Planetary Precession Research Articles

On the 'thickness' of Saturn's rings caused by satellite and solar perturbations and by planetary precession

In the present paper, long-period and secular variations of the longitude of ascending node are derived for a particle orbiting an oblate precessing planet subjected to perturbation by an exterior satellite moving along a low-inclination orbit. It is shown that precession of Saturn under the solar torque, which causes the Laplace plane to be noninertial, is also effective in producing a forced inclination. The height above the Laplace plane associated with this variation is several meters for a particle located in the middle of the ring.

Calculation of the perihelion advance of planets in a field approach to gravitation

It is shown that, when taking into account the self-gravity of field energy of a gravitational field, one obtains a modified field equation for the intensity of gravitational field, the solution of which, when inserted in Kepler's problem, furnishes a formula for the perihelion precession of planets which (except of a fitting numerical factor) is identical with Einstein's. In Appendix 1 we point out the significance of an analogous equation in electrodynamics, and in Appendix 2 we shall try to construct a field model within the relativistic field theory which justifies the previous perihelion-shift calculation.

Planetary precession in gravitation theory

A simple derivation of the general relativistic correction to planetary orbits is given, without explicit reference to Einstein’s field equations. The calculation is compared to Schiff’s investigation of the bending of light. Restrictions on the line element of curved space, which follow from the weak and strong equivalence principles are discussed. The weak equivalence principle and the weak field approximation are exploited to give a simple derivation of the correction to planetary motion in the Brans-Dicke theory.

New impetus to astrometry

In 1964 a conference was held at Flagstaff, Arizona, in honour of Ejnar Hertzsprung. At this conference Martin Schwarzschild presented the inaugural address. The title was 'New Impetus to Astrometry'. I was so much impressed by everything what he, as an astrophysicist, had to say that I have always remembered his analysis of important astrometric problems with admiration. Nine years after the Flagstaff Conference, I find it appropriate to open this Symposium in referring to Schwarzschild's lecture and in presenting my views on recent developments and on progress which I expect in the future. Major achievements in astrometry during the past decade resulted mainly from the introduction and development of new instrumental techniques, the application of astrometric methods in new areas of astronomy, and from the vigorous and successful work in large international undertakings. An important part of the recent progress was unforeseen, namely, the progress made in the absolute measurement of positions of objects by means of radio techniques. Let us first consider the classical areas of astrometry. I will follow here Schwarzschild in first citing the determination of the local inertial frame of rest, which in practice, is given by a system of positions and proper motions of fundamental stars and the knowledge of accurate values of the so-called constants of precession, nutation and aberration. While in 1963 the Fourth Fundamental Catalogue {FK4} was completed on the basis of observations before about 1950, an enormous effort began with the aim of improving the system and the individual data of the FK4. The observations have been carried out with the transit circle, the vertical circle, and with Danjon's astrolabe. By means of improved techniques the errors of observations have been decreased by a factor of about two compared with the observations on which the FK4 was based, and it has become possible to push the magnitude limit of meridian circles to stars fainter than visual magnitude nine. Furthermore, considerable contributions have been made to the improvement of the system in the southern sky, which in the FK4 was based almost entirely on observations made at the Cape Observatory alone. The number of absolute and differential observations made since 1950 is already sufficiently large to justify an extensive analysis with the aim of an improvement of the FK4 and its extension from magnitude 7.5 to 9.0. Progress has also been made in determining precession. It has become clear that Newcomb's planetary precession requires a small correction due to recent improvements of the values of the planetary masses. The point has been reached where further correc-