Simulation model for anomalous precession of the perihelion of mercury's orbit

The ‘anomalous perihelion precession’ of Mercury, announced by Le Verrier in 1859, was a highly controversial topic for more than half a century and invoked many alternative theories until 1916, when Einstein presented his theory of general relativity as an alternative theory of gravitation and showed perihelion precession to be one of its potential manifestations. As perihelion precession was a directly derived result of the full General Theory and not just the Equivalence Principle, Einstein viewed it as the most critical test of his theory. This paper presents the computed value of the anomalous perihelion precession of Mercury's orbit using a new relativistic simulation model that employs a simple transformation factor for mass and time, proposed in an earlier paper. This computed value compares well with the prediction of general relativity and is, also, in complete agreement with the observed value within its range of uncertainty. No general relativistic equations have been used for computing the results presented in this paper.     

Newtonian gravitational field theory: Two-body problem

The effects of a dual force which appears in a consistent field theory of Newtonian gravitation are explored by a study of the motion of two bodies which interact with each other through the gravitational field. The equations of motion are solved exactly. Among the results obtained, we find that the present theory formulated in accordance with the Special Theory of Relativity leads to the same analytical result for the precession of the perihelion of the orbit as does Einstein's General Theory of Relativity. Another result is that classical particles are endowed with an intrinsic angular momentum of constant magnitude—a helicity of classical origin. Other results, such as the period of revolution, are similar to Kepler's law, except for relativistic corrections. A slight deviation from the planar orbit of classical theory results, and may be observable. This deviation is related to the magnitude of the precession of the perihelion of the orbit. The significance of these results for charged particles, viewed classically or quantum mechanically, are discussed.     

The Effect of Dark Matter on Solar System and Perihelion Precession of Earth Planet

This paper visualizes effect of dark matter on solar system and especially perihelion precession of Earth planet. The relation between the rate of perihelion shift of Earth planet and dark matter are obtained.     

Relativistic perihelion precession of orbits of Venus and the Earth

Among all the theories proposed to explain the “anomalous” perihelion precession of Mercury’s orbit first announced in 1859 by Le Verrier, the general theory of relativity proposed by Einstein in November 1915 alone could calculate Mercury’s “anomalous” precession with the precision demanded by observational accuracy. Since Mercury’s precession was a directly derived result of the full general theory, it was viewed by Einstein as the most critical test of general relativity from amongst the three tests he proposed. With the advent of the space age, the level of observational accuracy has improved further and it is now possible to detect this precession for other planetary orbits of the solar system — viz., Venus and the Earth. This conclusively proved that the phenomenon of “anomalous” perihelion precession of planetary orbits is a relativistic effect. Our previous papers presented the mathematical model and the computed value of the relativistic perihelion precession of Mercury’s orbit using an alternate relativistic gravitational model, which is a remodeled form of Einstein’s relativity theories, and which retained only experimentally proven principles. In addition this model has the benefit of data from almost a century of relativity experimentation, including those that have become possible with the advent of the space age. Using this model, we present in this paper the computed values of the relativistic precession of Venus and the Earth, which compare well with the predictions of general relativity and are also in agreement with the observed values within the range of uncertainty.      

Quantum gravity, minimum length and Keplerian orbits

We conjecture that the modified commutation relations suggested in the context of quantum gravity (QG) persist also in the classical limit, if the momentum of the classical object is not too large, and calculate the corresponding perihelion precession rate for Keplerian orbits. The main result obtained in this Letter is not new. However the derivation is much simpler than the one proposed by Benczik et al. in [S. Benczik, L.N. Chang, D. Minic, N. Okamura, S. Rayyan, T. Takeuchi, Phys. Rev. D 66 (2002) 026003, arXiv:hep-th/0204049] where the corresponding precession rate was calculated for the first time. Our interpretation of the result is also quite different.     

对卫星近日点旋进现象的分析——"地球的扁率对卫星运动的影响"一文的疏忽

指出了一篇相关文献中的疏漏,讨论了卫星近日点的旋进现象,得出了在一般情况下卫星近日点旋进的快慢程度与近日点本身所处的位置有关的结论.     

On the significance of perihelion shift calculations

In this paper an attempt is made to resolve a confusion which exists in the literature over whether the perihelion precession of planetary orbits is a linear or non-linear effect. The problem is both one of physics and semantics.     

Cosmological black holes: A black hole in the Einstein-de Sitter universe

As an example of a dynamical cosmological black hole, a spacetime that describes an expanding black hole in the asymptotic background of the Einstein-de Sitter universe is constructed. The black hole is primordial in the sense that it forms ab initio with the big bang singularity and its expanding event horizon is represented by a conformal Killing horizon. The metric representing the black hole spacetime is obtained by applying a time dependent conformal transformation on the Schwarzschild metric, such that the result is an exact solution with a matter content described by a two-fluid source. Physical quantities such as the surface gravity and other effects like perihelion precession, light bending and circular orbits are studied in this spacetime and compared to their counterparts in the gravitational field of the isolated Schwarzschild black hole. No changes in the structure of null geodesics are recorded, but significant differences are obtained for timelike geodesics, particularly an increase in the perihelion precession and the non-existence of circular timelike orbits. The solution is expressed in the Newman-Penrose formalism.     

On the phenomenological three-graviton vertex

In General Relativity, the graviton interacts in three-graviton vertex with a tensor that is not the energy-momentum tensor of the gravitational field. We consider the possibility that the graviton interacts with the definite gravitational energy-momentum tensor that we previously found in the G ² approximation. This tensor in a gauge, where nonphysical degrees of freedom do not contribute, is remarkable, because it gives positive gravitational energy density for the Newtonian center in the same manner as the electromagnetic energy-momentum tensor does for the Coulomb center. We show that the assumed three-graviton vertex does not lead to contradiction with the precession of Mercury’s perihelion. In the S-matrix approach used here, the external gravitational field has only a subsidiary role, similar to the external field in quantum electrodynamics. This approach with the assumed vertex leads to the gravitational field that cannot be obtained from a consistent gravity equation.     

Regge calculus and observations. II. Further applications

The method, developed in an earlier paper, for tracing geodesies of particles and light rays through Regge calculus space-times, is applied to a number of problems in the Schwarzschild geometry. It is possible to obtain accurate predictions of light bending by taking sufficiently small Regge blocks. Calculations of perihelion precession, Thomas precession, and the distortion of a ball of fluid moving on a geodesic can also show good agreement with the analytic solution. However difficulties arise in obtaining accurate predictions for general orbits in these space-times. Applications to other problems in general relativity are discussed briefly.     

Calculation of the Precession of the Perihelion of Mercury’s Orbit Within the Framework of the Generalized Law of Universal Gravitation with Allowance for the Ellipticity of Planet Orbits

Russian Physics Journal - The precession of the perihelion of Mercury’s orbit is simulated numerically within the framework of the generalized law of universal gravitation in the field of the...     

Machian Mechanics with Isotropic Inertia

A nonrelativistic theory is discussed here which contains an interaction which produces isotropic inertia for anisotropic matter distributions. The interaction is a 4-body interaction and it is explained why it is necessary to have this type of interaction. The consequences of the theory are discussed for celestial mechanics including the predicted perihelion precession. Frame dragging effects are calculated and compared with other theories. Possible ways to extend the theory to noninstantaneous interactions are briefly discussed. This theory demonstrates that Mach's principle in the form considered here is not necessarily inconsistent with isotropic inertia.     

Gravitons and photons: The methodological unification of source theory

The phenomenological, nonspeculative attitude of source theory is used in parallel developments of electromagnetism and gravitation, based on the analogous properties of the massless particles, photon and graviton, thus providing a methodological unification of these two areas of physics. The power and economy of the approach is illustrated by an application to perihelion precession.This essay received the second award from the Gravity Research Foundation for the year 1975. (Editor)     

Quasi-periodic solutions and asymptotic properties for the nonlocal Boussinesq equation

We construct the Hirota bilinear form of the nonlocal Boussinesq(nlBq) equation with four arbitrary constants for the first time. It is special because one arbitrary constant appears with a bilinear operator together in a product form. A straightforward method is presented to construct quasiperiodic wave solutions of the nl Bq equation in terms of Riemann theta functions. Due to the specific dispersion relation of the nl Bq equation, relations among the characteristic parameters are nonlinear, then the linear method does not work for them. We adopt the perturbation method to solve the nonlinear relations among parameters in the form of series. In fact, the coefficients of the governing equations are also in series form.The quasiperiodic wave solutions and soliton solutions are given. The relations between the periodic wave solutions and the soliton solutions have also been established and the asymptotic behaviors of the quasiperiodic waves are analyzed by a limiting procedure.     

Exact Solution to Geodesic Motion Equation in the Braneworld Black Hole Spacetime and the Perihelion Precession of Mercury

The exact solution to geodesic equation in the braneworld black hole spacetime is found by method of Jacobian elliptic function, and the angle of perihelion precession is obtained by the zero point of Jacobian elliptic function for Mercury. Comparing numerical result with observation data, we give the value range of tidal charge.     

The two-body problem in Rosen's bimetric theory of gravitation

This is a continuation of a previous paper, in which the field equations in successive approximations and the post-Newtonian equations of motion in Rosen's theory of gravitation were derived. In this paper the energy integral and the center of mass for an insular system with an arbitrary structure are obtained in the post-Newtonian approximation. A many-body system is considered, and in the extreme case of point bodies (particles) the center-of-mass coordinates are found to be identical with the Einsteinian ones. The two-body problem is considered. For a system of two identical neutron stars of mass 1.3M (a possible model of the Hulse-Taylor binary pulsar system) the trajectory and the perihelion precession are calculated. It is found that the expressions obtained depend on the gravitational self-energy of the stars. The relations deduced from Rosen's bimetric gravitation in the case of small velocities and weak fields are compared with those of general relativity.In partial fulfillment of the requirements for Dr.Sc. degree at the Technion-Israel Institute of Technology.     

Nonlocal forces of inertia in cosmology

This paper reviews the origin of inertia according to Mach's principle and Weber's law of gravitation. The resulting theory is based on simultaneous nonlocal gravitational interactions between particles in the solar system and others in the remote universe beyond the Milky Way galaxy. It explains the precession of the perihelion of Mercury. A most important implication of the Mach-Weber theory of the force of inertia is the necessity for a large amount of uniformly distributed matter in the galactic universe. This matter could be the source of the cosmic background radiation. Nonlocal inertia forces are compatible with a static universe and also with an expanding universe but the latter would demand slow changes in the mass of particles and the gravitational constant.     

Energy spectrum of the dirac equation for the Scharzschild and Kerr fields

We consider the effect of relativistic corrections and rotation of the central body on the structure of the energy spectrum of a particle with spin in the Schwarzchild and Kerr fields. A splitting of levels is obtained, which corresponds to the classical shift of the perihelion of the orbit and precession of the plane of the gravitational spin-orbit interaction and several nonlinear spin effects are calculated.Translated from Izvestiya Vysshykh Uchebnykh Zavedenii, Fizika, No. 2, pp. 86–92, February, 1988.     

Long-range antigravity

We consider a theory in which fermionic matter interacts via longe-rage scalar, vector and tensor fields. In order not to be in conflict with experiment, the scalar and vector couplings for a given fermion must be equal, as is natural in a dimensionally reduced modell. Assuming that the Sun is not approximately neutral with respect to these new scalar-vector charges, and if the couplings saturate the experimental bounds, then their strength can be comparable to that of gravity. Scalar-vector fields of this strength can compensate for a solar quadropole moment contribution to Mercury's anomalous perihelion precession.