Perturbations in the Anomalistic Period of Artificial Satellites Caused by the Direct Solar Radiation Pressure Centre for Astronomy and Space Sciences,Satellite Tracking Station No. 1132

Approximate formulae for the evaluation of the influence of direct solar radiation pressure (neglecting the POYNTING -ROBERTSON effect) on the anomalistic period of artificial satellites with quasi-circular and completely illuminated orbits are derived.     

Libration Points in Schwarzschild's Circular Restricted Three-Body Problem

The restricted three-body problem in Schwarzschild's gravitational field is analyzed. The existen- ce of the equilibrium points in the orbital plane is discussed and the corresponding positions are established. There are three collinear libration points, and, if they exist, two triangular libration points (situated in the orbital plane of the primaries). If triangular points exist, they may not form equilateral triangles; the triangles are isosceles for equal masses of the primaries, and scalene else.     

Groups of symmetries in the two‐body problem associated to Einstein's PN field

The two‐body problem associated to a spherical post‐Newtonian (PN) field with Einsteinian parameterization is revisited from the single standpoint of symmetries. The corresponding vector fields, in Hamiltonian and standard polar coordinates, or in collision‐blow‐up and infinity‐blow‐upMcGehee‐type coordinates, present symmetries that form diffeomorphic commutative groups endowed with a Boolean structure. The existence of such symmetries is of much help in understanding characteristics of the global flow, or in finding symmetric periodic orbits in more complex problems depending on a small parameter.     

The Gyldén‐type problem revisited: More refined analytical solutions

We resume and consistently extend our previous researches concerning the Gyldén‐type problem (a two‐body problem with time‐dependent equivalent gravitational parameter). To approach most of the concrete astronomical situations to be modelled in this way, we consider a periodic small perturbation. For the nonresonant case, we present a second‐order analytical solution. For the resonant case, we adopt the most realistic astronomical situation: only one dominant term of the Hamiltonian. In this case we point out a fundamental model of resonance, common to every resonant situation, and, moreover, identical to the first fundamental model of resonance . Considering the simplest model of periodic change of the equivalent gravitational parameter, we .nd that all possible resonances are con.ned to the first fundamental model. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Enzymological classification of salt lakes in Romania

Sediments of 56 salt lakes from Romania were studied enzymologically. The following 7 enzymatic and nonenzymatic catalytic activities have been measured: phosphatase, H₂O₂-splitting in nonautoclaved (catalase) and autoclaved samples, TTC reduction in nonautoclaved (dehydrogenase) and autoclaved samples, without or with glucose addition. A formula is proposed for the evaluation of the enzymatic potential of salt lake sediments or other habitats. A hierarchy of the studied lakes has been established on the basis of the enzymatic potential of their sediments expressed as enzymatic indicator.     

A look at global seismicity during 1999 in the longer-term time frame

An analysis and discussion of the main features and effects of the 1999global seismicity based especially on the inferred patterns of strong(M_w 7) earthquakes using NEIC/USGS data is presented.Based on the above data and their statistical features (see also Table 1)one may state that from the point of view of occurrence rate (number/yr)the 1999 global seismicity was fairly regular, but from the moment (orenergy) release standpoint it is well under the long-term average. The spacepartition was again rather typical and time distribution was quasi-Poissonian,noteworthy, the 1999 worldwide seismicity had an anomalously high deathtoll, to be discussed later. Two main new insights are brought by ouranalysis: (i) a (mega)quiescence along the whole south American segmentof circum-Pacific earthquake belt, which was inferred and rated asanomalous while it was underway and which, in retrospect, ended with thegreat (M_w = 8.4 HRV) 2001 Arequipa (Peru) event; (ii) an intriguingmonotonous rate decrease within only magnitude class 5.0 to 5.9 duringthe analyzed period (i.e., 1990–1999).     

Orbits in an anisotropic radiation field

The elliptic-type motion around a source whose luminosity is anisotropic is being perturbatively treated. Using a Fourier expansion for the perturbing force, exact expressions describing the evolution of each orbital element are determined from Newton-Euler equations. For near-unit frequency the resonant solutions are pointed out. An approximate expression for the variation of the nodal period is determined, too. The behaviour of the radius vector of the unstable orbit (resonance case) is pointed out, showing periodic variations of constantly increasing amplitude. The (both angular and physical) time scale for escape is estimated. Concrete astronomical situations modellable in this way are mentioned.     

Elliptic-type motion in Fock's gravitational field

The elliptic-type motion in the gravitational field found by Fock as exact solution of Einstein's vacuum equations in the case of spherical symmetry (Solution called here Fock's gravitational field) is studied by means of a classic method based on the perturbation theory. Regarding the deviations of the orbit from a Kepleian orbit as perturbations, the first and second order variations of the Keplerian orbital elements over one nodal period as well as those of the nodal period itself are determined.     

On the determination of potential function

Szebehely's renowned equation given in 1974, allowing for potential determination from a given orbit or family of orbits, is proved to be equivalent with an equation deduced in 1963 by Drǎmbǎ. This basic equation in the inverse problem of dynamics, for which the denomination of Drǎmbǎ –Szebehely equation is proposed, is generalized for the motion in the n-dimensional Euclidean space. A method for the determination of the potential function from motion equations is extended to this space.