After a presentation of the problem posed by the construction of a system of astronomical constants, the author describes the new catalogue FK 4. He then reviews recent progress in the knowledge of the orbits of major planets and in the determination of solar parallax, the constant of aberration and the constant of precession.

It is recommended that the parametric values which are currently most used in orbital computation be adopted as provisional standards rather than those which may be the best available and from which they differ only slightly. It is remarked that the most serious geodetic errors affecting astronomy are tracking station positions. Standard methods of describing positions are suggested.

The author discusses the set of constants required to describe the external gravitational field of the Earth : a set of form factors and two scale factors. Some problems in relating the external field as derived from the motions of satellites to the quantities observed at the surface are mentioned. The fondamental parameters cannot be derived from the data without a knowledge of other astronomical constants, and it is shown how a general adjustment of data of different origins can be made. The results enable suggestions to be made about the way in which new conventional values of these parameters should be chosen.

The author discusses various determinations of zonal and tesseral harmonics of the Earth's gravitational field, the values of the solar parallax, and the constants related to the figure of the Moon and its motion.

The results of 1959-1960 radar measurements of the distance of the Moon are given. The method of reduction of the data is described The possible effects of lunar topography and errors of other origins are discussed, as well as the effects of different constants such as the radii of the Earth and of the Moon.

The author analyses the advantages of the use of the gaussian heliocentric gravitational constant. He proposes that a geocentric gravitational constant should be defined in an analogous way, that would present similar advantages.

The author comments upon the different needs of the astronomical constants in ephemeris work and space trajectory computations.

The author discusses the dependence of the constants of nutation and precession upon the values of other fundamental constants such as the dynamical ellipticity of the Earth, the mass of the Moon and the solar parallax in the case of two different theoretical models of the Earth.

The author compares amplitudes of the main terms of nutation as derived from various theories with the observed values. He also reports on the discovery, by Popov, of a term in the variation of latitude, with a period slightly shorter than a sideral day.

In this paper, an investigation is made of the changes in the constant of precession, parameters of solar motion and of galactic rotation, caused by the transition from the FK 3 to the FK 4 system.

The author discusses the effects of the error in the conventional value of the constant of aberration upon the precision of modern observations for time and latitude. He proposes 20″.50 as a new conventional value for k, suggesting that the change should be made as soon as possible.

Preliminary results on the observation of the constant of aberration by the photographic polar tube of Pulkovo Observatory are presented.

It is suggested that the adoption of a physical definition of the unit of time-interval, to replace the ephemeris second, would have no serious effect on the theory and practice of dynamical astronomy, or on the system of astronomical constants.

Report on the work in progress using Clemence's theory of the motion of Mars.

In the construction of analytical theories of planetary motion, the effect is considered of errors in the adopted values of masses, orbital elements and ephemeris time upon the accuracy of computed co-ordinates of the inner planets in accordance with Newcomb's expansions and constants (with Ross's elements for Mars). These are accurate to five decimal places. The errors in the orbital elements are the principal source of inaccuracy in the positions of the planets. The precision of the ephemerides can be considerably improved by introducing appropriate corrections.

This paper is devoted to an exact discussion of the determination of the astronomical unit with radar and to an extensive error analysis of the technique. Theoretical relationships between the constants are used to construct a consistent set of numerical values of constants based on these results.

A comprehensive review is given of the Earth-Venus measurements made with the Lincoln Laboratory Millstone radar in 1959 and 1961. The time-delay and Doppler shift data yield a value for the Astronomical Unit of 499.0052 ± 0.001 light-sec. Using 299 792.5 km/s for the speed of light leads to an AU of 149 598 000 ± 300 km. With the radius of Earth taken as 6 378.15 km, the solar parallax then becomes 8″.79416 ± 0″.00002. This value is consistent with measurements made at various other laboratories to about one part in 105.

Results of observations made at Jodrell-Bank with the radio-telescope.

The author investigates whether the adoption of a value of the solar parallax determined by radar measures would permit an acceptable representation of the observations of Eros. The solution he obtaines leaves important residuals and leads to a rather unlikely value for the mass of Mars.