The principal purpose of IAU Colloquium No. 9 on the IAU System of Astronomical Constants was to discuss whether further action should be taken to revise those fundamental constants (namely the constants of precession and nutation and the system of planetary masses) that were left unchanged when new values of the other constants were adopted at Hamburg in 1964. The opportunity to discuss other relevant matters was also taken.

Recent determinations of lunisolar precession and of the motion of the equinox are reviewed. Methods of determination are discussed which are based on proper motions referred to fundamental systems, on planetary motions, and on proper motions referred to galaxies. It is concluded that a new fundamental catalogue, which will replace the FK4 at some future date, should be based on revised values of precession and freed from errors in the motion of the equinox.

One of the principal aims of the Lick proper motion program, as conceived and initiated by Wright (1950), was to derive the correction to precession. Ideally, proper motions of stars from a fundamental catalogue should be measured with respect to galaxies. Unfortunately, these stars are too bright for a direct reference to faint galaxies, even with an objective grating and two systems of exposures (2 h and 1 min) on every plate, as employed at Lick. For this reason a cooperative project with the U.S. Naval Observatory was initiated in 1953 (Scott, 1954; Vasilevskis, 1954), with an intention to establish a direct relationship between meridian circle and Lick observations. When Heckmann (1954) proposed the formation of the AGK3, it was agreed to discontinue the cooperation mentioned, so as to make the resources of the U.S. Naval Observatory available for observing the AGK3 reference stars, and then to use the AGK3 as an intermediary for relating the Lick proper motions to a fundamental system. An obvious advantage of this change was offered by the abundance of AGK stars for measurement on Lick plates; a disadvantage is the absence of the AGK3 data south of declination –2.°5.

Criticisms of the senior author’s paper (1967) are examined, and it is found that there still seems to be a possibility that the cause of the excess secular change is in the mantle-core coupling. Part II is devoted to an improvement of the previous result (Aoki, 1969) using a model of the elastic mantle and fluid core. In order to give the observed value of excess secular change of the obliquity, a value of the coupling coefficient of the Earth’s rotation is 3.5 times larger than Rochester’s (1968) value is required. This is not impossible from the geophysical view-point. In fact, if we take into account Hide’s argument (1969), then the coupling coefficient will be much larger than the present geophysical value.

The coordinate system defined by the locations of distant galaxies should be an inertial coordinate system. Until that system becomes better observed, we must use the stars of our own Galaxy, and make certain assumptions in order to achieve an inertial system. Basically, we assume that the stellar proper motions consist of a component due to galactic rotation (a function of distance from the galactic center), a component due to solar motion, and a random component, peculiar to each star. The random component should not cause the star system as a whole to rotate in any particular direction – in other words, the sum of the random components of proper motion will be zero (to within their standard deviation) in every direction.

We are here concerned with the nutations that appear in the motion of the Earth because of the existence of the external forces due to the Sun and Moon, that is, the forced nutations.

We can consider the nutations divided in two groups from the point of view of their values and the precision attained by astronomical observations. The first group comprises the nutations that have values greater than 1″ and in this group we have the nutation of period 18.6 yr called the principal nutation and the value of this nutation in obliquity is called the constant of nutation. The second group comprises the nutations with values smaller than 1″ and corresponds to the great majority of all other nutations.

We have previously established (Melchior and Georis, 1968) the equations connecting the development of precession-nutation with the tesseral part of the tidal potential. These equations are:

where

ωiAi respectively represent the frequencies and amplitudes of the tidal waves, ω the Earth’s rotation velocity,

La présente revue ne donne pas une liste complète des déterminations des masses planétaires. La liste la plus complète récemment publiée est due à Kozlovskaya (1963); elle contient toutes les déterminations effectuées entre 1826 (masse de Jupiter par Encke)et 1961.

Depuis, quelques autres listes ont été publiées. Elles sont incomplètes, car elles ont surtout pour but de proposer de valueurs des masses qui apparaissaient comme étant les plus probables à ces auteurs. Signalons ainsi les listes de Böhme et Fricke (1965) et de Kulikov (1965), préparées pour le colloque sur les constantes fondamentales de Paris (Symposium UAI N° 21). Une liste analogue a été préparée par Clemence (1966) pour l’UAI. Citons encore les revues préparées par le Jet Propulsion Laboratory (Mulholland, 1967) et une autre liste, rassemblée il y a deux ans, qui vient d’ère publiée par l’auteur (Kovalevsky, 1970). La présente synthèse est une suite de ce premier travail, compte-tenu des nombreuses nouvelles déterminations qui ont été effectuées depuis deux ans.

Planetary masses are determined from an extensive analysis of observations of the five outer planets and of seven selected minor planets.

The Jet Propulsion Laboratory has developed a set of computer programs known as the Solar System Data Processing System (SSDPS) which is employed in improving the ephemerides of the major planets and for improving the values of several associated astronomical constants. A group of solutions for the masses of the major planets, together with the AU and radii of Mercury, Venus, and Mais, is presented. These solutions based upon optical, radar, and spacecraft radio tracking data are preliminary. The relative power of radar and radio tracking data vis-à-vis purely optical data in a solution is shown. The problems which could arise by adopting solutions based upon a single data type are demonstrated.

Numerical tests are the basis of a study about the effects caused in the orbits of the planets (l)-(4) by possible errors in the system of planetary masses. The masses of five major and three minor planets are considered. Especially, the effects caused by (1) Ceres in the orbit of (2) Pallas since the time of discovery are found to be large enough for a determination of the mass of Ceres. A first result for this mass is (6.7 ±0.4) x 10-10 solar masses.

An analysis of the observations of the minor planets (153) Hilda, (279) Thule and (334) Chicago yields the following values for the reciprocal mass of Jupiter: (153) Hilda 1047.378 ±0.019, (279) Thule 1047.347 ±0.023, (334) Chicago 1047.325 ± 0.010. A possible error in the mass of Saturn that might affect these results is discussed.

A set of masses for the principal planets is derived systematically from all available fundamental and independent determinations. In deriving these values an attempt has been made to treat independently those determinations based on differing observational types or analytical methods.

Corrections to Newcomb’s lunisolar precession and to motion of the equinox are evaluated from proper motions of 77 Cepheids, employing recently determined values of their distances. Results are diverse, depending on the weighting method. If the effect of the cosmic dispersion is neglected and ω0 is imposed to be 25 km/s/kpc, then Δp1 = 1.″1 ±0.″2 and Δλ′ + Δe = 1.″0 ±0.″1 per century in the FK4 system.

La valeur conventionnellement admise pour la précession est trop faible. Il est bien connu que la correction à apporter à cette valeur est de l’ordre de 1” par siècle. On peut situer cette correction dans l’intervalle suivant (Fricke, 1967):

In 1964, the IAU adopted, among the primary constants of its system, the following three constants especially related to the shape, dimensions and gravitational field of the Earth:

a = 6378160 m

GM = 398603 × 109m3/s2

J2 = 0.0010827

These values were discussed in 1967 by the IAG and adopted by the IUGG as the basis of a ‘Geodetic Reference System 1967’. Although at that time better values of these constants were available, IUGG decided to adopt the values of the IAU system in order to keep consistency with the values agreed upon by the astronomers.