** **

**PRIMARY
LIGHT MINIMA OF X TRIANGULI BETWEEN 1921-1995**

**GHEORGHE DORIN CHIS, ALEXANDRU POP, VLAD TURCU**
**Astronomical Institute of the Romanian AcademyAstronomical Observatory
Cluj-NapocaStr. Ciresilor 19, 3400 Cluj-Napoca, Romania**
**E-mail: academy1@mail.soroscj.ro****
**

*Abstract*. An extensive collection of primary light minima
of X Tri is listed. The O-C diagram reveals a complex, but also an interesting
structure, while the observations statistics shows an undesirable decrease
of the observed minima number for this variable. This paper is intended
to contribute to the revival of the interest for observing X Tri.

*Key words:*astrophysics - variable stars - eclipsing binary
systems

** **

** **

**NUMERICAL
MODEL FOR THE STUDY OF WAVE-MEAN FLOW INTERACTIONS IN SOLAR MAGNETOHYDRODYNAMICS**

**MIHAI S. GHIZARU**
**Astronomical Institute of the Romanian Academy**
**Str. Cutitul de Argint 5, 75212 Bucharest 28, Romania**

**MARCEL GOOSSENS**
**Center for Plasma Astrophysics, K.U., Leuven**
**Celestijnenlaan 200 B, B-3001 Leuven, Belgium****
**

*Abstract*. A 2D MHD model in cylindrical geometry is developed
for the study of the behaviour of MHD waves incident on critical layers
in the presence of shearing in magnetic and velocity fields in the solar
plasma The MHD code described in this paper is based on the resistive MHD
equations written in (*r,z*) coordinates. The non-divergence constraint
for the magnetic field is satisfied by using a vector potential. For the
time advancing, an operator splitting procedure is performed when including
the different physical effects, as well as for alternating direction in
the advection terms. The rotating cone test is used for numerical experiments
with different advenction schemes. The model equations are integrated on
an Arakawa *b* grid, with *B*ø in the cell center and
*A*ø in the velocity points. Second order schemes are used
for the mass, momentum and energy advection with a monotonicity maintaining
scheme applied periodically. Implicit methods, treated by gaussian elimination
are used for the toroidal and poloidal magnetic field diffusion.

*Key words*: resistive MHD equations - numerical modeling -
advection schemes

** **

** **

**CCD PHOTOMETRY
ON THE ASTEROID 2419 MOLDAVIA**

**MIREL BIRLAN**

**Astronomical Institute of the Romanian Academy**
**Str. Cutitul de Argint 5, 75212 Bucharest 28, Romania**

*Abstract*.On September 26, 27 and October 2, 1995, observations
were made at the Haute Provence Observatory on the asteroid 2419 Moldavia.
The results show a fast rotator asteroid with the synodic period of 2.412
0.003 hours.

*Key words: *asteroids - CCD - photometry

** **

** **

**ON THE GENERATORS OF THE NEW PERTURBATION METHODS**

**EUGENIU GREBENICOV**
**Institute for Supercomputers of the Russian Academy of Sciences**
**37, Vavilova St., Moscow 117312, Russia**
**E-mail: greben @ ext1.ccas.ru**

*Abstract*. Some basic concepts (generator of the theory, generating
equation) and ideas of the modern theory of perturbations are presented.
Compared with the classical theory, the modern one has two essential advantages:
the determination of the perturbation does not require the preliminary
solution of the generating equation, and the choice of the new initial
conditions is large. The algorithm of constructing the solution is presented.

*Key words*: celestial mechanics - theory of perturbations

** **

**FAMILY BOUNDARY
CURVES IN ROTATING SYSTEMS**

**GEORGE BOZIS**
**Department of Theoretical Mechanics, University of ThessalonikiGR-540
06 Thessaloniki, GreeceE-mail: Bozis@ ccf.auth.gr**

**MIRA-CRISTIANA ANISIU**
**"T.Popoviciu" Institute of Numerical AnalysisP.O.Box 68, 3400 Cluj-Napoca,
Romania**
**E-mail: anisiu @ math.ubbcluj.ro****
**

*Abstract*. In the framework of the two-dimensional inverse
problem of Dynamics with autonomous forces, we discuss the creation of
the family boundary curves (FBC) with the aid of Dainelli's formulae. We
then extend the notion of FBC to the case of rotating systems and we prove
that these curves are loci either of points of equilibrium for the corresponding
forces or points where the given family of orbits is "exterminated".

*Key words*: inverse problem - family boundary curves

** **

** **

**ANALYTIC-NUMERICAL
SOLUTIONS OF THE RESTRICTED THREE-BODY PROBLEM**

**YU. A. RYABOV**
**Moscow's Automobile and Highway Engineering University**
**Leningradsky pr. 64, 125829 Moscow, Russia**

*Abstract*. The planar, circular, restricted three-body problem
is being considered for the Sun-Jupiter-asteroid case. A classical algorithm
with simple iterations and one consisting of iterations with rapid convergence
are proposed for constructing quasi-periodic solutions in trigonometric
form.

*Key words:* celestial mechanics - restricted three -body problem

**NONLINEAR
INSTABILITY OF SOME RELATIVE EQUILIBRIUM CONFIGURATIONS IN THE ( n
+ 1)-BODY PROBLEM**

**BADAOUI ELMABSOUT**

**Universite Paris 6, Unite de Formation et de Recherche de Mecanique,
Laboratoire des Systemes Dynamiques**
**4, Place Jussieu, Tour 66, 75252 Paris cedex 05, France**
**E-mail: bae@ccr.jussieu.fr****
**

*Abstract*. We study analytically the second order nonlinear
stability of a degenerate configuration of relative equilibrium where *n*
bodies having the same mass *m* are at the vertices of a regular polygon
with *n* sides, while a body having a nonzero mass *m0* is at
the center of the polygon. It is shown that at this configuration of relative
equilibrium the matrix of the second derivatives of the energy-momentum
functional has always negative and positive eigenvalues, for any choice
of *n* and of the ratio µ = *m/m0*. Consequently, the above
configuration is nonlinearly unstable for any choice of *n* and µ,
even if for *n* > 6 it is linearly stable for µ larger than
some third degree polynomial of *n*, as we had shown in a previous
paper.

*Key words*: celestial mechanics - (*n* + 1)-body problem
- stability

** **

** **

**LA METRIQUE
DE MAUPERTUIS DANS L'ESPACE DES CONFIGURATIONS D'UN SYSTEME DYNAMIQUE CONSERVATIF**

**MIHAIL BARBOSU**
**Universite "Babes-Bolyai", Faculte de Mathematiques et Informatique1,
rue Kogalniceanu, 3400 Cluj-Napoca, Roumanie**
**E-mail: mbarbosu@math.ubbcluj.ro**

*Resume*. Le but de ce travail est de mettre au point et de
justifier l'interet pour une methode qualitative (tres peu utilisee) d'etude
de la stabilite des trajectoires d'un systeme dynamique conservatif. La
methode est basee sur la liaison existante entre le signe des courbures
riemanniennes (ou sectionnelles) et le comportement des geodesiques.

*Key words*: celestial mechanics - dynamical systems - differential
geometry

** **

** **

**A QUALITATIVE
STUDY OF THE TWO-BODY PROBLEM IN MANEFF-TYPE FIELDS**

**CRISTINA STOICA**

**Institute for Gravitation and Space SciencesLaboratory for GravitationBd.
Ana Ipatescu 21, 71111 Bucharest, Romania**
**E-mail: cstoica@math.uvic.ca**

**VASILE MIOC**
**Astronomical Institute of the Romanian AcademyAstronomical Observatory
Cluj-Napoca**
**Str. Ciresilor 19, 3400 Cluj-Napoca, Romania**
**E-mail: vmioc@roastro.astro.ro**

*Abstract*. The qualitative evolution of the relative motion
in the two-body problem for Maneff-type potential laws (of the form *A/r*
+ *B/r²*) is being studied. Using the first integrals of angular
momentum and energy, the trajectories in the phase plane are constructed
for the whole allowed interplay among field parameters, angular momentum
and total energy. All possible scenarios for the relative motion are found
to be nine, illustrating four essential trends: path ending in collision,
path leading to escape, trajectory tending to equilibrium, and quasiperiodic
(or periodic) orbit. The cases of nonrectilinear motion are treated separately.

*Key words*: celestial mechanics - two-body problem - Maneff-type
fields

** **

**ORBITS AROUND
STARS OF LINEARLY INCREASING MAGNITUDE**

**VASILE MIOC**
**Astronomical Observatory of the Romanian Academy,Astronomical Observatory
Cluj-Napoca,Str. Ciresilor 19, 3400 Cluj-Napoca, Romania**
**E-mail: vmioc@roastro.astro.ro**

*Abstract*. The elliptic-type motion of a particle around a
star of linearly increasing magnitude (exponentially decreasing luminosity)
is being studied using Delaunay-type canonical variables and a method due
primarily to von Zeipel. The behaviour of every orbital element is determined.
The solution of motion equations points out constancy of semilatus rectum
and orbit plane positions, and first order mixed perturbations in semimajor
axis and eccentricity (orbit deformation), argument of periastron (apsidal
motion) and mean anomaly. The model is shown to belong to the two-body
problem with changing equivalent gravitational parameter.

*Key words*: dynamical astronomy - perturbations

** **

** **

**SOFTWARE
PACKAGE FOR PREPARING AND PROCESSING OF AN ASTRONOMICAL OBSERVATION**

**OVIDIU VADUVESCU, MIREL BIRLAN**
**Astronomical Institute of the Romanian Academy,Str. Cutitul de Argint
5, 75212 Bucuresti 28, Romania****
**

*Abstract*. This paper presents an astronomical software package
which draws celestial charts. It was conceived taking into account the
technical possibilities available for the Romanian astronomers and the
actual trend of the observational astronomy. The software package, now
to its third version, comes to decrease the time to prepare an observation
and to perform accurate charts for searching and identification.

*Key words*: software - astrometry - star database - celestial
maps

** **

** **

**ROMANIAN ASTRONOMICAL JOURNAL, VOL. 6, NO. 2, 1996**

** **

** **

**COLOUR
GRADIENTS IN CLUSTERS OF GALAXIES (1)**

**NEDELIA ANTONIA POPESCU, DORU MARIAN SURAN**
**Astronomical Institute of the Romanian Academy,Str. Cutitul de Argint
5, 75212 Bucharest 28, Romania**
**E-mail: delia@roastro.astro.ro, suran@roastro.astro.ro****
**

*Abstract*. The analysis of the photometrical observations for
galaxies with *z *>* *0.2 is of great importance for both Extragalactic
Astronomy and Cosmology. This reveals a large variety of phenimena and
cosmological effects. We use the method of *colour gradients* in clusters
of galaxies in order to study some of these evolutive effects. The results
concerning the colour gradients in 15 clusters of galaxies with 0 <
*z* < 0.81 and the implications in the morphology and evolution
of the clusters are presented. The connexion between the colour gradient
and the Butcher-Oemler effect, the problem of colour evolution of galaxies
in clusters are also discussed.

*Key words*: cosmology - clusters evolution - colour gradients

** **

** **

**STUDY
OF THE ECLIPSING BINARY GO CYGNI BASED ON OBSERVATIONS OF BUCHAREST AND
ATHENS OBSERVATORIES FROM 1985 TO 1994**

** **

**G. OPRESCU (1), A. DUMITRESCU (1), M.D. SURAN (1), P.ROVITHIS (2),
H. ROVITHIS-LIVANIOU (3)**

**(1) Astronomical Institute, Romanian Academy, Str. Cutitul de Argint
No. 5,**
**75212 Bucharest 28, Romania**
**E-mail: goprescu@roastro.astro.ro, alex@roastro.astro.ro, suran@roastro.astro.ro**

**(2) Astronomical Institute, National Observatory of Athens, P.O.
Box 20 048,GR-118 10 Athens, Greece**

**(3) Section of Astrophysics, Astronomy & Mechanics, Physics Dept.,**
** University of Athens, GR- 157 84 Zografos, Greece**

*Key words*: stellar photometry - close binary systems

** **

** **

**MULTIPERIODIC
BEHAVIOUR OF RT PERSEI**

**ALEXANDRU POP (1), IOAN TODORAN (1) and FRANZ AGERER (2)**

**(1) Astronomical Institute of the Romanian Academy**
**Astronomical Observatory Cluj-Napoca**
**Str. Ciresilor 19, 3400 Cluj-Napoca, Romania**

**(2) Bundesdeutsche Arbeitsgemeinschaft fur Veranderliche Sterne e.V.
(BAV),**
**Zweikirchen, Dorfstrasse 19, D-84184 Tiefenbach, Germany****
**

*Abstract*. The period variation of RT Persei is resumed. A
new, semi-empirical ephemeris, consisting in a polynomial term and a "multiperiodic"
term, is established on the basis of 577 individual times of primary minimum
light, covering 98 years. The frequencies detected in the amplitude spectrum
of the O-C curve are believed to characterize the physical mechanisms occuring
in the system.

*Key words*: variable stars - eclipsing binary systems - Algol
binaries.

** **

** **

**THE
USE OF CHARACTERISTIC TIME TO THE STUDY OF PERIOD VARIABILITY PHENOMENA**

**ALEXANDRU POP**
**Astronomical Institute of the Romanian Academy**
**Astronomical Observatory Cluj-Napoca**

**Str. Ciresilor 19, 3400 Cluj-Napoca, Romania Abstract. The
notion of characteristic time associated with a variable star with changing
period is resumed. A possibility to use it in order to classify period
variation phenomena is described. The practical aspects of the application
in concrete observational situations are approached by taking into acccount
an ephemeris for light time extrema with high degree of generality. The
observation planning is also considered from the viewpoint of the characteristic
time.**

*Key words*: variable stars - stellar photometry - periodicity
analysis - data analysis

** **

** **

**GENERAL
FORMULATION OF SOME PROBLEMS OF CELESTIAL MECHANICS FOR CONSTRUCTING SOLUTIONS
USING COMPUTERS**

**EUGENIU GREBENICOV**
**Institute for Supercomputers of the Russian Academy of Sciences37,
Vavilova ST., Moscow 117312, Russia**
**E-mail: greben@ext1.ccas.ru**

**ARPAD PAL**
**Babes-Bolyai University, Department of Mathematics and Computer
Science**
**1, M. Kogalniceanu St., 3400 Cluj-Napoca, Romania**
**E-mail: apal@math.ubbcluj.ro**
*Abstract*. Some problems of celestial mechanics are exposed
in a modern way, the characteristic of the motion theory being not the
order (power of a small parameter), but an *a priori* given accuracy
(even if the theory accuracy depends implicitly on the small parameter).
The mathematical formulation is given for six special problems, whose solutions
can be obtained with the aid of the "Bogolyubov processor".

*Key words*: celestial mechanics - theory of motion - symbolic
processors

** **

** **

**MODIFIED
LAGRANGE-BURMANN SERIES FOR REPRESENTING KEPLER'S EQUATION SOLUTION**

**EUGENIU GREBENICOV**
**Institute for Supercomputer Systems of the Russian Academy of Sciences,**
**37, Vavilova St., Moscow 117312, Russia**
**E-mail: greben @ ext1.ccas.ru**

*Abstract. *New series representing the solution of Kepler's
transcendent equation are being obtained. Their covergence domain is larger
than the convergence domain of the well-known Lagrange series for the same
solution.

*Key words*: celestial mechanics - Kepler's equation

** **

**ON
THE SIMULTANEOUS TOTAL COLLISION FOR PARTICLE SYSTEMS**
**WITH QUASIHOMOGENEOUS POTENTIALS**

**VASILE MIOC**
**Astronomical Institute of the Romanian Academy**
**Astronomical Observatory Cluj-Napoca**
**Str. Ciresilor 19, 3400 Cluj-Napoca, Romania**
**E-mail: vmioc@roastro.astro.ro**

**CRISTINA STOICA**
**Institute for Gravitation and Space Sciences**
**21-25 Mendeleev St., Bucharest, Romania**
**E-mail: cstoica@math.uvic.ca**

*Abstract*. The *n*-body problem in an attracting field
featured by a quasihomogeneous potential is considered. Based on an equality
concerning the moment of inertia and on the Lagrange-Jacobi relation transposed
for this case, one proves the impossibility of the simultaneous total collision
in infinite time.

*Key words*: celestial mechanics, *n*-body problem, quasihomogeneous
potentials

** **

** **

**SMALL
STOCHASTIC PERTURBATIONS OF INTEGRABLE CANONICAL SYSTEMS**

**GHEORGHE STOICA**
**University of Bucharest, Mathematics Department**
**14, Academiei St., Bucharest, Romania**

**CRISTINA STOICA**
**Institute for Gravitation and Space Sciences**
**21-25 , Mendeleev St., Bucharest, Romania**
**E-mail: cstoica@math.uvic.ca**

*Abstract.*We consider the integrable canonical systems perturbed
by a Brownian motion and we present an asymptotic estimation (in probability
and in uniform norm) of the difference between the coordinates, the momenta
and their small stochastic perturbations. The typical examples of application
of these estimates are the exactly harmonic systems.

*Key words*: canonical systems - Brownian perturbations - celestial
mechanics

** **

**PERIOD
CHANGES OF SATELLITE CIRCULAR MOTIN DUE TO ODD ZONAL HARMONICS OF GEOPOTENTIAL**

**STELIAN COJOCARU**
**Naval Academy, Str. Fulgerului 1-3, 8700 Constantza, RomaniaE-mail:
cojocarus@yahoo.com****
**

*Abstract*. The initially circular motion of an artificial satellite
in the terrestrial gravitational field is being considered. The first order
difference between the nodal period and the Keplerian one caused by all
odd zonal harmonics of the geopotential is analytically determined. The
effect of every such harmonic can be pointed out separately.

*Key words*: artificial satellites - terrestrial gravitational
field

** **

**MEASUREMENT AND ASTROMETRIC REDUCTION OF CCD IMAGES IN BUCHAREST**

**GHEORGHE VASS, GABRIEL STEFANESCU, OVIDIU VADUVESCU**
**Astronomical Institute of the Romanian Academy,**
**Str. Cutitul de Argint 5, 75212, Bucuresti, Romania**
**E-mail: gvass@roastro.astro.ro, gsteph@roastro.astro.ro**

*Abstract*. The paper presents the methods of measurement and
astrometric reduction of the CCD images made at Bucharest Astronomical
Observatory beginning with 1995. We present the programs for the automatic
measurement and the astrometric reduction methods, as well as the accuracy
of the astrometric positions obtained.

*Key words*: CCD - astrometry

** **

**TIME RECORDING IN
CCD OBSERVATIONS**

**GABRIEL STEFANESCU**
**Astronomical Institute of the Romanian Academy,**
**Str. Cutitul de Argint 5, 75212 Bucharest 28, Romania**
**E-mail: gsteph@roastro.astro.ro****
**

*Abstract*. This paper presents some methods improving the precision
of time recording and time measurements in the image acquisition technique
by CCD, using PCs equipped with chronographic cards. At the Astronomical
Institute of the Romanian Academy a chronographic card designed by M. Dequin
And F. Chollet, Paris Observatory, was used. The results show that the
accuracy can come of the order of the commutation time of the CCD camera's
shutter.

*Key words*: CCD - image acquisition - programming

** **

**REDUCTION
OF ASTEROIDAL APPULSES. FIRST RESULTS IN BUCHAREST**

**OVIDIU VADUVESCU**
**Astronomical Institute of the Romanian Academy,**
**Cutitul de Argint Str. 5, 75212 Bucharest 28, Romania**

*Abstract*. The method presented is applied to asteroidal approaches
to catalogue stars ans ocultations, and derives the minimum separation
at conjunction and the corresponding time of these ones. Three CCD observations,
reported to the European Asteroidal Occultation Network, illustrate the
method.

*Key words*: astrometry – CCD - asteroidal occultation - appulse