Eddingtons Zahlen,Einsteins Kriterium und Rydbergs rationelles Dimensionssystem

The discussions about the meaning of the “hierarchy of interactions” and in connection with this about the role of Eddington's “cosmological number” imply the question of the “big numbers” in physics. According to Einstein's and Bridgman's criteria such “big numbers” are hints at unsolved problems in the foundations of physics. Eddington gives a theory of the big number like cosmological quantities. – A new point of view on this question may be to remember Rydberg's suggestion on independigly physical dimensions of lengths L, surfaces S, and volumina V, and to remember Dällenbach's suggestion to introduce a new universal constant α which describes the operational connections between the quardrate of lengths L² and the surface S in microphysics. Coulomb's and Nwton's laws have the same structure. But, the electrical forces are depending on L^-2 and the gravitational forces are depending on S^-1 ∼ (1/α) L^-2 because “gravitation is geometry”. In Planck's elementary units h, c and f Dällenbach's “surface-constant of the vacuum” α is a pure number α ≈ hc/fm², th. i. Eddington's cosmological number ω ∼ 10⁴⁰. However, Rydberg's physical dimensions in geometry and Dällenbach's constant suggest new formulations of the question of “geometrization of physics” and “physicallization of geometry” and the connections between cosmology and microphysics.     

Die Asymmetrie der kosmischen Zeit und RIEMANNS Gravitationstheorie1)

RIEMANN himself has considered his formulation of the differential geometry of curved spaces as a first step to a unified geometrical theory of “one ether of gravity, electricity and magnetism”. RIEMANN has pointed out that a fundamental point in such a theory of gravitation has to be the asymmetry of its sources: only positive masses exist. – According to RIEMANN this asymmetry of sources to be coupled with an asymmetry of gravitation field equation against the time-reversion t → - t. Therefore, the gravitation field equation is of the type of a continuity-equation of a velocity field v_i˜g^ikθ _k Φ. RIEMANN 's ether is incompressible in empty space-domains: θ _k (g^1/2v^k) = o. But, in domains with a massdensity σ > o it is θg^1/2/θt = −2 kcσ = − 2 kcg^1/2σ₀ (with a universal constant kc). The matter-density defines depressions of the ether. In a general-relativistic approach RIEMANN 's ansatz means that in empty space-time domains the world-geometry is the purely metrical “RIEMANN ian” geometry. However, in domains with a non-vanishing matter-tensor T_μ^v ≠ o the geometry becomes “non-RIEMANN ian” affine connecting and is of the type of WEYL 's geometry or of the “EINSTEIN -CARTAN theories of gravitation”. Especially, RIEMANN 's field equation for the empty space θ _k ((g^1/2g^ikθ _k Φ) = o. is the EINSTEIN equation (-|g_μv|)^1/2 R₀⁰ = o with g₀₀ = - Φ²c^-4.     

Lymanα forests and the evolution of the universe

The Lyα forest absorption lines in the spectra of quasars are interpreted as caused by the crossings of the light beam with the walls of a bubble structure (expanding with the Hubble flow only). Then, the typical separation between the absorption lines is proportional to the mean size of the bubbles. The variable factor is the expansion rate H[z]. The Friedmann regression analysis of the observed line separations determines the density parameter ω₀ and the normalized cosmological term λ₀ = λc²/3H²₀ of the appropriate cosmological model: ω₀ = 0.014 ± 0.002, λ₀ = 1.080 ± 0.006. Depending on the Hubble parameter this method reveals the values of the present mean matter density pm,0 = 2.6 h² · 10⁻²⁸ kg m⁻³ and of the cosmological constant Λ = 3.77 h² · 10⁻⁵² m⁻² (with h = H₀/(100 km/s·Mpc)). According to our analysis all models with Λ = 0 must be excluded. The curvature of space is positive. The curvature radius R₀ is 3.3 times the Hubble radius (c/H₀). The age t₀ is 2.8 times the Hubble age (H₀⁻¹).     

Zur kosmologischen Testung des Machschen Prinzips

The Machian models of isotropic expanding universes according to the “inertia-free” gravo-dynamics imply the equations between the instantan values H₀ and q₀ of the HUBBLE parameter H, the acceleration q, and the matter density o. Therefore, in Machian universes with linear expansion q₀ = 0 the energy integral E = -1/2ϵc² is zero and the matter density becomes (with H₀²R₀² = c²/3) (f₀ the Newtonian gravitational constant). This is the critical density in general relativistic cosmology.     

Newtonian cosmology with a varying gravitational constant

Newtonian cosmology is developed with the assumption that the gravitational constantG diminishes with time. The functional form adopted forG(t), a modification of a suggestion of Dirac, isG=A(k+t) ^–1, wheret is the age of the Universe and a small constantk is inserted to avoid a singularity in the two-body problem. IfR is the scale factor, normalized to unity at an epoch time , the differential equation is then . Here ₀ is the mean density at the epoch time. With the above form forG(t), the solution is reducible to quadratures.The scale factorR either increases indefinitely or has one and only one maximum. LetH ₀ be the present value of Hubble's constant /R and _0c the minimum density for a maximum ofR, i.e., for closure of the Universe. The conditions for a maximum lead to a boundary curve of _0c versusH ₀ and the numbers indicate strongly that thisG-variable Newtonian model corresponds to an open universe. An upward estimate of the age of the Universe from 10¹⁰ yr to five times such a value would still lead to the same conclusion.The present Newtonian cosmology appears to refute the statement, sometimes made, that the Dirac model forG necessarily leads to the conclusion that the age of the Universe is one-third the Hubble time. Appendix B treats this point, explaining that this incorrect conclusion arises from using all the assumptions in Dirac (1938). The present paper uses only Dirac's final result, viz,G(k+t)^–1, superposing it on the differential equation .     

The value of the superstring tension and dark matter

The last line of the abstract should read “about μ = 10^–5c ²/G. This corresponds to 1.2 · 10³⁹ Newton”. The main text remains unchanged. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Artificial contradiction between cosmology and particle physics: the Λ problem

It is shown that the usual choice of units obtained by taking G=c=ℏ=1, giving the Planck’s units of mass, length and time, introduces an artificial contradiction between cosmology and particle physics: the lambda problem that we associate with ℏ. We note that the choice of ℏ=1 does not correspond to the scale of quantum physics. For this scale we prove that the correct value is ℏ≈1/10¹²², while the choice of ℏ=1 corresponds to the cosmological scale. This is due to the scale factor of 10⁶¹ that converts the Planck scale to the cosmological scale. By choosing the ratio G/c ³=constant=1, which includes the choice G=c=1, and the momentum conservation mc=constant, we preserve the derivation of the Einstein field equations from the action principle. Then the product Gm/c ²=r _g , the gravitational radius of m, is constant. For a quantum black hole we prove that ℏ≈r _g ²≈(mc)². We also prove that the product Λℏ is a general constant of order one, for any scale. The cosmological scale implies Λ≈ℏ≈1, while the Planck scale gives Λ≈1/ℏ≈10¹²². This explains the Λ problem. We get two scales: the cosmological quantum black hole (QBH), size ∼10²⁸ cm, and the quantum black hole (qbh) that includes the fundamental particles scale, size ∼10⁻¹³ cm, as well as the Planck’ scale, size ∼10⁻³³ cm.      

Variable cosmological “constant” and motion of a test particle in a cloud of dust

We find that Einstein’s like field equations with coordinate-dependent cosmological “constant” Λ(x ⁱ ) imply a non geodesic law of motion for test particles moving in a continuous distribution of incoherent matter (“dust”). The deviation from the geodesic law depends on the derivatives ?Λ/? x ⁱ and, in the weak field approximation, causes an anomalous acceleration A～(Vc ²/γ ρ)?Λ/? t+(c ⁴/γ ρ)?Λ/? r where V=dr/dt, c=the speed of light, γ=8π G with G=the gravitational coupling, ρ=the mass density of the cloud, r and t are the radial and time coordinate respectively. Reasonable assumptions on Λ=Λ(t) give A<10^?8 cm/s² when ρ>10^?29 g/cm³ i.e. in all known astrophysical systems. A possible connection with the anomalous Pioneer acceleration is shortly discussed in the case of a cosmological “constant” coupled to matter.     

Velocity dispersion in N‐body simulations of CDM models

This work reports on a study of the spatially coarse‐grained velocity dispersion in cosmological N‐body simulations (OCDM and ΛCDM models) as a function of time (redshifts z = 0–4) and of the coarsening length (0.6–20 h⁻¹ Mpc). The main result is the discovery of a polytropic relationship ℐ₁ ∝ ϱ^2–η between the velocity‐dispersion kinetic energy density of the coarsening cells, ℐ₁, and their mass density, ϱ. The exponent η, dependent on time and coarsening scale, is a compact measure of the deviations from the naive virial prediction η_virial = 0. This relationship supports the “polytropic assumption” which has been employed in theoretical models for the growth of cosmological structure by gravitational instability. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Gravitation und weitreichende schwache Wechselwirkungen bei Neutrino-Feldern Gedanken zu einer Theorie der solaren Neutrinos

The strange non-evidence of the solar-neutrino current by the experiments of DAVIS et al. postulates a fundamental revision of the theory of weak interactions and of its relations to gravitation theory. (We assume that the astrophysical stellar models are not completely wrong.) – Our paper is based on PAULI 's grand hypothesis about the connection between weak and gravitational interactions. According to PAULI and BLACKETT the (dimensionless) gravitation constant is the square of the (dimensionless) FERMI -interaction constant and according to the hypotheses of PAULI, DE BROGLIE , and JORDAN the RIEMANN -EINSTEIN gravitational metric g_ik is fusioned by the four independent WEYL ian neutrino fields (β-neutrinos and β-antineutrinos, μ-neutrinos and μ-antineutrinos). This fusion gives four reference tetrads h_i^A(x^l) as neutrino-current vectors, firstly. Then, the metric g_ik is defined by the equation g_ik = η_AB h_i^Ah_η^B according to EINSTEIN 's theory of tele-parallelism in RIEMANN ian space-times. The relation of the gravitation field theory to FERMI 's theory of weak interactions becomes evident in our reference-tetrads theory of gravitation (TREDER 1967, 1971). – According to this theory the coupling of the gravitation potential h_i^A with the matter T_ιⁱ is given by a potential-like (FERMI -like) interaction term. In this interaction term two WEYL spinor-fields are operating on the matter-tensor, simultanously. Therefore, the gravitation coupling constant is PAULI 's square of the FERMI -constant. Besides of the fusion of the RIEMANN -EINSTEIN metric g_ik by four WEYL spinors we are able to construct a conformal flat metric ĝ_ik = ϕ²η_ik by fusion from each two WEYL spinors. (This hypothesis is in connection with our interpretation of EINSTEIN 's hermitian field theory as a unified field-theory of the gravitational metric g_ik and a WEYL spinor field [TREDER 1972].) Moreover, from the reference-tetrads theory is resulting that the WEYL spinors in the “new metric” ĝ_ik are interacting with the DIRAC matter current by a FERMI -like interaction term and that these WEYL spinors fulfil a wave equation in the vacuum. Therefore, we have a long-range interaction with the radiced gravitational constant \documentclass{article}\pagestyle{empty}\begin{document}$ \sqrt {\frac{{tm^2 }}{{hc}}} $\end{document} as a coupling constant. That means, we have a long-range interaction which is 10¹⁸ times stronger than the gravitation interaction. – However, according to the algebraic structure of the conform-flat this long-range interaction is effective for the neutrino currents, only. And for these neutrinos the interaction is giving an EINSTEIN -like redshift of its frequences. The characteristic quantity of this “EINSTEIN shift” is a second gravitation radius â of each body: N = number of baryons, m = mass of a baryon.) This radius â is 10¹⁸ times larger than the EINSTEIN -SCHWARZSCHILD gravitation radius a = fM/c²: But, this big “weak radius” â has a meaning for the neutrinos, only.–The determination of the exterior and of the interior “metrics” ĝ_ik is given by an “ansatz” which is analogous to the ansatz for determination of strong gravitational fields in our tetrads theory. That is by an ansatz which includes the “self-absorption” of the field by the matter. For all celestial bodies the “weak radius” â is much greater than its geometrical dimension. Therefore, a total EINSTEIN redshift of the neutrino frequences v is resulting according to the geometrical meaning of our long-range weak interaction potential ĝ_ik = ϕ²η_ik. That means, the cosmic neutrino radiation becomes very weak and unable for nuclear reactions. Theoretically, our hypothesis means an ansatz for unitary theory of gravitation and of weak interaction. This unitary field theory is firstly based on EINSTEIN 's hermitian field theory and secondly based on our reference-tetrads theory of gravitation.     

Chemical processes in Triton's atmosphere and surface

Liquid solutions of N₂ containing up to one-third CH₄ can exist on Triton's surface in regions T > 62.5°K. More generally, subsurface oceans of N₂ solution are expected to be stable beneath overlying, thermally insulating, less dense layers of the abundant light hydrocarbon products of radiochemical synthesis: C₂H₆, C₃H₈, and C₄H₁₀. Cosmic rays are the main source of energy, capable of producing synthesis of organic compounds from N₂CH₄ solutions on the surface. For baseline Triton models with R = 2500 km, ϱ = 2.1 g cm⁻³, and T_s = 65 or 55°K, respectively, 4 × 10⁻³ or 7 × 10⁻³ erg cm⁻² sec⁻¹ (49 or 87% of the total incident flux) is deposited within a few meters below the surface. Using yields from laboratory experiments, we estimate the quantities of products produced: over 4.5 billion years, the cosmic ray flux alone produces 2 to 4 m of organic product, about half of which is C₂H₆. For ocean depths <250 m, C₂H₆ will reach its saturation limit and form a surface “slick.” For ocean depths <10 km, all of the other products also oversaturate and exsolve, adding to the surface slick and/or to a denser bottom sediment. Products produced from solid N₂CH₄ mixtures will accumulate as evaporite deposits because of the rapid volatile transport (of N₂ and CH₄) over Triton's surface. The complex, reddish organic solid found in laboratory simulations is probably the source of Triton's reddish color. Estimated yields over 4.5 billion years (for 7 × 10⁻³ erg cm⁻² sec⁻¹) are 190 (C₂H₆), 58 (NH₃), 17 (HCN), 3.5 (HN₃), 2.5 (C₄H₁₀), 0.35 (CH₃CN), and 0.14 (C₂H₅N₃) g cm⁻². More basic laboratory work on the low-temperature, low-pressure solvent properties and phase equilibria of N₂-hydrocarbon systems is clearly needed.     

Singularitäten in der Allgemeinen Relativitätstheorie

“Regular solutions of EINSTEIN 's equations” mean very different things. In the case of the empty-space equations, R_ik = 0, such solutions must be metrics g_ik(x^l) without additionaly singular “field sources” (EINSTEIN 's “Particle problem”). – However the “phenomenological matter” is defined by the EINSTEIN equations R_ik – 1/2g_ikR =–xT_ik itselves. Therefore if 10 regular functions g_ik(x^l) are given (which the inequalities of LORENTZ -signature fulfil) then these g_ik define 10 functions T_ik(x^l) without singularities. But, the matter-tensor T_ik must fulfil the two inequalities T ≥ 0, T ≥ 1/2 T only and therefore the EINSTEIN -equations with “phenomenological matter” mean the two inequalities R ≥ 0, R ≤ 0 which are incompatible with a permanently regular metric with LORENTZ -signature, generally.     

The Sun and the transcendental world of binaries

The theory of gravity says that a binary with orbital frequency ν should be a source of gravitational waves at the double frequency and higher harmonics. This implies that long-term exposure of an ensemble of binaries to gravity waves with frequency ν _G can result in (a) a lack of binaries with frequencies near frequency ν _G /2 and its higher harmonics (the effect of unstable orbits) and/or (b) an excess of binaries whose orbital frequencies are “absolutely” incommensurable with ν _G /2 and its higher harmonics (the effect of stable orbits). It is assumed that the stable-orbit frequencies are almost equal to multiples of πν _G /2 and ν _G /2π, where π plays the role of a “perfect” factor ensuring the best antiresonance of binaries. The statistical analysis of frequencies of 5774 Galactic close binary systems (CBSs) with periods P less than 10 days is based on calculating the resonance spectrum that indicates the best common multiple for a given set of frequencies with allowance for the factor π. The CBS distribution turns out to be modulated by the frequency ν _G = 104.4(5) μHz, and this effect is the most pronounced for superfast and compact rotators, such as cataclysmic variables (CVs) and related objects. The frequency ν _G is, within the error, equal to the “enigmatic” frequency ν₀ = 104.160(1) μHz com discovered earlier in the power spectra of the Sun and brightness variations of some extragalactic sources. This confirms the existence of a “coherent cosmic oscillation” of the Universe with frequency ν₀(ν _G ). The new astrophysical phenomenon naturally explains an “CV period gap” at frequencies ≈πν _G /3 (P ≈ 153 min) and maxima at the neighboring frequencies ≈πν _G /2 and ≈πν _G /4 (P ≈ 102 and ≈204 min, respectively). The remarkable and “mysterious” role of the transcendental number π for the world of binaries is emphasized, and the mystery of physical nature of the “universal” oscillation ν₀(ν _G ) is highlighted.     

The most resonant pulsation frequency of δ Scuti stars

Pulsation of the Sun with a period of P₀ ≈ 160 min discovered about two decades ago, is still waiting explanation. In view of the hypothesis about its cosmological origin, and attempting to find signature of this P₀ periodicity among other (short-period variable) stars, the pulsation frequencies of δ Sct stars are subjected to specific analysis. With a confidence level ≈ 3.8σ it is found that the frequency v₀ = P₀⁻¹ ≈ 104 m̈Hz, within the error limits, appears indeed to be the most “resonant” one for the total sample of 318 pulsating stars of δ Sct type (the most commensurable, or “synchronizing”, period for all these stars occurs to be 162 ± 4 min). We conjecture that a) the P₀ oscillation might be connected with periodic fluctuations of gravity field (metrics), and b) the primary excitation mechanism of pulsations of δ Sct stars, reffected by this “ubiquitous” P₀ resonance, must be attributed perhaps to superfast rotation of their inner cores (their rates tend to be in near-resonance with the “universal” v₀ frequency). The arguments are given favouring a cosmoogical nature of the P₀ oscillation.     

New concept for testing General Relativity: the Laser Astrometric Test Of Relativity (LATOR) mission

This paper discusses a Fundamental physics experiment that will test relativistic gravity at the accuracy better than the effects of the second order in the gravitational field strength, ∝ G². The Laser Astrometric Test Of Relativity (LATOR) mission uses laser interferometry between two micro‐spacecraft whose lines of sight pass close by the Sun to accurately measure deflection of light in the solar gravity. The key element of the experimental design is a redundant geometry optical truss provided by a long‐baseline (100 m) multi‐channel stellar optical interferometer placed on the International Space Station (ISS). The spatial interferometer is used for measuring the angles between the two spacecraft and for orbit determination purposes. In Euclidean geometry, determination of a triangle's three sides determines any angle therein; with gravity changing the optical lengths of sides passing close by the Sun and deflecting the light, the Euclidean relationships are overthrown. The geometric redundancy enables LATOR to measure the departure from Euclidean geometry caused by the solar gravity field to a very high accuracy. LATOR will not only improve the value of the parameterized post‐Newtonian (PPN) γ to unprecedented levels of accuracy of 1 part in 10⁸, it will also reach ability to measure effects of the next post‐Newtonian order (c⁻⁴) of light deflection resulting from gravity's intrinsic non‐linearity. The solar quadrupole moment parameter, J₂, will be measured with high precision, as well as a variety of other relativistic effects including Lense‐Thirring precession. LATOR will lead to very robust advances in the tests of Fundamental physics: this mission could discover a violation or extension of general relativity, or reveal the presence of an additional long range interaction in the physical law. There are no analogs to the LATOR experiment; it is unique and is a natural culmination of solar system gravity experiments. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A new limit on time dependence of the gravitational constant from gravity modified quantum electrodynamics

The time variation of the gravitational constantG is discussed in the light of the gravity modified form of quantum electrodynamics. From the experimental upper limit |a/| < 5 × 10^–15 yr^–1 on the time variation of the electromagnetic fine structure constant one finds |/G| < 5 × 10^–13 yr^–1.     

About Bianchi I with VSL

In this paper we study how to attack, through different techniques, a perfect fluid Bianchi I model with variable G,c and Λ, “but” taking into account the effects of a “c-variable” into the curvature tensor. We study the model under the assumption, div(T)=0. These tactics are: Lie groups method (LM), imposing a particular symmetry, self-similarity (SS), matter collineations (MC) and kinematical self-similarity (KSS). We compare both tactics since they are quite similar (symmetry principles). We arrive to the conclusion that the LM is too restrictive and brings us to get only the flat FRW solution. The SS, MC and KSS approaches bring us to obtain all the quantities depending on (∫ c(t)dt). Therefore, in order to study their behavior we impose some physical restrictions like for example the condition q<0 (accelerating universe). In this way we find that c is a growing time function and Λ is a decreasing time function whose sing depends on the equation of state ω, while the exponents of the scale factor must satisfy the conditions ∑ _i=1 ³ α _i =1 and ∑ _i=1 ³ α _i ² <1, ? ω, i.e. for all equation of state, relaxing in this way the Kasner conditions. The behavior of G depends on two parameters, the equation of state ω and ε, a parameter that controls the behavior of c(t), therefore G may be growing or decreasing. We also show that through the Lie method, there is no difference between to study the field equations under the assumption of a c-var affecting to the curvature tensor which the other one where it is not considered such effects. Nevertheless, it is essential to consider such effects in the cases studied under the SS, MC, and KSS hypotheses.     

The future evolution of white dwarf stars through baryon decay and time varying gravitational constant

Motivated by the possibility that the fundamental “constants” of nature could vary with time, this paper considers the long term evolution of white dwarf stars under the combined action of proton decay and variations in the gravitational constant. White dwarfs are thus used as a theoretical laboratory to study the effects of possible time variations, especially their implications for the future history of the universe. More specifically, we consider the gravitational constant G to vary according to the parametric relation G=G ₀(1+t/t _? )^?p , where the time scale t _? is the same order as the proton lifetime t _P . We then study the long term fate and evolution of white dwarf stars. This treatment begins when proton decay dominates the stellar luminosity, and ends when the star becomes optically thin to its internal radiation.     

The cosmic age crisis and the Hubble constant in a non-expanding universe

The present paper outlines a cosmological paradigm based upon Dirac’s large number hypothesis and continual creation of matter in a closed static (nonexpanding) universe. The cosmological redshift is caused by the tired-light phenomenon originally proposed by Zwicky. It is shown that the tired-light cosmology together with continual matter creation has a universal Hubble constant H ₀=(512π ²/3)^1/6(GC ₀)^1/3 fixed by the universal rate C ₀ of matter creation, where G is Newton’s gravitational constant. It is also shown that a closed static universe has a finite age τ ₀=(243π ⁵/8GC ₀)^1/3 also fixed by the universal rate of matter creation. The invariant relationship H ₀ τ ₀=3π ²6^1/2 shows that a closed static universe is much older (≈one trillion years) than any expanding universe model based upon Big-Bang cosmology. It is this property of a static universe that resolves any cosmic age crisis provided that galaxy formation in the universe is a continual recurring process. Application of Dirac’s large number hypothesis gives a matter creation rate C ₀=4.6×10^?48 gm?cm^?3?s^?1 depending only on the fundamental constants of nature. Hence, the model shows that a closed static universe has a Hubble constant H ₀=70 km?s^?1?Mpc^?1 in good agreement with recent astronomical determinations of H ₀. By using the above numerical value for H ₀ together with observational data for elongated cellular-wall structures containing superclusters of galaxies, it is shown that the elongated cellular-wall configurations observed in the real universe are at least one hundred billion years old. Application of the microscopic laws of physics to the large-scale macroscopic universe leads to a static eternal cosmos endowed with a matter-antimatter symmetry. It is proposed that the matter-antimatter asymmetry is continuously created by particle-antiparticle pair annihilation occurring in episodic cosmological gamma-ray bursts observed in the real universe.     

The seasonal variation of the newtonian constant of gravitation and its relationship with the “classical tests” of general relativity

The ratio between the Earth's perihelion advance (Δθ) _E and the solar gravitational red shift (GRS) (Δø _s e)a ₀/c ² has been rewritten using the assumption that the Newtonian constant of gravitationG varies seasonally and is given by the relationship, first found by Gasanalizade (1992b) for an aphelion-perihelion difference of (ΔG)_a?p . It is concluded that $$\begin{gathered} (\Delta \theta )_E = \frac{{3\pi }}{e}\frac{{(\Delta \phi _{sE} )_{A_0 } }}{{c^2 }}\frac{{(\Delta G)_{a - p} }}{{G_0 }} = 0.038388 \sec {\text{onds}} {\text{of}} {\text{arc}} {\text{per}} {\text{revolution,}} \hfill \\ \frac{{(\Delta G)_{a - p} }}{{G_0 }} = \frac{e}{{3\pi }}\frac{{(\Delta \theta )_E }}{{(\Delta \phi _{sE} )_{A_0 } /c^2 }} = 1.56116 \times 10^{ - 4} . \hfill \\ \end{gathered} $$ The results obtained here can be readily understood by using the Parametrized Post-Newtonian (PPN) formalism, which predicts an anisotropy in the “locally measured” value ofG, and without conflicting with the general relativity.