Calculation of the perihelion advance of planets in a field approach to gravitation

It is shown that, when taking into account the self-gravity of field energy of a gravitational field, one obtains a modified field equation for the intensity of gravitational field, the solution of which, when inserted in Kepler's problem, furnishes a formula for the perihelion precession of planets which (except of a fitting numerical factor) is identical with Einstein's. In Appendix 1 we point out the significance of an analogous equation in electrodynamics, and in Appendix 2 we shall try to construct a field model within the relativistic field theory which justifies the previous perihelion-shift calculation.     

A phenomenological model for the precession of planets and bending of light

We presented a phenomenological mode that attributes the precession of perihelion of planets to the relativistic correction. This modifies Newton’s equation by adding an inversely cube term with distance. The total energy of the new system is found to be the same as the Newtonian one. Moreover, we have deduced the deflection of light formula from Rutherford scattering. The relativistic term can be accounted for quantum correction of the gravitational potential and/or self energy of objects.     

Spectrophotometric variability of the magnetic CP star 56 Arietis in spectral region from 1950 to 3200 Å

We presented a phenomenological mode that attributes the precession of perihelion of planets to the relativistic correction. This modifies Newton’s equation by adding an inversely cube term with distance. The total energy of the new system is found to be the same as the Newtonian one. Moreover, we have deduced the deflection of light formula from Rutherford scattering. The relativistic term can be accounted for quantum correction of the gravitational potential and/or self energy of objects.     

Three classical tests of Hořava-Lifshitz gravity theory

Recently, a renormalizable gravity theory has been proposed by Hořava, and it might be an ultraviolet completion of general relativity or its infrared modification. Particular limit of the theory allows for the Minkowski vacuum. A spherical asymptotically flat black hole solution that represents the analogy of Schwarzschild solution of general relativity has been obtained. It will be very interesting to find the difference between traditional general relativity and Hořava-Lifshitz gravity theory. The three classical tests of general relativity including gravitational red-shift, perihelion precession of the planet Mercury, and light deflection in gravitational field in the spherical asymptotically flat black hole solution of infrared modified Hořava-Lifshitz gravity are investigated. The first order corrections from the standard general relativity is obtained. The result can be used to limit the parameters in Hořava-Lifshitz gravity and to show the viability of the theory.     

On a nonlinear and lorentz-invariant version of Newtonian gravitation — II

This paper gives a full nonlinear version of Newtonian gravity in which the gravitational energy acts as a source of the gravitational field. The generalized field equation for the scalar gravitational potential is solved for a spherically symmetric localized distribution of matter. It is shown that the perihelia of orbits of test particles in such a field precess steadily. The effect is, however, too small to account for the observed shift in the perihelion of planet Mercury. Further, the bending of light in this theory is zero. It is suggested that these inadequacies of the quasi-Newtonian framework call for more sophisticated approaches to gravity.     

Can observations inside the Solar System reveal the gravitational properties of the quantum vacuum?

The understanding of the gravitational properties of the quantum vacuum might be the next scientific revolution. It was recently proposed that the quantum vacuum contains the virtual gravitational dipoles; we argue that this hypothesis might be tested within the Solar System. The key point is that the quantum vacuum (“enriched” with the gravitational dipoles) induces a retrograde precession of the perihelion. It is obvious that this phenomenon might eventually be revealed by more accurate studies of orbits of planets and orbits of the artificial Earth satellites. However, we suggest that potentially the best “laboratory” for the study of the gravitational properties of the quantum vacuum is the recently discovered dwarf planet Eris with its satellite named Dysnomia; the distance of nearly 100 AU from the Sun makes it the unique system in which the precession of the perihelion of Dysnomia (around Eris) is strongly dominated by the quantum vacuum.     

五维Einstein-Wesson引力理论的几个结果

本文介绍五维广义相对论及Schwarzschild外部解,然后推导Schwarzschild内部解,最后着重采用五维引力理论计算水星近日点进动,光线在太阳附近的偏折,无线电信号延迟三个问题。结果表明,在现在实验条件下,五维理论对四维理论的修正是极其微小的,在与宇宙年龄相比拟情况下,两个理论的差别能显示出来。     

Exponential metric fields

The Laser Interferometer Space Antenna (LISA) mission will use advanced technologies to achieve its science goals: the direct detection of gravitational waves, the observation of signals from compact (small and dense) stars as they spiral into black holes, the study of the role of massive black holes in galaxy evolution, the search for gravitational wave emission from the early Universe. The gravitational red-shift, the advance of the perihelion of Mercury, deflection of light and the time delay of radar signals are the classical tests in the first order of General Relativity (GR). However, LISA can possibly test Einstein’s theories in the second order and perhaps, it will show some particular feature of non-linearity of gravitational interaction. In the present work we are seeking a method to construct theoretical templates that limit in the first order the tensorial structure of some metric fields, thus the non-linear terms are given by exponential functions of gravitational strength. The Newtonian limit obtained here, in the first order, is equivalent to GR.     

Possible relation between galactic flat rotational curves and the Pioneers’ anomalous acceleration

We consider a generic minimal modification of the Newtonian potential, that is a modification that introduces only one additional dimensional parameter. The modified potential depends on a function whose behavior for large and small distances can be fixed in order to obtain: (i) galactic flat rotational curves and (ii) a universal constant acceleration independent of the masses of the interacting bodies (Pioneer anomaly). Then using a dimensional argument we show that the Tully–Fisher relation for the maximal rotational velocity of spiral galaxies follows without any further assumptions. This result suggests that the Pioneer anomalous acceleration and the flat rotational curves of galaxies could have a common origin in a modified gravitational theory. The relation of these results with the Modified Newtonian Dynamics (MOND) is discussed.     

Perihel-Bewegung und kosmologische Singularität in TREDERS Gravitationstheorie

In the framework of TREDER 's gravitational theory we elaborate the consequences of a class of field equations for some solar-system effects and their connection to the problem of cosmological singularity. These equations read on special conditions with components of the energy momentum tensor, KRONECKER 's symbol, tetrad components). ω is a real parameter. If we choose the integration constants of the static spherically symmetric vacuum case in such a way that red shift is the same like that of EINSTEIN 's theory and the source of gravitational field is that of a point mass we obtain for the perihelion rotation the expression is EINSTEINS value of the perihelion rotation.) For we obtain But only if ω > 2/5 cosmological models exist which have no cosmological singularity. On the other hand for ω > 2/5 the value is greater than.     

Gravitation,global four-momentum conservation and the strong equivalence principle

It is shown that global four-momentum conservation provides all the necessary structure toderive a metric gravity theory which conforms to the requirements of the Strong Equivalence Principle (Will, 1981), and which satisfies all empirical tests up to, and including, those derived from the binary pulsar measurements. Significant consequences arising from this theory are: concepts of curved spacetimes become strictly superfluous to the function of describing gravitational physics; gravitational processes become direct particle/particle interactions; these interactions are arbitrated by wave processes of a kind familiar in electromagnetism; gravitational waves carry energy-momentum in the direction of their propogation vector; the essential singularities at gravitational origins, which are features of both Newtonian gravitation and General Relativity, do not exist.     

Angular momentum and gyroscope in flat space-time theory of gravitation

The study of a previously proposed theory of gravitation in flat space-time (Petry, 1981a) is continued. A conservation law for the angular momentum is derived. Additional to the usual form, there must be added a term coming from the spin of the gravitational field. The equations of motion and of spin angular momentum for a spinning test particle in a gravitational field are given. An approximation of the equations of the spin angular momentum in the rest frame of the test particle is studied. For a gyroscope in an orbit of a rotating massive body (e.g., the Earth) the precession of the spin axis agrees with the result of Einstein's general theory of relativity.     

Secular influence of change in the heliocentric gravitation constant <Emphasis Type="Italic">GM</Emphasis><Subscript>⊙</Subscript> on evolution of orbits of Meteor Streams

The Secular influence of the change in the heliocentric gravitational constant on the evolution of orbits of Meteor Streams is examined by using the method of celestial mechanics with variable mass and variable gravitational constant. The change in the heliocentric gravitational constant includes the combined changes in the sun’s mass and gravitational constant obtained from the modern observation of planets and spacecraft. The perturbation equations are solved by expanding series with mean anomaly. The solutions of the secular and periodic variation of orbital elements are derived. The theoretical results for the secular variables of the semi-major axes, solar distances at perihelion and orbital periods are given for three Meteor Streams: Dracorids, Quadrantids, and Ursids. The numerical results are shown in Table 2. The discussion and conclusion are drawn.     

Perihelion precession

By means of affine decomposition of oblique frame, a simple general formula is established which is convenient for calculating the precession of the perihelion point of a Keplerian ellipse under perturbation.     

Secular Post-NEWTONian Effects for the Restricted Three-Body Problem in TREDER'S Dynamics with Induced Inertia

In the framework of TREDER'S dynamics, in which according to the MACH -EINSTEIN -doctrin the inertial masses are induced by the gravitational interaction with the particles of the cosmos, we calculate the secular post-NEWTON ian effects for the restricted three-body problem. The dominant secular post-NEWTON ian variation of nodes and apsides is shown to be the same as in EINSTEIN'S theory of gravitation. The formulation of the gravodynamics in the HERTZ ian configuration space allows – as in General Relativity – the explanation of the effect as an “geodetic precession” of the lines of nodes and apsides.     

An explanation for long flares from extragalactic globular cluster X-ray sources

We compare orbits in a thin axisymmetric disc potential in Modified Newtonian Dynamics (MOND) with those in a thin disc plus near-spherical dark matter halo predicted by a ΛCDM cosmology. Remarkably, the amount of orbital precession in MOND is nearly identical to that which occurs in a mildly oblate CDM Galactic halo (potential flattening   q = 0.9  ), consistent with recent constraints from the Sagittarius stream. Since very flattened mass distributions in MOND produce rounder potentials than in standard Newtonian mechanics, we show that it will be very difficult to use the tidal debris from streams to distinguish between a MOND galaxy and a standard CDM galaxy with a mildly oblate halo.
If a galaxy can be found with either a prolate halo or one that is more oblate than   q ∼ 0.9  this would rule out MOND as a viable theory. Improved data from the leading arm of the Sagittarius dwarf – which samples the Galactic potential at large radii – could rule out MOND if the orbital pole precession can be determined to an accuracy of the order of  ±1°  .     

Helioseismic determination of the solar gravitational quadrupole moment

One of the most well-known tests of general relativity (GR) results from combining measurements of the anomalous precession of the orbit of Mercury with a determination of the gravitational quadrupole moment of the Sun J ₂. The latter can be done by inference from an integral relation between J ₂ and the solar internal rotation. New observational data of high quality obtained from the Solar Heliospheric Satellite ( SoHO ) and from the Global Oscillations Network Group (GONG) allow the determination of the internal rotation velocity of the Sun as a function of radius and latitude with unprecedented spatial resolution and accuracy. As a consequence, a number of global properties of the Sun can also be determined with much higher accuracy, notably the gravitational quadrupole moment of the Sun. The anomalous precession of the orbit of Mercury is primarily due to GR effects, but there are classical corrections, the largest of which is that due to J ₂. It is shown here that the data are currently consistent with the predictions of GR.     

Minimal Energy and Gravitation

Quantum theory in Robertson – Walker spacetime suggests the existence of a minimal energy ε of the order of 10⁻⁴⁵ erg. Reasonable forms for ε give the expansion factor R=R(t)(t= the cosmic time) with no need of gravitational field equations.Einstein's theory should be modified in gravitational fields of strength less than ε c/ħ ∼ 10⁻⁸ cm/s² where c is the speed of light and ħ is the reduced Planck constant. The cosmological term λ is expected to decrease as the universe expands.In the Appendix, ε is derived from a big bang – big crunch Newtonian cosmology.     

Dynamical effect of torsion in gravitaional field

In this paper we discuss the dynamical properties of a spinning body in a gravitational gauge theory containing torsion. Formulae are given for the precession of the Earth in the static spherically-symmetric field of the Sun and of the gyroscope. These formulae are valid for any model of gauge theory that includes torsion.