques amélioré; les Services chargés de l'établissement des éphémérides appliqueront cette recommandation dès qu'ils seront en mesure de le faire. Le nouveau système devraêtre défini par un ensemble non surabondant de constantes fondamentales, et par des relations explicites entre celles-ci et celles qui en seront dérivées.

Résolution 1. — In order to remedy the inconsistencies and inadequacies of the present system of astronomical constants, and to take account of the better determination of such constants provided by recent observations, we recommend that the national and international ephemerides should be based on an improved system of astronomical constants; and that this system should be put into use as soon as it is practicable to the Ephemeris Offices. The new system shall be defined by a non-redundant set of fundamental constants, and by explicit relations between these and the constants derived from them.