DERIVATION OF WEINBERG’S RELATION IN AN INFLATIONARY UNIVERSE

IOANNIS IRAKLIS HARANAS

Department of Physics and Astronomy

E-mail:
ioannis@yorku.ca

*Abstract*. We propose a
derivation of the empirical Weinberg
relation for the
mass of an elementary particle in an inflationary-type

universe. Our derivation
produces the well-known standard Weinberg relation for the mass of an
elementary particle, along with an

extra-term that depends on the inflationary
potential, as well as Hubble’s constant. This derivation is based on
Zeldovich’s result for

the cosmological constant L, in the context of quantum field theory. The extra-term
can be
understood as a small correction to the

mass of the elementary particle due to
inflation. This term also enables us to obtain an expresion for the
initial
value of the field f_{O}

and for two different kinds of inflationary potentials chosen. For
this value of the field f_{O}, Weinberg’s relation
can be possible in its

original form. Closed, flat,
and open universes give the mass of an elementary particle close to
that of a
pion, or 140 MeV/*c*^{2}.

*Key
words*: inflationary cosmology – quantum
theory of field
–cosmological
constant.

PHOTOMETRIC STUDY OF THE ECLIPSING BINARY VW LEONIS MINORIS

ALEXANDRU DUMITRESCU

Astronomical
Institute of the

Str.
Cuţitul de Argint 5,
RO-752121

E-mail:
alex@aira.astro.ro

*Abstract*. VW LMi (HIP
54003) was discovered by HIPPARCOS/TYCHO as
a

of this star. A photometric solution is derived with the Djurasevic
model. The binary, having the temperatures of the components

approximately
equal, is an overcontact system. Phase shifts of the light curve maxima
were
observed.

*Key
words*: astrophysics – stars – eclipsing
binaries – VW LMi –
photometric
solutions.

HIGH-SPEED PLASMA STREAMS ANALYSIS DURING THE SOLAR POLAR FIELD REVERSALS

GEORGETA
MARIŞ^{1}, OVIDIU MARIŞ^{2,3,4}

^{1}Astronomical
Institute of the

Str.
Cuţitul de Argint 5,
RO-040558

gmaris@aira.astro.ro

^{2}Institute
for Space Sciences

P.O.Box
MG-23, RO-77125

maris@venus.nipne.ro

^{3}Research
Associate at: Astronomical Institute of the

^{4}Research
Associate at: Istituto Nazionale di Fisica
Nucleare,
Sezione di Perugia

Via
A.
Pascoli, 06123 Perugia, Italy

Ovidiu.Maris@pg.infn.it

*Abstract.* The behavior of
the high-speed plasma streams (HSPSs) in
the solar
wind is investigated during the period of the solar

cycles (SCs) Nos. 20–22
(1964–1996) and the intervals of the solar polar field reversal. The
analysis
is performed taking into account

the following parameters: the* *durations (in days); the
maximum
velocities;* * the velocity gradients; the importance of the
streams. The

time variation of the high-speed plasma stream parameters and
their occurrence rate shows an 11-year periodicity with some
differences

between the considered SCs. The increased activity of high-speed plasma
streams
on the descendant phases of the cycles, regardless of

their solar source,
proves the existence of some special local conditions for the solar
plasma and
the magnetic field on a large scale that

allow the ejection of high velocity
plasma streams. This fact led us to analyse the high-speed plasma
stream
parameters during the solar

magnetic field reversal intervals. The significant
increase of the flare-generated high-speed plasma stream (FG_HSPS)
parameters
during

a reversal interval can be explained considering their “blob” structure
and the topology of the poloidal magnetic field during this interval.

Then, any
shield of the solar poloidal field lines is absent and the stream will
not lose
its energy in any reconnection. Besides this, the quadrupole

or even octupole
structure of the large-scale solar field could bring small-scale
magnetic field
topologies (in active regions) that allow the

gathering of greater energies as
well as stronger accelerations in a solar eruption. The decrease of the
mean
values of the coronal hole generated

high-speed plasma stream (CH_HSPS)
parameters in reversal intervals could be determined by some relaxation
of the
CH magnetic field due to

the absence of the general magnetic field lines which
would result in less efficient particle acceleration.

*Key
words*: solar wind – high-speed plasma
streams – 11-year solar
cycle - solar polar field reversal.

SOLAR CYCLE 23: FORECASTS AND OBSERVATIONS

GEORGETA
MARIŞ^{1}, MIRUNA DANIELA
POPESCU^{1, 2}, DIANA
BEŞLIU^{1}

^{1
}Astronomical Institute of the

Str.
Cuţitul de
Argint 5, RO-040558 1 Bucharest, Romania

E-mails:
gmaris@aira.astro.ro; deanna@aira.astro.ro

^{2
}

E-mail:
mdp@star.arm.ac.uk

*Abstract*. We shortly
analyse the solar cycle (SC) 23 behaviour
during May
1996-July 2003, making also a
comparison
with

the previous three cycles. Some aspects concerning the forecasts of its
maximum are presented. In accordance to some early

predictions for the
following cycle, our empirical method, based on observing the flare
energy
release during the descendant

phase of the precedent SC, estimate that the
amplitude of SC 24 will be low. Furthermore, it
is likely
that the Sun may be heading

towards a “Maunder” type of minimum, continuing a
rapid decline, which started with SC 23.

*Key words*:
Solar 11-year cycles - solar cycle 23 - forecast
methods.

SPHEROIDAL
AND TOROIDAL MODES FOR
TIDAL KINETIC ENERGY
IN AXISYMMETRIC,

SLIGHTLY ELLIPTICAL,
ELASTIC BODIES

JUAN GETINO^{
1}, ALBERTO
ESCAPA^{ 2}, AMELIA GARCÍA^{ 3}

^{1
}Grupo 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*. This paper is an
extension of the previous one by
Getino et
al.(2002), where we studied the increase of the kinetic energy of

spherical
elastic bodies due to the tidal perturbation, taking into account the
spheroidal and toroidal modes of the displacement vector.

In this paper we
consider axisymmetrical, slightly elliptical bodies, whose density and
rheological parameters are expressed as a sum of

a term with radial dependence,
corresponding to a spherical body, and terms that depend on the radius and on the latitude. By using the

well-known properties of the Legendre polynomials, we prove that for
the
spheroidal modes, the only terms of the expansion of the

perturbing potential
that intervene in the kinetic energy correspond to *n* =
0, 2, 4, while for the toroidal modes we have the contributions

of *n* = 1, 3. The corresponding tensor
of inertia of each of these terms is obtained as a function of some
integrals
in *r* whose numerical

values depend on
the internal structure of the body. The result thus obtained are the
general
one, and is valid for any elastic body in the

linear theory of the elasticity
under the above-mentioned symmetrical properties.

*Key
words*: celestial mechanics – tides –
elastic bodies – Earth’s
rotation.

LIBRATION POINTS IN MANEV’S CIRCULAR RESTRICTED THREE-BODY PROBLEM

RODICA
ROMAN ^{1}, VASILE
MIOC ^{2}

^{1
}Astronomical Institute of the

Astronomical
Observatory Cluj-Napoca

Str.
Cireşilor
19, RO-3400 Cluj-Napoca, Romania

E-mail:
rroman@math.ubbcluj.ro

^{2
}Astronomical Institute of the

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

E-mail:
vmioc@aira.astro.ro

*Abstract*. We tackle the
circular restricted three-body problem
within the
framework of Manev’s classical post-Newtonian field,

associated to a potential
of the form *A*/*r* + *B*/*r*^{2}. We establish the
equations of motion and prove the existence of an analog of the

Jacobian first
integral. After emphasizing some features of the zero-relative-velocity
surfaces, we approach the main topic: libration

points. As in the Newtonian
case, there are three collinear libration points, and, if they exist,
two
triangular libration points (situated

in the orbital plane of the primaries).
We give the positions of all these points. If triangular points exist,
they may
not form equilateral

triangles; the triangles are isosceles (always possible
situation) for equal masses of the primaries, and scalene else.

*Key
words*: celestial mechanics – restricted
three-body problem –
libration
points – post-Newtonian fields – Manev’s field.

THE
photogravitational model

MIRA-CRISTIANA
ANISIU

T.
Popoviciu
Institute of Numerical Analysis

Str.
Republicii 37, R0-3400 Cluj-Napoca, Romania

E-mail:
mira@math.ubbcluj.ro

*Abstract*. The
photogravitational model of Constantin Popovici
combines the
Newtonian attracting force with a radiative repelling one.

We consider a
post-Newtonian attracting force, namely the one generated by a
Manev-type
potential, and the same repelling force

defined by Popovici. We prove that for
this new problem the integration of the motion equations can be
performed in a
similar way

as in Popovici’s model. The study of the equilibria reveals
specific situations for the Popovici-Manev model, as the existence of
saddles.

*Key
words*: photogravitational models –
equilibria.

SYMMETRIES IN THE ISOSCELES THREE-BODY PROBLEM

VASILE
MIOC ^{1}, DORINA
STANCU ^{1,
2}

^{1
}Astronomical Institute of the

Str.
Cuţitul de Argint 5,
RO-752121

E-mail: vmioc@aira.astro.ro

^{2
}Institute of Space Sciences,
Gravitational Research Laboratory

P.O.
Box MG-6, RO-76900

E-mail: doramatro@yahoo.com

*Abstract*. We tackle the
spatial three-body problem from a single
standpoint:
symmetries. The vector field that features the

general problem presents nice
symmetries that form a sixteen-element Abelian group endowed with an
idempotent
structure.

The reduced isosceles problem (obtained by fixing the angular
momentum constant), which includes the celebrated circular

and elliptic
Sitnikov problems, exhibits a four-element group of symmetries with the
same
properties.

*Key
words*: celestial mechanics – isosceles
three-body problem –
symmetries.

THE
VERTICAL DEVIATION DETERMINATION BY
AN ASTRONOMICAL GEODETIC
METHOD

(I): PRESENT CONTEXT

OCTAVIAN
BĂDESCU ^{1,2},
PETRE POPESCU ^{2}, RADU
POPESCU ^{2}

^{1
}Technical University of Civil
Engineering

Bd.
Lacul Tei 124,

E-mail:
octavian@aira.astro.ro

^{ }

^{2,
}Astronomical
Institute of the

Str.
Cuţitul de
Argint 5, RO-040558 Bucharest, Romania

E-mail:
petre@aira.astro.ro, pradu@aira.astro.ro

*Abstract*. This paper
represents the first of a series in which we
intend to
describe and use an astronomical geodetic method for the

determination of
vertical deviation. We shall present some reasons for developing the
method. We
emphasize the advantage of vertical

deviation determination by astronomical and
geodetic measurements in the present context of GPS technology and
electronic
devices

for high-accuracy angular measurements.

*Key
words*: astrometry – geodesy – vertical
deviation.