Abstracts vol. 12

TEMPERATURE OF A BLACK HOLE

IN A DE SITTER SPACETIME

IOANNIS IRAKLIS HARANAS

Department of Physics and Astronomy

York University, Toronto, Ontario, Canada

E-mail: ioannis@yorku.ca

Abstract. A relation for the black-hole temperature in a De Sitter-type universe is determined. As a result, the upper and the lower temperature limits of the black hole are calculated, and then the limits of the radius of the universe containing the black hole. All calculations are based on the present values of the cosmological constant L . Further relations for the dependance of this temperature on Hubble’s constant and the gravitational energy of the hadrons are also derived.

Key words: De Sitter metric – cosmological constant – Hubble’s constant.

KEPLER ANGULAR VELOCITY

FOR SLOWLY ROTATING RELATIVISTIC STARS

ALEXANDRU MIRCEA IMBROANE

Babes-Bolyai University, Faculty of Geography

Str. Clinicilor 5-7, RO-3400 Cluj-Napoca, Romania

E-mail: alex@geografie.ubbcluj.ro

Abstract. Rapidly rotating objects of a given mass can remain stable up to a critical angular velocity, beyond which they can undergo instabilities leading to disruption. The Kepler angular velocity is an absolute limit for the rotation of a star. The present paper is devoted to the study of Kepler angular velocity in General Relativity, for a class of relativistic configurations with power-law density distribution, namely stepenars. This class of models is very general. For some particular values of parameters we obtain other known models: homogeneous, linear, and polytropic. The rotation is considered sufficiently slow to keep the star spherically symmetric. The results are reported from a numerical investigation of the structure of slowly rotating stars.

Key words: relativistic stars – rotation– angular velocity.

COMPUTATIONAL ALGORITHM FOR ORBIT AND MASS DETERMINATION OF VISUAL BINARIES

MOHAMED SHARAF¹, MOHAMAD NOUH ², ABDEL NABY SAAD ²,

MAGDY ELKHATEEB ², SOMAYA SAAD ²

¹ Department of Astronomy, Faculty of Science

King Abdul-Aziz University, Jeddah, Saudi Arabia

^{2 Department of Astronomy}

^{National Research Institute of Astronomy and Geophysics, Helwan,
Egypt}

^{E-mail: abdo_nouh@hotmail.com}

^{Abstract. In this paper we introduce an algorithm for
determining the orbital elements and individual masses of visual binaries.
The algorithm uses an optimal point, which minimizes a specific function
describing the average length between the least-squares solution and the
exact solution. The objective function to be minimized is exact, without
any approximation. The algorithm is applied to Kowalsky’s method for orbital
parameter computation, and to Reed’s method for the determination of the
dynamical parallax and individual masses. The procedure is applied to A
1145 and ADS 15182.}

^{Key words: visual binaries – orbit– masses – optimization.}

THE NORTH–SOUTH ASYMMETRY

OF SOFT X-RAY SOLAR FLARES

GEORGETA MARIS¹, MIRUNA DANIELA POPESCU^{1, 2}, MARILENA MIERLA^{1, 3}

¹Astronomical Institute of the Romanian Academy

Str. Cutitul de Argint 5, RO-752121 Bucharest, Romania

E-mail: gmaris@aira.astro.ro

^{2 Armagh Observatory, College Hill,}

^{Armagh BT61 9DG, N. Ireland}

^{E-mail: mdp@star.arm.ac.uk}

^{3 Max-Planck Institut für Aeronomie}

^{Max-Planck-Str. 2, D 37191, Katlenburg-Lindau, Germany}

^{E-mail: mierla@linmpi.mpg.de}

^{Abstract. We analyse the North-South (N-S) asymmetry of
soft X-ray (SXR) solar flares during the 11-year solar cycle (SC). After
reviewing the literature on flare dominance in the northern and southern
hemispheres of the solar disk for SCs 17–23, we analyse the SXR flare distribution
in the two hemispheres during the period 1976–2001. The analysis was made
using the number of flares (N) and the Q_x index,
which evaluates the energy emitted by flares in soft X-ray. The monthly
and annual N-S asymmetry values computed by us for the mentioned period
are in agreement with the results from the literature. The degree of the
N-S asymmetry for both N and Q_x indices confirmed
the antiphase of SXR flare emergence for spectral classes M and X, and
class C, respectively, noted by Maris et al. (2000). Finally, we consider
that the detailed study of the descending and minimum phases of the SCs,
at the stage when magnetic phenomena from both the old and the new cycle
interact in the solar atmosphere, would be useful for inferring information
about the activity level of the next cycle.}

^{Key words: Sun - solar flares
– soft X-ray - N-S asymmetry.}

FINAL EVOLUTIONS IN THE CHARGED THREE-BODY

PROBLEM

ARTURO CRIOLLO, ERNESTO PÉREZ-CHAVELA

Departamento de Matemáticas

Universidad Autónoma Metropolitana-Iztapalapa

Av. San Rafael Atlixco # 186, Col. Vicentina

México D.F. 09340 D.F.

E-mail:

acpi@xanum.uam.mx, epc@xanum.uam.mx

Abstract: We study the motion of three point particles endowed with mass and electrostatic charge under the influence of the respective Newtonian and Coulombian forces. We focus on the behaviour of the mutual distances between the particles as time approaches infinity. We classify all possible final evolutions in this model with respect to the signs of the total energy and the parameters (masses and charges).

Key words: celestial mechanics – central configurations – Lagrange-Jacobi identity – three-body problem.

THE TWO-BODY PROBLEM IN THE POINT MASS APROXIMATION FIELD. IV. SYMMETRIES

VASILE MIOC ¹, IHARKA CSILLIK ²

¹ Astronomical Institute of the Romanian Academy

Str. Cutitul de Argint 5, RO-752121 Bucharest, Romania

E-mail: vmioc@aira.astro.ro

^{2 Babes-Bolyai University, Faculty of Mathematics and Computer
Science}

^{Str. M. Kogalniceanu 1, RO-3400 Cluj-Napoca, Romania}

^{E-mail: iharka@math.ubbcluj.ro}

^{Abstract. The only fields for which the correctness of
the point-mass representation (Newton's theorem) can be proved are those
featured by potentials of the form .
The two-body problem in such a field is tackled from the only standpoint
of symmetries. The motion equations, written in Cartesian or polar coordinates,
present nice symmetries that form eight-element Abelian groups endowed
with an idempotent structure. It is the same for McGehee-type coordinates
that extend the phase space to collision or escape. All these groups are
proved to be isomorphic. Expressed in Levi-Civita collision-regularizing
coordinates, the vector field of the problem exhibits symmetries that form
a sixteen-element group with the same characteristics.}

^{Key words: celestial mechanics – two-body problem – point-mass
approximation – symmetries.}

SPHEROIDAL AND TOROIDAL MODES

FOR TIDAL KINETIC ENERGY

IN SPHERICAL ELASTIC BODIES

JUAN GETINO¹, ALBERTO ESCAPA², AMELIA GARCIA³

¹Grupo de Mecanica Celeste

Facultad de Ciencias, Universidad de Valladolid, 47005 Valladolid, Spain

E-mail: getino@maf.uva.es

^{2 Grupo de Mecanica Celeste}

^{Departamento de Matemática Aplicada, Universidad de Alicante,
apdo. 99}

^{03080 Alicante, Spain}

^{E-mail: Alberto.Escapa@ua.es}

^{3 Grupo de Mecanica Celeste}

^{Departamento de Matemática Aplicada a la Ingeniería}

^{E.T.S.I.I., Paseo del Cauce s/n, 47011 Valladolid, Spain}

^{E-mail: amegar@wmatem.eis.uva.es}

^{Abstract. In this work, the total expression of the perturbation
of the kinetic energy of rotation, when an elastic spherical solid is deformed
due to the gravitational attraction of external bodies, is studied. We
do not limit this study to any order in the expansion of the perturbing
potential in spherical harmonics, and we consider in the expression of
the displacement vector the complete solution, composed by spheroidal and
toroidal modes. We show in a very simple way, by using the properties of
the Legendre polynomials, that the toroidal modes have no contribution
at all under the hypothesis of spherical body, and, among the spheroidal
modes, only the term n = 2 acts, therefore the perturbation produced
by the spheroidal component for n = 2 gathers the total perturbation.}

^{Key words: celestial mechanics – Earth’s rotation – elastic
Earth – tides.}

MÜCKET-TREDER’S TWO-BODY PROBLEM:

INFINITY MANIFOLD

VASILE MIOC

Astronomical Institute of the Romanian Academy

Str. Cutitul de Argint 5, RO-75212 Bucharest, Romania

E-mail: vmioc@aira.astro.ro

Abstract. The two-body problem in the Mücket-Treder post-Newtonian classical field is revisited. Starting from the motion equations and first integrals in standard polar coordinates, we apply McGehee-type transformations of the first and second kind to suitably describe the escape/capture dynamics. To this end, the infinity manifold is defined, and the flow on it is depicted. The behaviour of orbits that neighbour infinity is wholly similar to the cases corresponding to some relativistic models.

Key words: celestial mechanics – two-body problem – post-Newtonian fields.

PRELIMINARY ORBIT DETERMINATION.

APPLICATION TO (2) PALLAS

GHEORGHE BOCSA

Astronomical Institute of the Romanian Academy

Str. Cutitul de Argint 5, RO-752121 Bucharest, Romania

E-mail: gbocsa@aira.astro.ro

Abstract. We have elaborated a FORTRAN program intended to the determination of preliminary orbits on the basis of Gauss’ method. We performed an application to the asteroid (2) Pallas, based on three precise positions obtained at the Astronomical Observatory of Bucharest in 1969. The results agree well with the elements given by Efemeridy Malykh Planet 1969.

Key words: preliminary orbits – (2) Pallas.