GEODYNAMICS

The basic goal of this study (as the first step) is to collect the appropriate set of the fundamental astronomic-geodetics parameters for their further use to obtain the components of the density distributions for the terrestrial and outer planets of the Solar system (in the time interval of more than 10 years). The initial data were adopted from several steps of the general way of the exploration of the Solar system by iterations through different spacecraft. The mechanical and geometrical parameters of the planets allow finding the solution of the inverse gravitational problem (as the second stage) in the case of the continued Gaussian density distribution for the Moon, terrestrial planets (Mercury, Venus, Earth, Mars) and outer planets (Jupiter, Saturn, Uranus, Neptune). This law of Gaussian density distribution or normal density was chosen as a partial solution of the Adams-Williamson equation and the best approximation of the piecewise radial profile of the Earth, including the PREM model based on independent seismic velocities. Such conclusion already obtained for the Earth’s was used as hypothetic in view of the approximation problem for other planets of the Solar system where we believing to get the density from the inverse gravitational problem in the case of the Gaussian density distribution for other planets because seismic information, in that case, is almost absent. Therefore, if we can find a stable solution for the inverse gravitational problem and corresponding continue Gaussian density distribution approximated with good quality of planet’s density distribution we come in this way to a stable determination of the gravitational potential energy of the terrestrial and giant planets. Moreover to the planet’s normal low, the gravitational potential energy, Dirichlet’s integral, and other planets’ parameters were derived. It should be noted that this study is considered time-independent to avoid possible time changes in the gravitational fields of the planets.

On a new field theory formulation and a space-time adjustment that predict the same precession of Mercury and the same bending of light as general relativity

This article introduces a new field theory formulation. The new field theory formulation recognizes vector continuity as a general principle and begins with a field that satisfies vector continuity equations. Next, independent of the new formulation, this article introduces a new space-time adjustment. Then, we solve the one-body gravitational problem by applying the space-time adjustment to the new field theory formulation. With the space-time adjustment, the new formulation predicts precisely the same precession of Mercury and the same bending of light as general relativity. The reader will find the validating calculations to be simple. The equations of motion that govern the orbital equations are in terms of Cartesian coordinates and time. An undergraduate college student, with direction, can perform the validations.

The Binaries from Unstable Triples. Dynamical Processes of Formation

The dynamical processes of formation, evolution and disruption of binaries may be effectively studied by computer simulations in the N > 3-body gravitational problem. As a result of analysis of these investigations of diverse authors, the classification of the dynamical processes of formation of wide and close binaries may be proposed (see Table 1). This Table shows the following general processes: I-triple approaches of the single bodies; II-approaches of binaries with single bodies; Ill-escape from physical triples. The actions of these processes, and kinetics of a frequency of binaries in general field were studied at the Astronomical Observatory of the Leningrad State University (1965-1988) by computer simulations in the three-body problem. More than 3.104 orbits with negative total energy E < 0 and 5.104 with E > 0 have been run on the computers. The film “Dynamical evolution of triple systems” was produced. Part I of this movie shows the evolution of the unstable non-hierarchical triplet as well as the processes of formation, evolution, and disruption of temporary wide and final close binaries inside the physical triples. Part II of film presents in detail the trajectories of the bodies on the triple approaches of “fly-by”-and of “exchange”-types. The triple approach of “fly-by”-type results often in an escape from triple as well as the formation of final close binary. The triple approach of “exchange”-type consists as a rule of a few close double approaches of bodies and rarely results in an escape from triplet, it results in formation of temporary wide binary inside triplet. Part III of movie presents the trajectories of the different-mass bodies: an escape of the minimum-mass body, the intermediate-mass body, and the maximum-mass body as well as a formation of binaries with different-mass components.