On Equilibrium Figures of Particle Clouds around the Sun and Stars

Equilibrium figures of cold gas-dust (or cometary) clouds are studied in a more general setting than the classical Roche problem. The cloud is considered to be under the influence of gravitational attraction of the central star and the tidal field of the Galaxy. Our analysis also takes into account the centrifugal forces due to the rotation of the cloud, which moves around the center of the stellar system together with the star. The limit equilibrium figure is found to have three planes of symmetry and to be shaped like a “lemon” with lateral swellings and two singular points. The shape of this figure and its cusp angles in the planes of two main sections are calculated. The average density inside the equilibrium figure is shown to be almost exactly equal to the average density of matter in the Galaxy. This coincidence cannot be accidental and means that equilibrium figures with the critical level of the total surface potential fill the entire volume of the Galaxy. A possible consequence is that the cometary clouds of neighboring stars in the Galaxy may touch each other (or even intersect because of the presence of dark matter). Hence stars may exchange comets and part of the comets in the Solar System may belong to other stars.

Non-Linear Oscillations and Beats in the Beta Canis Majoris Stars

Notwithstanding a great number of hypotheses, suggested for explaining superpositions of the light- and of the velocity variations of the ß Canis Majoris stars, no one of these does it satisfactorily. Possibly it is due to an inadequate elaboration of the non-linearly oscillation theory. Analysis and critical evaluation of the existing hypotheses are given by Mel’nikov and Popov (1970). Our explanation consists in existence of close frequencies corresponding to various oscillation modes which are non-linearly interacting.Equations of motion of an ideal incompressible fluid under condition of preserving the equilibrium figure symmetry with respect to the equatorial plane (lateral oscillations) have the form (Baranov 1988):

Computer Simulations of Astronomical Phenomena

The basic idea of this project is to introduce a senior student to an astronomical phenomenon that he analyses carefully and simulates on the graphic screen of a personal computer. In a second step, this simulation serves as a demonstration for junior students.Three examples are presented here: the retrograde motion of the planets, the Earth’s rotation, and the precession and the equilibrium figure of the Earth due to tides. Programs have been written on an IBM PC/AT.It would be highly desirable to start an exchange program of material of didatic interest among the international astronomical community