Perihelion Of Mercury Research Articles

The advance of Mercury’s perihelion

A very famous ‘test’ of the General Theory of Relativity (GTR) is the advance of Mercury’s perihelion (and of other planets too). To be more precise, this is not a prediction of General Relativity, since the anomaly was known in the 19th century, but no consistent explanation had been found yet at the time GTR was elaborated. Einstein came up with a solution to the problem in 1914. In the case of Mercury, the closest planet to the Sun, the effect is more pronounced than for other planets, and observed from Earth; there is an advance of the perihelion of Mercury of about 5550 arc seconds per century (as/cy). Among these, about 5000 are due to the equinox precession (the precise value is 5025.645 as/cy) and about 500 (531.54) to the influence of the external planets. The remaining, about 50 as/cy (42.56), are not understood within Newtonian mechanics. Here, we revisit the problem in some detail for a presentation at the undergraduate level.

An exact stationary axisymmetric vacuum solution within a metric-affine bumblebee gravity

Within the framework of the spontaneous Lorentz symmetry breaking (LSB), we consider a metric-affine generalization of the gravitational sector of the Standard Model Extension (SME), including the Lorentz-violating (LV) coefficients u and sμν . In this model, we derive the modified Einstein field equations in order to obtain a new axisymmetric vacuum spinning solution for a particular bumblebee's profile. Such a solution has the remarkable property of incorporating the effects of LSB through the LV dimensionless parameter X = ξb 2, with ξ is the nonminimal coupling constant, and b 2 = bμbμ , with bμ is the vacuum expectation value of the bumblebee field; as the LSB is turned off, X = 0, we recover the well-established result, the Kerr solution, as expected. Afterwards, we calculate the geodesics, the radial acceleration and thermodynamic quantities for this new metric. We also estimate an upper bound for X by using astrophysical data of the advance of Mercury's perihelion.

Precession of planets' orbits between Newtonian gravity and Einstein's general relativity

The recent result that, contrary to a longstanding conviction older than 160 years, the precession of Mercury perihelion can be achieved in Newtonian gravity with a very high precision by correctly analyzing the situation without neglecting Mercury's mass is confirmed. Orbit's precession does not occur in an inertial (in Newtonian sense) frame of reference, but it occurs in the non-inertial frame of reference of the Sun because in Newtonian theory, the distance which is travelled by a body depends on the frame of reference in which the motion of the body is analyzed. After reviewing a previous solution, the precession is directly obtained from the orbit equation in the non-inertial frame of reference of the Sun. The Newtonian formula of the precession of planets' perihelion breaks down for the other planets because the predicted Newtonian result is indeed too large for Venus and Earth. In a previous paper, it was shown that corrections due to gravitational and rotational time dilation, in an intermediate framework (a particular post-Newtonian approximation of general relativity) which analyzes gravity between Newton and Einstein, solve the problem in accordance with some other results in the literature. By adding such corrections, a result consistent with the one of general relativity was indeed obtained. Those corrections also are re-analyzed in this paper by stressing the difference between general relativity and Newtonian physics by evoking the Einstein Equivalence Principle, and the third postulate of relativity. This framework of gravity between Newton and Einstein seems consistent with global covariance. Finally, it is important to stress that a better understanding of gravitational effects in an intermediate framework between Newtonian theory and general relativity, which is one of the goals of this paper, could, in principle, be crucial for a better understanding of the famous Dark Matter and Dark Energy problems.

Assuming Photon as Extended Point Particle in the HyperSoft Topological Space and other Hypotheses: Issues and Trend Analysis

Following our preceding article, where we discussed alternative interpretations of the advanced perihelion of Mercury, the present article revisits the 1919 solar eclipse expedition led by Arthur Eddington, which famously provided the first observational confirmation of Einstein's theory of general relativity. We focus on the deflection of starlight data obtained during the eclipse, a cornerstone of this validation. Here, we explore three alternative explanations for the observed light bending that challenge the sole attribution to general relativity. Firstly, the paper begins by arguing based on criticisms raised by Tullio Levi-Civita, a contemporary mathematician, regarding Einstein's use of pseudo-tensors in his calculations. Levi-Civita argued that this approach introduced unnecessary complexity and obscured alternative interpretations of the data. Secondly, we delve into astrophysical phenomena that could mimic the observed light deflection, based on the varying speed of light, by assuming a photon has mass. (cf. ‘t Hooft et al., Light is Heavy). Moreover, in the literature, Molodtsov initiated soft set theory as an extension of fuzzy set theory to deal with uncertainties occurring in the natural and social sciences. It attracted the attention of mathematicians as well as social scientists due to its potential to unify certain mathematical aspects and applications in decision making processes; therefore, we shall discuss a bit how to model the photon as an extended massive particle of light, possibly related to such a soft set point [15, 16]. For further exploration, it is possible to assume the crystalline lattice of subvacuum structure (cf. Gremaud) as part of hypersoft topological spaces [16, 16a]. We strongly believe that the true strength of science lies in its continuous search for evidence and refinement of existing models. Therefore, it can be expected that new data can be helpful to reevaluate these matters, for instance, in the upcoming eclipse in the next month of 2024.

CAUSAL PHYSICS: CROSS-SECTIONAL AREA INSTEAD OF MASS

A review and analysis on the topic of mass and physical interaction within the framework of causal physics is presented. Mass is considered as a special case of a quantity that is proportional to the cross-sectional area of physical objects. Replacing the mass with this quantity allows further development of the kinetic theory of gravity by Le Sage. Physical interaction is considered as a result of mutual shielding of elementary mass–forming elements - nucleons and systems consisting of them - atomic nuclei in the path of movement of cosmic ether particles. It is shown that the applied approach makes it possible to create a visual and causal picture of physical interaction, both in the microcosm and in the macrocosm, leading to completely new results. The existence of gravitational shielding is substantiated, a visual picture of the mass defect is created, the presence of hidden mass in massive celestial bodies is revealed, the reason for the precession of the perihelion of Mercury and artificial Earth satellites is indicated, semi-daily behavior in the diurnal variation of gravity is described and interpreted, features in the manifestation of tidal processes are described. The applied approach allows to consider the issues of interaction in the micro and macrocosm from a single mechanism.

About the theory of relativity

It is shown that the Earth, the Sun and the stars are not inertial systems. The speed of movement of one inertial system relative to another does not affect the parameters of the moving system. Photons, electrons, protons, neutrons move in space in helical spirals. The equations of the special theory of relativity are not applicable to particles that have particle‑wave properties. It is shown that the fifth coordinate is needed for the curvature of the four‑dimensional space of general relativity. Therefore, gravity cannot be interpreted from the position of the curvature of a four‑dimensional space in a four‑dimensional space. In non‑inertial systems, the forces of inertia are not equivalent to the forces of gravity. Photons moving in space in helical spirals with huge rotational frequencies are stabilized in the direction of rectilinear motion. The gravitational field does not affect the energy of photons and the trajectory of their rectilinear motion. The deviation of the trajectory of stellar photons near the Sun is due to the effect of the atmospheric lens of the Sun. The atmospheres of stars absorb photon energy, which is recorded as a red shift in the radiation spectrum. The displacement of the perihelion of Mercury occurs due to the precession of the axis of Mercury’s orbit under the influence of the gravitational forces of the Sun.

On the Attribution of Mercury’s Perihelion Precession

Although Newtonian gravity and general relativity predicted the precession of Mercury perihelion historically, many improved methods continue to predict the precession of Mercury during recent decades of years. Uncertainties in various predictions and observations suggest that the attribution of Mercury’s precession is still not well understood. This paper argues that the cause of Mercury’s precession is not gravity, but the inertia of material motion left over from the formation of the solar system. According to this inertia theory, the planetary precession is associated with the ratio of total mass-energy density of the system to the mass-energy of the Sun and its change over time. If other factors are not changed with time, the perihelion precession of planets per orbit is proportional to his distance relative to the Sun. The conclusions of this paper can provide more effective factor considerations for the complete description of various astronomical events and phenomena using general relativity equations.

How to Decipher the Seegers-Tisserand-Gerber-Einstein Formula and the Soldner-Einstein Formula?

The famous Seegers-Tisserand-Gerber-Einstein Formula describing correctly the Mercury perihelion advance passed through hands of many scholars who tried to decipher the physical meaning of the perturbation factor Ω introduced by Carl Seegers in 1864. Based on the Gauss´s law for gravity we have newly interpreted this perturbation factor Ω as the active solid angle of the Solar gravitational field Ω = 3 steradians. We have inserted this model of the active solid angle of the Solar gravitational field the famous Soldner-Einstein Formula describing the light deflection in the vicinity of the Sun with 1 ≤ Ω ≤ 8. The enormous scatter of experimental data of the light deflections measured during the Solar eclipses was interpreted as the quantum jumps of the deflection angle with the quantum jump 0”.44. All known existing data on the light deflection taken during the last hundred years were depicted into the graphs. In some cases we have discovered these quantum jumps of the deflection angle during the individual runs of the Solar eclipse experiment. We propose to reanalyze all historical data taken for individual stars and to search for a hidden structure in these data. Moreover, we want to initiate new experimental activities for the coming Solar eclipses in order to collect more precise data that might guide us towards the model of quantum gravity.

Einstein–Besso Manuscript on the Perihelion Motion of Mercury Sold for Record Amount

AbstractIn 1913, Albert Einstein and Michele Besso tried to explain the anomalous advance of Mercury's perihelion on the basis of the precursor theory of general relativity. A manuscript bundle documents their work. This manuscript was recently auctioned for a record amount. The paper gives a brief discussion of the significance and history of this manuscript.

On planetary orbits in entropic gravity

Starting with an entropy that includes volumetric, area and length terms as well as logarithmic contributions, we derive the corresponding modified Newtonian gravity and derive the expression for planetary orbits. We calculate the shift of the perihelion of Mercury to find bounds to the parameters associated to the modified Newtonian gravity. We compare the parameter associated to the volumetric contribution in the entropy-area relationship with the value derived for galactic rotation curves and the value obtained from the cosmological constant.

The phenomenology of the quantum-corrected gravitational force

The Newtonian gravitational force can be derived from the Heisenberg uncertainty principle. In the realm of high-energy physics, it is necessary to replace the standard uncertainty principle by the generalized uncertainty principle (GUP). The generalized uncertainty principle can provide some corrections into the gravitational force. In this paper, we have applied the GUP to modify the gravitational force. The modified gravitational force has been applied to find the GUP corrections into Binet's equation. The modified Binet's equation has been used to study the advance of the perihelion of Mercury. It is shown that the GUP may provide the precession of Mercury's perihelion in the context of Newtonian physics. The modified gravitational force can also be applied to find the modified Friedmann equation in which the correction terms may play the role of dark energy to provide an accelerating universe.

Modified black hole solution with a background Kalb\u2013Ramond field

We study the gravitation effects on a static and spherically symmetric spacetime due to the vacuum expectation value (VEV) of a Kalb–Ramond field. The Kalb–Ramond VEV is a background tensor field which produces a local Lorentz symmetry breaking (LSB) of spacetime. Considering a non-minimal coupling between the Kalb–Ramond (VEV) and the Ricci tensor, we obtain an exact parameterdependent power-law modified black hole. For a particular choice of the LSB parameter, the Lorentz violation produces a solution similar to the Reissner–Nordstrom, despite the absence of charge. The near-horizon geometry is modified by including a new inner horizon and shifting the Schwarzschild horizon. Asymptotically, the usual Minkowski spacetime with a background tensor field is recovered. The vacuum configurations are studied considering the energy conditions and the Lorentz violating source properties. By means of the mercury perihelion test, an upper bound to the local Lorentz violation (LV) is obtained, and its corresponding effects on the black hole temperature is investigated.

Simulating general relativity and non-commutative geometry by non-paraxial quantum fluids

We show that quantum fluids enable experimental analogs of relativistic orbital precession in the presence of non-paraxial effects. The analysis is performed by the hydrodynamic limit of the Schrödinger equation. The non-commutating variables in the phase-space produce a precession and an acceleration of the orbital motion. The precession of the orbit is formally identical to the famous orbital precession of the perihelion of Mercury used by Einstein to validate the corrections of general relativity to Newton’s theory. In our case, the corrections are due to the modified uncertainty principle. The results may enable novel relativistic analogs in the laboratory, also including sub-Planckian phenomenology.

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

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 Sun and planets taking into account the ellipticity of the planet orbits and new data on the flattening, the mass of the Sun, and the gravitational constant. Calculations were carried out with increased accuracy (up to 19–20 decimal places) and iteration steps of 0.00005 s and 0.0001 s starting from the asteroid belt. It has been shown that the average precession of the perihelion of Mercury’s orbit in 100 years calculated within the framework of the generalized law of universal gravitation and averaged over long time periods from several hundred years to several thousand years taking into account the ellipticity of planet orbits is ~554.2”. This is less than the observed shift of the perihelion of Mercury’s orbit by ~19.9”. As is well known, the observed shift is ~574.1”. That is, the question on the adequacy of the generalized law of universal gravitation to the observances still remains open. However, it is possible that an object of small size (or several such objects) may be located inside Mercury’s orbit, and one more object, whose mass should not exceed at least ~0.2 of the Earth mass may be located at the diametrically opposite point of the Earth orbit behind the Sun. The results obtained are valid to within 1–2 decimal places.

Yukawa Potential Orbital Energy: Its Relation to Orbital Mean Motion as well to the Graviton Mediating the Interaction in Celestial Bodies

Research on gravitational theories involves several contemporary modified models that predict the existence of a non-Newtonian Yukawa-type correction to the classical gravitational potential. In this paper we consider a Yukawa potential and we calculate the time rate of change of the orbital energy as a function of the orbital mean motion for circular and elliptical orbits. In both cases we find that there is a logarithmic dependence of the orbital energy on the mean motion. Using that, we derive an expression for the mean motion as a function of the Yukawa orbital energy, as well as specific Yukawa potential parameters. Furthermore, various special cases are examined. Lastly, expressions for the Yukawa range λ and coupling constant α are also derived. Finally, an expression for the mass of the graviton mgr mediating the interaction is calculated using the expression its Compton wavelength (i.e., the potential range λ). Numerical estimates for the mass of the graviton mediating the interaction are finally obtained at various eccentricity values and in particular at the perihelion and aphelion points of Mercury’s orbit around the sun.

Theory of The Three Fields of Space


 This article is a logical and rational analysis of the physical phenomena produced by the three fields that are generated in space: gravity field; field of terrestrial nuclear magnetism; and orbital field.
 Eduardo Guimarães, through the studies of the three nuclear masses of the Sun's nucleus, the three nuclear masses of the moon's nucleus, and the three nuclear masses of the Earth's nucleus.
 We discover the three spatial fields that are generated in the solar system and in the planets.
 Then, from the general theory of the three fields of space, we can understand all the mechanics that generate the dynamics and kinematics of celestial bodies.
 So now we can understand why the smaller celestial bodies orbit the orbital field of the largest celestial bodies.
 So now we can understand why the planets produce orbits of elliptical motions, around the orbital field of the Sun.
 Then we understand the orbital mechanics of the little planet Mercury, and its abnormal orbit around the orbiting field of the Sun.
 Then Mercury has a perihelion precession of 2 degrees per century, due to an approximation of the perihelion of Mercury which is attracted by the micro-gravity of the Sun, generating an orbital deviation of 2 degrees per century.
 In the future the planet Mercury will lose energy from its nucleus and will not be able to make the orbital curve of the perihelion because it will have been attracted by the gravitational field of the Sun's nucleus.
 The fall of Mercury on the Sun will generate two thermonuclear explosions of SUPERNOVA.
 The first thermonuclear explosion of SUPERNOVA will be generated by the thermonuclear collision of the gravity mass attraction of Mercury debris with the Sun's nucleus.
 The second thermonuclear explosion of SUPERNOVA will be generated by the thermonuclear collision of attraction of the mass of orbital attraction of Mercury debris with the nucleus of the Sun.
 These two thermonuclear explosions of SUPERNOVA will generate two immense thermonuclear shockwaves that will devastate the entire fragile geo-biome of the solar system.
 

Concerning the Paper by A. Einstein “Explanation of the Perihelion Motion of Mercury from the General Theory of Relativity”

It is shown that in A. Einstein’s 1915 paper “Explanation of the perihelion motion of Mercury from the general theory of relativity” an error was actually incurred in the integration of the equation $$ \phi =\left[1+\upalpha \left({\upalpha}_1+{\upalpha}_2\right)\right]\underset{\upalpha_1}{\overset{\upalpha_2}{\int }}\frac{dx}{\sqrt{-\left(x-{\upalpha}_1\right)\left(x-{\upalpha}_2\right)\left(1-\upalpha x\right)}} $$ , and in the result instead of $$ \phi \approx \uppi \left[1+\frac{5}{4}\upalpha \left({\upalpha}_1+{\upalpha}_2\right)\right] $$ (if we limit ourselves to first-order terms in the small quantity (α1 + α2)) the value $$ \phi \approx \uppi \left[1+\frac{3}{4}\upalpha \left({\upalpha}_1+{\upalpha}_2\right)\right] $$ was obtained, where α1 and α2 are the inverse values of the maximum and minimum distances of Mercury from the Sun, $$ \upalpha =\frac{2G{m}_0}{c^2} $$ is the gravitational radius, G is the gravitational constant, m0 is the mass of the Sun, c is the velocity of light (i.e., the Chinese mathematician Hua Di was actually right). And, as a result, for the precession of the orbit of Mercury in the gravitational field of a spherical Sun in the general theory of relativity (after 100 years) one obtains not ~43”, as A. Einstein obtained, but ~71.63”. Exactly this latter result is obtained by direct numerical modeling of the precession of the perihelion of Mercury’s orbit in the gravitational field of the Sun within the framework of the general theory of relativity if the fitting coefficient α in the equation of motion of Mercury (not to be confused with α in the above equations) is set equal to zero. The result $$ \phi \approx \uppi \left[1+\frac{3}{4}\upalpha \left({\upalpha}_1+{\upalpha}_2\right)\right] $$ , obtained by A. Einstein if it is obtained, happens only upon integration of either the equation $$ \phi =\left[1+\frac{\upalpha}{2}\left({\upalpha}_1+{\upalpha}_2\right)\right]\underset{\upalpha_1}{\overset{\upalpha_2}{\int }}\frac{dx}{\sqrt{-\left(x-{\upalpha}_1\right)\left(x-{\upalpha}_2\right)\left(1-\upalpha x\right)}} $$ (if we also limit ourselves to first-order terms in the small quantity (α1 + α2)), i.e., in front of the integral in brackets the coefficient 1/2 should stand in front of the quantity α, or the equation $$ \phi =\left[1+\upalpha \left({\upalpha}_1+{\upalpha}_2\right)\right]\underset{\upalpha_1}{\overset{\upalpha_2}{\int }}\frac{dx}{\sqrt{-\left(x-{\upalpha}_1\right)\left(x-{\upalpha}_2\right)\left(1-\upalpha x\right)}} $$ (if we also limit ourselves to first-order terms in the small quantity (α1 + α2)), i.e., in the denominator under the differential in the integral, inside the square root\ a plus sign should stand in front of the quantity αx.

Kozai–Lidov Resonant Behavior Among Atira-class Asteroids

Atira-class asteroids have aphelia greater than 0.718 au and smaller than 0.983 au. It has been found that the orbits of many of them remain relatively stable for at least 1 Myr, but it is unclear what can make them so stable when they cross the orbit of Venus and some may reach, in heliocentric terms, as far as Earth's perihelion and as close as inside Mercury's perihelion. The analysis of their orbits shows that many of them have values of the argument of perihelion close to 0 or 180 degrees. Such an orbital arrangement means that the nodes are located at perihelion and at aphelion, i.e. for many known Atiras, away from the path of Venus. Here, we show that the orbits of some Atiras are strongly affected by the Kozai-Lidov resonance, which translates into enhanced long-term stability.

A Study of Redundancy of Time Dilation in Theory of Relativity

Objectives: In this Paper a generic approach of ISM band channel scanner design module is proposed to identify available free white spaces to utilize under secondary communication network. Method/Analysis: The feature of opportunistic spectrum access (OSA) is to identify free channel to deployment purpose, the channel is compared on the basis of RSSI level individually amongst total available channel were in normally 80% channel are mostly vacant due to dominating nature of channel. The output of the OSA based ISM band channel brings a free channel identification and noise free path to continue communication in between other ISP. Findings: The result indicates that the available channels are having bunch of availability of total 14 no of channels in general. In which channel no 1-6 and 11 are comes under high dominating index ratio. The channel always forcing every new SSID/service provider to accommodate in between these three channels only; due to this a normal channel Co-channel conjunction/Interference occurs in crowed area. This may lead to call/request lost data packets in bulk! As a result users always share more data beyond a normal, causing more power consumption/ battery in cell phone/laptop. So for channel identification OSA technique is implemented which is actually determines dynamic spectrum access by comparing received power in –dB on -90dB to -20dB range were on results comparison above -50dB range signal is mostly having week strength/the origin of base channel is on far distance to other nearby channels. Once the low signal channel or non operational channel is detected it effectively deployed for secondary user network communication. Novelty/Improvements: In this novel design, portable OSA channel estimator-indicator is actively scanned in real time in live data fields; in future it helps to bi-pass the used channel to remove interference. Keywords: Bending of Light, Caesium Atomic Clock, Perihelion of Mercury, Shapiro Delay, Space-time Fabric, Time Dilation, Theory of Relativity

Free fall in gravitational theory

Einstein's explanation of Mercury's perihelion motion has been verified by astronomical observations. His formula could also be obtained in Schwarzschild metric and was published already in 1898. Motion along a straight geodesic, however, namely, free fall into a gravitational center with vanishing angular momentum, is incorrectly described both by Einstein's and by Schwarzschild's equation of motion. A physical solution for free fall may be obtained by taking into account the dependence of mass on velocity in Newton's gravitational law as adopted in the physics of accelerators.