Abstracts Details

In this paper we examine the recently introduced Dvali-Gabadadze-Porrati (DGP) gravity model. We use a space-time metric in which the local gravitation source dominates the metric over the contributions from the cosmological flow. Anticipating ideal possible solar system effects, we derive expressions for the signal time delays in the vicinity of the Sun, and for various ranges of the angle *theta* of the signal approach. The time contribution due to DGP correction to the metric is found to be proportional to *b ^{3/2}/c^{2}r_{0}*. For

*r*equal to 5 Mpc and

_{0}*theta*in the range [-

*Pi/3*,

*Pi/3*],

*delta t*is equal to 0.0001233 ps. This delay is extremely small to be measured by today's technology, but it could be probably measurable by future experiments.

There has been a renewed interest in the recent years in the possibility of deviations from the predictions of Newton's "inverse-square law" of universal gravitation. One of the reasons for renewing this interest lies in various theoretical attempts to construct a unified elementary particle theory, in which there is a natural prediction of new forces over macroscopic distances. Therefore the existence of such a force would only coexist with gravity, and in principle could only be detected as a deviation from the inverse square law, or in the "universality of free fall experiments". New experimental techniques such that of Sagnac interferometry can help explore the range of the Yukawa correction lamda > = 10^{14} m where such forces might be present. It may be, that future space missions might be operating in this range which has been unexplored for very long time. To study the effect of the Yukawa correction to the gravitational potential and its corresponding signal delay in the vicinity of the Sun, we use a spherically symmetric modified space time metric where the Yukawa correction its added to the gravitational potential. Next, the Yukawa correction contribution to the signal delay is evaluated. In the case where the distance of closest approach is much less than the range , it results to a signal time delay that satisfies the relation t(b

In the study of an Earth orbiting satellite, the terms of the series expansion of the Earth's gravitational potential can be expressed as functions of the eccentricity of the satellite. These functions are also known as eccentricity functions. The series expansion of these functions given by Kaula [2] appears to result in instabilities at high eccentricities. When calculating the eccentricity functions, researchers resort to numerical integration techniques instead. The approach followed in this contribution bypasses the problem of instability at high eccentricities by using a Hansen coefficient definition. As a test, we first calculate analytical expressions for various known eccentricity functions and then we proceed with the calculation of the eccentricity functions associated with degree and order 20, 30, 40, 50 sectorial harmonic coefficient expansion of the gravitational potential. Our calculation demonstrates the efficiency of Hansen coefficient approach that differs from that given by Kaula. It is efficient, fast, and can easily be performed with the help of a personal computer, with no instabilities at higher eccentricities.

We study the effects of a non-singular gravitational potential on satellite orbits calculating the corresponding changes of its orbital elements, using Gauss' planetary equations. We derive two non-zero expressions for the changes of the argument of the perigee and the mean anomaly, and we compare them to those derived by the general theory relativity. Using the GRACE satellite system, we obtain numerical results from which we conclude that the effect of such a potential, on the perigee cannot be separated from that of general relativity. Furthermore we conclude that the effect on the mean anomaly can probably be observed by today's technology.

We study the effects of a non-singular gravitational potential on satellite orbits by deriving the corresponding time rates of change of its orbital elements. This is achieved by expanding the non-singular potential into power series up to second order. This series contains three terms, the first been the Newtonian potential and the other two, here R1 (first order term) and R2 (second order term), express deviations of the singular potential from the Newtonian. These deviations from the Newtonian potential are taken as disturbing potential terms in the Lagrange planetary equations that provide the time rates of change of the orbital elements of a satellite in a non-singular gravitational field. We split these effects into secular, low and high frequency components and we evaluate them numerically using the low Earth orbiting mission Gravity Recovery and Climate Experiment (GRACE). We show that the secular effect of the secondorder disturbing term R2 on the perigee and the mean anomaly are 4 .307 ? 10−9/a, and −2 .533 ? 10−15/a, respectively. These effects are far too small and most likely cannot easily be observed with today?s technology. Numerical evaluation of the low and high frequency effects of the disturbing term R2 on low Earth orbiters like GRACE are very small and undetectable by current observational means

GRT predicts the existence of relativistic corrections to the static Newtonian

potential, which can be calculated and verified experimentally. The idea leading to quantum

corrections at large distances consists of the interactions of massless particles, which only

involve their coupling energies at low energies. Using the quantum correction term of the

potential we obtain the perturbing quantum acceleration function. Next, with the help of the

Newton-Euler planetary equations, we calculate the time rates of changes of the orbital

elements per revolution for three different orbits around the primary. For one solar mass

primary and an orbit with semimajor axis and eccentricity equal to that of Mercury we obtain

that Delta-omega(qu) = 1.517*10?81 deg/cy, while DeltaM(qu) = ?1.840*10^?46 rev/cy.

In this paper we calculate the effect of atmospheric dust on the orbital elements of a satellite. Dust storms that originate in the Martian surface may evolve into global storms in the atmosphere that can last for months and can affect low orbiter and lander missions. We model the dust as a velocitysquare depended drag force acting on a satellite and we derive an appropriate disturbing function that accounts for the effect of dust on the orbit, using Lagrangean formulation. A first-order perturbation solution of Lagrange's planetary equations of motion indicates that for a local dust storm cloud that has a possible density of 8.323?e10-10 kg m-3 at an altitude of 100 km affects the orbital semimajor axis of a 1000kg satellite up -0.142 m day-1. Regional dust storms of the same density may affect the semimajor axis up to of -0.418 meters per day. Other orbital elements are also affected but to a lesser extend.

Many of today's gravity theories predict the existence of a non-Newtonian Yukawa-type correction to the gravitational potential. New experimental techniques, such as Sagnac interferometry, can help in exploring the range Lamda > 10^{14}, where such forces are possibly measurable. It is expected that future space missions will operate in this range which has not been examined for a very long time. Restricting ourselves to an Earth orbiting satellite we follow a perturbing potential approach applied on the Lagrange planetary equations, in order to study the effect of such a non-Newtonian potential in the range Lamda=1.073 R. This is achieved by calculating the time rates of change of the orbital elements for the earth orbiting satellite GRACE-A. All these time rates have been calculated on the Keplerian and the precessing Keplerian ellipse of the body under study. Of all the orbital elements, the argument of the perigee is most affected by this potential.

Several contemporary modified models of gravity predict the existence of a non-Newtonian Yukawa-type correction to the classical gravitational potential. We study the motion of a secondary celestial body under the influence of the corrected gravitational force of a primary. We derive two equations to approximate the periastron time rate of change and its total variation over one revolution (i.e., the difference between the anomalistic period and the Keplerian period) under the influence of the non-Newtonian radial acceleration. Kinematically, this influence produces apsidal motion. We performed numerical estimations for Mercury, for the companion star of the pulsar PSR 1913+16, and for the extrasolar Planet b of the star HD 80606. We also considered the case of the artificial Earth satellite GRACE-A, but the results present a low degree of reliability from a practical standpoint.

Recent observations confirm that galactic red-shifts might be quantized and hint a possible

new form of quantum mechanics, which could probably explain these observed

properties of the galaxies. This brief note investigates some expressions for the mass of

the universe M(u), which were obtained with the help of the definition of the new cosmic

Planck constant h bar subscript g.

Using a non-singular gravitational potential which appears in the literature we analytically

derived and investigated the equations describing the precession of a body?s spin

orbiting around a main spherical body of mass M. The calculation has been performed

using a non-exact Schwarzschild solution, and further assuming that the gravitational

field of the Earth is more than that of a rotating mass. General theory of relativity predicts

that the direction of the gyroscope will change at a rate of 6.6 arcsec/year for a

gyroscope in a 650 km high polar orbit. In our case a precession rate of the spin of a

very similar magnitude to that predicted by general relativity was calculated resulting

to a (Delta)S_{geo} / Sgeo = -5.570x10^{-2}.

General Relativity predicts the existence of relativistic corrections to the static Newtonian potential which can be calculated and verified experimentally. The idea leading to quantum corrections at large distances is that of the interactions of massless particles which only involve their coupling energies at low energies. In this short paper we attempt to propose the Sagnac intrerferometric technique as a way of detecting the relativistic correction suggested for the Newtonian potential, and thus obtaining an estimate for phase di

erence using a satellite orbiting at an altitude of 250 km above the surface of the Earth.

The important tool for studying the gravitational field in Einstein?s theory of general relativity is his set of field equations. In this short paper, Einstein?s field equations will be derived for the Freeman cosmological model using the known form of the metric, and for the Ricci tensor, making use of an alternative, not very well known, method, called ?the Harrison method?. In our opinion, this is a much easier and faster approach, and a more reliable one, because the Cristoffel symbols do not have to be calculated separately one-by-one, thus avoiding a possible lengthy process where errors might easily be introduced.

In a new theory called Dynamic Theory of Gravity, the gravitational potential is is derived from gauge relations and has a different form than the classical Newtonian potential. In the same theory an analytical expression for the pressure is derived from the equation of the hydrodynamic equilibrium which is solved for a star of constant density and the results are compared with those of Newtonian gravity. Changes then in the central pressure and radius are also calculated and finally a redshift calculation is performed so that the dynamic gravity effects if any might be shown to be of some detectable magnitude.

*Serb. Astron. J., V168, 49-54 (2004).* There is a new theory gravity called the dynamic theory, which is derived from thermodynamic principles in a ve dimensional space, radar signals traveling times and delays are calculated for the major planets in the solar system, and compared to those of general relativity. This is done by using the usual four dimensional spherically symmetric space-time element of classical general relativistic gravity which has now been slightly modified by a negative inverse radial exponential term due to the dynamic theory of gravity potential.

In a new theory gravity called the dynamic theory, which is derived from

thermodymical principles in a five dimensional space, the deflection of a light signal is

calculated and compared to that of general relativity. This is achieved by using the dynamic

gravity line element which is the usual 4 D space-time element of Newtonian

gravity modified by a negative inverse radial exponential term. The dynamic theory of gravity

predicts this modification of the original Newtonian potential by this exponential term.

Recent evidence suggests that the fine-structure constant α = ke^{2}/hc, a measure of the strength of the electromagnetic interaction between photons and electrons, is slowly increasing over cosmological timescales. High-resolution measurements of quasar spectra suggest that there has been a variation Δα/α = -0.72 ? 0.18?10^{-5} over the past 6^{-10} Gyr. To model this, we propose variability in the speed of light that produces a cosmological time variation α& /α = 10^{-15} and 10^{-16} yr-1 at z = 3 which also agrees with the observational spectral data.

We propose a derivation of the empirical Weinberg relation for the mass of an elementary

particle and in an inflationary type of universe. Our derivation produces the standard

well known Weinberg relation for the mass of an elementary particle, along with an extra

term which depends on the inflationary potential, as well as Hubble's constant. The

derivation is based on Zeldovich's result for the cosmological constant Λ, 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 calculate,

the initial value of the field φO for two kinds of potentials chosen, which makes

Weinberg's relation possible. Closed and flat and open universes give the mass of the

particles close to the mass of a pion, 140 MeV/c2 or as the one also predicted by

Weinberg's relation.

A relation for the black-hole temperature in a De-Sitter type universe is determined in the

first step of this paper. As a result of that, 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

these calculations are based upon the present values of the cosmological constant Λ. Further

relations for the dependence of this temperature on Hubble?s constant and the gravitationsal

energy of the hardons was also derived.