ALBERT

Notizen: Abstract The effect of resonant planetary perturbations on the evolution of the orbit of a satellite driven by tidal forces is studied in this paper. The basic equations that govern it are similar to the equations found in orbit-orbit and in spin-orbit couplings. The general form of these equations is: A general treatment of such equations, proposed earlier (J. Kovalevsky, in Dynamical Trapping and Evolution of the Solar system, IAU Colloquium no74, V. V. Markellos and Y. Kozai, eds., 1983) is sketched. In particular, the effects of the large long periodic variations of the excentricity e' of the planet are analysed on an example taken from the lunar theory and the Earth's general theory due to Bretagnon. The argument of the well known planetary term θ=18 V-16Tℓ due to the tidal friction and quasi-periodic variations due to the presence of e' in the expression of the mean motion of the Moon. Their joint effect, has been to produce in the past resonant situations for this argument that repeated more than 100 times. Every such situation can be treated by equation (1). Numerical integration, using conditions that might have occurred while θ or similar other arguments were quasi resonant, have produced the following results: (a) In some cases, the argument becomes temporarily resonant. Between the capture to and the escape from the resonance, the semi-major axis undergoes oscillations, but the tidal secular evolution is stopped. (b) In other cases, the argument is not trapped into a resonant conditions, but the semi-major axis undergoes a quick change while dθ/dt is close to zero. A number of arguments that have been quasi resonant in the past history of the Earth-Moon system has been identified from the Chapront and Chapront-Touzé Lunar Theory. It appears that the phenomena described are frequent features in the evolution of the Lunar orbit.

Notizen: Abstract After a short description of the present situation in Celestial Mechanics, the authors identify four different aspects (physical bases, mathematical aspects, computational techniques and astronomical techniques) and two criteria describing the importance and the difficulty of a given problem. Three main fields of application are considered: relativistic and Newtonian Celestial Mechanics and evolutionary problems. For each case, a number of examples of unsolved problems are listed and discussed in terms of the previously defined domains and criteria.

Notizen: Abstract The European Space Agency project of an astrometric satellite-HIPPARCOS-is shortly described. It will measure the angles between stars situated in fields separated by about 70°. The precision of the elementary measurements is expected to be of the order of 0″.005. A similar accuracy is found to apply to the basic reduction giving the abcissae of stars referred to great circles on the sky. The final overall reduction should yield accuracies better than 0″.002 in position and parallaxes and 0″.002 per year in proper motions. The main features of the final catalogue are described and some possible consequences for fundamental astronomy are given.

Notizen: Abstract The HIPPARCOS program may contribute to dynamical astronomy in two different ways: by determining the positions of some bodies of the solar system or by improving the positions of the reference stars with respect to which observations of members of the solar system are made. It is shown that only minor planets may be observed validly by HIPPARCOS but these observations alone cannot contribute significantly to the determination of a reference frame. However, they can be useful for the improvement of orbits and as a complement to a major observational effort in preparation of a new determination of dynamical system of reference. HIPPARCOS will provide a new global reference frame and improved proper motions of stars. This may be used to rediscuss earlier observations and provide corrections to the theory of motion of the Moon and planets. Such corrections may be rather large and their possible effect is indicated for several cases. Furthermore, the celestial reference system of HIPPARCOS will allow to avoid, in future observations, many of the presently existing biases.

Notizen: Abstract The development of digital computers induced major new developments in Celestial Mechanics. At present, one can hardly mention a project in Celestial Mechanics that does not use computers as the principal tool. One can distinguish many different manners of using computers in Celestial Mechanics. Among them, the following are presented and typical examples are given: algebraic manipulations for literal and semi-numerical theories, numerical integration of the equations of motion, determination of physical parameters, numerical checks of analytical results, studies of families of solutions, search for new conjectures, scanning the phase space. In all these approaches, and in others omitted here, major scientific achievements were obtained in the last 20 years and new problems can now be envisaged that were unaccessible even a few years ago.

Notizen: Summary The problem of the determination of the orbit of a celestial body is an old astronomical problem, of which solutions can be found in many classical books on elementary celestial mechanics. However, the introduction of new (radioelectric) means of observations for the artificial satellites have brought up new solutions of this old problem. The author reminds the definitions of the six elliptic elements of an orbit. The problem of their determination is usually divided into two separate steps: a preliminary orbit determination and the improvement of the preliminary elements. Two principal types of preliminary orbit determination exist: the Gaussian type, purely geometrical in which the positions of the body at two different times are determined, and the Laplacian type, of a more dynamical character, in which both position and velocity vectors are found for a given time. The improvement of the preliminary elements is usually obtained by a numerical solution of equations of variations of the elements, minimizing the sum of the squares of the angular distances between the computed and the observed points. The elements on which these variations are applied can be quite various. The coefficients of the equations are usually obtained numerically, although their analytical expressions can also be derived. Most of the modification proposed to the classical methods of orbit determination are more technical improvements in connection with the computation on electronic machines. The most interesting modifications are inspired by the fact that time measurements are less precise than the position (Batrakov, Iszak), the effects of this difference in errors are discussed in this paper. In some cases, using Laplace's method, no preliminary orbit is computed, and all the observations can be used at once (Barlier, Kovalevsky). The determination of orbits from radar measurements is discussed. The proposed methods are quite different in principle from the classical ones. They are actually improvements of a circular orbit whose determination is made by a method of undetermined coefficients (Baker). Some of the elements determined by these methods are quite unstable, and it is always wiser to use other informations together with radar measurements. The determination of orbits from Doppler data alone has been worked out by many investigators. It is the inverse problem of the main problem of all navigational systems. The method proposed by Patton is summarized. The principles of others are quite analogous. The results are improved when more than one receiver are used. The different types of corrections: refraction, perturbations, etc., should be introduced in later stages of the determination, and the whole frequency curve is to be used if a good determination of all elements is desired. Finally, the author quotes a method (Baker) using both Doppler and radar data, and the solution of a new problem: the determination of the orbit of a satellite of another planet from Doppler data alone (Deutsch).