The organizers of this workshop wish to express their deepest appreciation to the participants for their clearly displayed scientific competence, for their cooperation and for their untiring efforts during the long lecture and discussion sessions. The benefits were unquestionably mutual; the personal meetings of scientists interested in the same or similar subjects created natural resonances which will not dmp out easily. In fact, we expect that the forcing functions of mutual interests will lead to further exchange of information and to several joint projects. Examples of subjects of common interest to at least two or three participants were basic problems of geo-dynamics, motions of asteroids and quantitative and qualitative behavior of galaxies.
One purpose of publishing the Proceedings of this workshop os to stabilize the cooperations already established and to call the attention to other members of our profession, not so lucky as to attend our workshop, to the proposed cooperative effort. Our invitation is to all those interested in these projects to join our future activities.
We also wish to thank for the support, cooperation and understanding of our sponsors, the Hungarian Academy of Sciences and the United States National Science Foundation.
We offer this volume to our colleagues in both countries with the humbleness of the beginner, hoping that they will realize that any faults of the organizer and all credits should go to our participants and to our sponsors.

B. Balázs (Eötvös Loránd University, Budapest, Hungary) and V. Szebehely (University of Texas, Austin, Texas)

Dr. Victor Szebehely: Selected research problems in celestial mechanics at the University of Texas at Austin

This paper reports on recent research on the inverse problem, on stability, on accuracy and on undeterminancy in celestial mechanics.

B. Garfinkel: Recent progress in the theory of trojan asteroids

In previus publications the author has constructed a long-periodic solution of the problem of the motion of the Trojan asteroids, treated as the case of 1:1 resonance in the restricted problem of three bodies. The recent progress reported here is summarized under three headings.

B. Érdi: On the variation of the Jacobi constant of Trojan asteroids in the elliptic restricted problem of three bodies

A relation corresponding tothe Jacobian integral of the circular restricted problem of three bodies is derived in cylinderical coordinates for the elliptic restricted three-body problem. The unknown integral appearing in this relatio is evaluated for the case of Trojan asteroids using an asymptotic solution for their motion. Analytic expressionsfor the main variations of a parameter C^* correspondingto the Jacobi constant in the elliptic case are obtained. It is shown that the main variations of C^* depend on two long periods, the period of the libration around the point L₄ and the period of the motion of the perihelion of the asteroids. Upper limits for the amplitudes of the main variations of C^* are also given.

P. K. Seidelmann and R. L. Duncombe: Problems concerning the outer planets

P. K. Seidelman: Saturn-its rings and satellites, a celestial mechanics laboratory

F. Veres:Observatory of the Hungarian Academy of Sciences Baja, Hungary

The paper deals with the twice averaged restricted three body problems. First we show a general analitical solution for the planar case and then we give a particular solution for the spatial case. The results of the analitical solution are compared with results obtained by numerical integration.

W. T. Kyner: Nonsingular oscillator elements

G. Barta: A comparative study of the Earth's magnetic and gravity fields

The article contains a comprehensive summary of the results of investigations into the connections between magnetic and gravity fields of the Earth. It was shown more than 30 years ago by means of studies concerning long period variations of the permanent magnetic field of the Earth thet to the secular variation a wave of about 50 years period hsa been superimposed. The origin of the phenomenon should be found in the eccentricity of the inner core of the Earth bein similar to the eccentricity showing itself in the magnetic dipole. The more accurate expansions into series of the geoidal figure - carried out since the appearence of satellite observations - made it possible to study the problem from the gravity side too. Some ten years ago it was shown that the 6 big anomalies determining the geoid can be written as sums of two influences and the position of the two sources can be deduced from the characteristical points of the magnetic eccentricity. These similarities of the magnetic and gravity field of the Earth raise - of course - a lot of new problems /e.g. due to the shifting of eccentric dipole the gravity acceleraion observable on the Earth must show changes too/. Thus the study of connections between the two fields of force can not be regarded as being closed down in spite of many similarities detected as yet.

Professor W. M. Kaula:he next development in satellite determination of the Earth`s gravity field

Satellite-to-satellite tracking is expected to achieve ±10^-6 m/sec accuracy between co-orbiting satellites a few 100 km apart. The minimum sustainable altitude is about 160 km. It is estimated that features of the gravity field ~110 km in extent should be resolvable. TO achieve this resolution economically, the analysis process should be iterative, treating the residuals with respect to the best previous model as a time series for each orbit of limited duration (e.g., one revolution), and determining the mean correction to the potential for each duration by adjustments at trajectory crossings.

I. Almár - Sz. Mihály - T. Borza - J. Ádám: Orbit determination methods used in the satellite geodetic observator

The Satellite Geodetic Observatory of the Hungarian Institute of Geodesy and Cartography is adopting and developing different programs of satellite orbit determination connected with its tracking activity /photographic, laser and Doppler observations/.

E. M. Both: Effect of upper atmospheric variations on satellite lifetime

Without any perturbations an Earth satellite would remain on a Keplerian orbit endless. Of the perturbing forces of different origin, atmospheric drag causes a secular decrease of the semi-major axis and orbital eccent- ricity, so satellites have finite lifetimes.

L. Patkós: Dynamic processes in binary systems

According to the theory of the evolution of close binary systems the initially more massive component fills up the Roche lobe in the course of its evolution, and mass transfer is started. It usually proceeds in two steps. In the rapid phase the mass ratio is more then reve sed. The subsequent evolution proceeds on a slow, nuclear time scale while the originally more massive, but now less massive star continues to give futher masses to the other component.

L. G. Balázs: Role of random forces in stellar dynamics

Our Galaxy contains some 10¹¹ stars and diffuse material. A mechanical description of the stellar component would require the solution of a system of some 10¹¹ second order differential equations. There are several approximatons that can be utilized to solve this problem: numerical integration, numerical simulation, and the statistical approach. The force experienced by a star has some stochastic nature and so has the motion itself. The random effects of star-star encounters probably do not play an important role in the life of the Galaxy but cooperative phenomena and encounters with huge clouds of diffuse material and stars may be very significant. The time derivative of stochastic process in the equation of motion is interpreted by mean square differentiation. In the case of harmonic motion the approximate solution, which is consisent with observations is a random walk. In time scales longer than some 10⁸ years one probably cannot avoid taking into account te effect of random forces.

R. H. Miller: Dynamics of galaxies

A large computational project to study the dynamics of galaxies has been in progress at NASA-Ames Research Center in cooperation with Dr. Bruce F. Smith for the past 5 years. Galaxies are represented as self-consistent self- gravitating batches of particles whose responses are computed in a fully three-dimensional n-body treatment using 100 000 particles. Results are frequently unexpected and usually differ from prior guesses. The principal discoveries from this work in the past few years include: (1) Demonstration that "cold" axisymmetric disks, like our Galaxy, are dynamically unstable; (2) Discovery that a prolate bar, rotating end-over-end in space about a short axis, is the dynamically preferred form for rapidly rotating stellar systems; (3)Discovery of sharp contractions of both members as two galaxies pass near each other in a galaxy collosion. This sharp contraction precedes the "explosion" of the galaxy and is reponsible for most of the dynamical effects seen following a collosion; (4) Demonstration that the internal dynamics of a galaxy ina cluster of galaxies is affected on the timescale of the cluster crossing time; (5) Discovery that tidal braking of galaxies rotating in the force field of a cluster of galaxies can account for the observed slow rotation of elliptical glaxies; and (6) Demonstration that perturbations present as the Universe becomes mattergrowth rates to 1-2% accuracy, and that fluctuations 10^-4 to 10^-3 at decoupling are sufficient to produce present-day galaxy clusters and superclusters. Results from these numerical experiments are usually so complex that motion pictures are the only practical way to understand the dynamics. Motion pictures were shown for two experiments.

B. A. Balázs: On the observational vulnerability of the models for the galaxy

Any scientific model must be as simple as possible and vulnerable by measure- ments or observations. Herein some possible ways of checking the models for the Galaxy are discussed.