70 research outputs found

    Field Equations and Equations of Motion in Post-Newtonian Approximation of the Projective Unified Field Theory

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    The equations of motion of NN gravitationally bound bodies are derived from the field equations of Projective Unified Field Theory. The Newtonian and the post-Newtonian approximations of the field equations and of the equations of motion of this system of bodies are studied in detail. In analyzing some experimental data we performed some numeric estimates of the ratio of the inertial mass to the scalaric mass of matter.Comment: 17 page

    Estimations of changes of the Sun's mass and the gravitation constant from the modern observations of planets and spacecraft

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    More than 635 000 positional observations (mostly radiotechnical) of planets and spacecraft (1961-2010), have been used for estimating possible changes of the gravitation constant, the solar mass, and semi-major axes of planets, as well as the value of the astronomical unit, related to them. The analysis of the observations has been performed on the basis of the EPM2010 ephemerides of IAA RAS in post-newtonian approximation. The obtained results indicate on decrease in the heliocentric gravitation constant per year at the level GMSun˙/GMSun=(5.0±4.1)1014(3σ). \dot {GM_{Sun}}/GM_{Sun} = (-5.0 \pm 4.1) 10^{-14} (3\sigma). The positive secular changes of semi-major axes a˙i/ai \dot a_i/a_i have been obtained simultaneously for the planets Mercury, Venus, Mars, Jupiter, Saturn, as expected if the geliocentric gravitation constant is decreasing in century wise. The change of the mass of the Sun MSunM_{Sun} due to the solar radiation and the solar wind and the matter dropping on the Sun (comets, meteors, asteroids and dust) was estimated. Taking into account the maximal limits of the possible MSunM_{Sun} change, the value G˙/G\dot G/G falls within the interval 4.21014<G˙/G<+7.51014 -4.2\cdot10^{-14} < \dot G/G < +7.5\cdot10^{-14} in year with the 95% probability. The astronomical unit (au) is only connected with the geliocentric gravitation constant by its definition. In the future, the connection between GMSunGM_{Sun} and au should be fixed at the certain time moment, as it is inconvenient highly to have the changing value of the astronomical unit.Comment: 20 pages, 4 tables, accepted for publication in Solar System Research, 2011 (Astronomicheskii vestnik

    On the perspectives of testing the Dvali-Gabadadze-Porrati gravity model with the outer planets of the Solar System

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    The multidimensional braneworld gravity model by Dvali, Gabadadze and Porrati was primarily put forth to explain the observed acceleration of the expansion of the Universe without resorting to dark energy. One of the most intriguing features of such a model is that it also predicts small effects on the orbital motion of test particles which could be tested in such a way that local measurements at Solar System scales would allow to get information on the global properties of the Universe. Lue and Starkman derived a secular extra-perihelion \omega precession of 5\times 10^-4 arcseconds per century, while Iorio showed that the mean longitude \lambda is affected by a secular precession of about 10^-3 arcseconds per century. Such effects depend only on the eccentricities e of the orbits via second-order terms: they are, instead, independent of their semimajor axes a. Up to now, the observational efforts focused on the dynamics of the inner planets of the Solar System whose orbits are the best known via radar ranging. Since the competing Newtonian and Einsteinian effects like the precessions due to the solar quadrupole mass moment J2, the gravitoelectric and gravitomagnetic part of the equations of motion reduce with increasing distances, it would be possible to argue that an analysis of the orbital dynamics of the outer planets of the Solar System, with particular emphasis on Saturn because of the ongoing Cassini mission with its precision ranging instrumentation, could be helpful in evidencing the predicted new features of motion. In this note we investigate this possibility in view of the latest results in the planetary ephemeris field. Unfortunately, the current level of accuracy rules out this appealing possibility and it appears unlikely that Cassini and GAIA will ameliorate the situation.Comment: LaTex, 22 pages, 2 tables, 10 figures, 27 references. Reference [17] added, reference [26] updated, caption of figures changed, small change in section 1.

    Quantum effects on Lagrangian points and displaced periodic orbits in the Earth-Moon system

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    Recent work in the literature has shown that the one-loop long distance quantum corrections to the Newtonian potential imply tiny but observable effects in the restricted three-body problem of celestial mechanics, i.e., at the Lagrangian libration points of stable equilibrium the planetoid is not exactly at equal distance from the two bodies of large mass, but the Newtonian values of its coordinates are changed by a few millimeters in the Earth-Moon system. First, we assess such a theoretical calculation by exploiting the full theory of the quintic equation, i.e., its reduction to Bring-Jerrard form and the resulting expression of roots in terms of generalized hypergeometric functions. By performing the numerical analysis of the exact formulas for the roots, we confirm and slightly improve the theoretical evaluation of quantum corrected coordinates of Lagrangian libration points of stable equilibrium. Second, we prove in detail that also for collinear Lagrangian points the quantum corrections are of the same order of magnitude in the Earth-Moon system. Third, we discuss the prospects to measure, with the help of laser ranging, the above departure from the equilateral triangle picture, which is a challenging task. On the other hand, a modern version of the planetoid is the solar sail, and much progress has been made, in recent years, on the displaced periodic orbits of solar sails at all libration points, both stable and unstable. The present paper investigates therefore, eventually, a restricted three-body problem involving Earth, Moon and a solar sail. By taking into account the one-loop quantum corrections to the Newtonian potential, displaced periodic orbits of the solar sail at libration points are again found to exist

    Stochastic motion of test particle implies that G varies with time

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    The aim of this letter is to propose a new description to the time varying gravitational constant problem, which naturally implements the Dirac's large numbers hypothesis in a new proposed holographic scenario for the origin of gravity as an entropic force. We survey the effect of the Stochastic motion of the test particle in Verlinde's scenario for gravity\cite{Verlinde}. Firstly we show that we must get the equipartition values for tt\rightarrow\infty which leads to the usual Newtonian gravitational constant. Secondly,the stochastic (Brownian) essence of the motion of the test particle, modifies the Newton's 2'nd law. The direct result is that the Newtonian constant has been time dependence in resemblance as \cite{Running}.Comment: Accepted in International Journal of Theoretical Physic

    Linearized f(R) Gravity: Gravitational Radiation & Solar System Tests

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    We investigate the linearized form of metric f(R)-gravity, assuming that f(R) is analytic about R = 0 so it may be expanded as f(R) = R + a_2 R^2/2 + ... . Gravitational radiation is modified, admitting an extra mode of oscillation, that of the Ricci scalar. We derive an effective energy-momentum tensor for the radiation. We also present weak-field metrics for simple sources. These are distinct from the equivalent Kerr (or Schwarzschild) forms. We apply the metrics to tests that could constrain f(R). We show that light deflection experiments cannot distinguish f(R)-gravity from general relativity as both have an effective post-Newtonian parameter \gamma = 1. We find that planetary precession rates are enhanced relative to general relativity; from the orbit of Mercury we derive the bound |a_2| < 1.2 \times 10^18 m^2. Gravitational wave astronomy may be more useful: considering the phase of a gravitational waveform we estimate deviations from general relativity could be measurable for an extreme-mass-ratio inspiral about a 10^6 M_sol black hole if |a_2| > 10^17 m^2, assuming that the weak-field metric of the black hole coincides with that of a point mass. However Eot-Wash experiments provide the strictest bound |a_2| < 2 \times 10^-9 m^2. Although the astronomical bounds are weaker, they are still of interest in the case that the effective form of f(R) is modified in different regions, perhaps through the chameleon mechanism. Assuming the laboratory bound is universal, we conclude that the propagating Ricci scalar mode cannot be excited by astrophysical sources.Comment: 19 pages, 1 figure; typos in Sec. VIII. A. correcte