Planetary Precession Research Articles

Relativistic periastron advance beyond Einstein theory: analytical solution with applications

We find a new solution to calculate the orbital periastron advance of a test body subject to a central gravitational force field for relativistic theories and models beyond Einstein. This analitycal formula has general validity that includes all the post-Newtonian (PN) contributions to the dynamics and is useful for high-precision gravitational tests. The solution is directly applicable to corrective potentials of various forms, without the need for numerical integration. Later, we apply it to the scalar tensor fourth order gravity (STFOG) and noncommutative geometry, providing corrections to the Newtonian potential of Yukawa-like form V(r)=αe-βrr\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$V(r)=\\alpha \\frac{e^{-\\beta r}}{r}$$\\end{document}, and we conduct the first analysis involving all the PN terms for these theories. The same work is performed with a Schwarzschild geometry perturbed by a Quintessence Field, leading to a power-law potential V(r)=αqrq\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$V(r)=\\alpha _q {r}^q$$\\end{document}. Finally, by using astrometric data of the Solar System planetary precessions and those of the S2 star around Sgr A*, we infer new theoretical constraints and improvements in the bounds for β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta $$\\end{document}. The resulting simulated orbits turn out to be compatible with general relativity.

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.

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.

Photon Theory of Gravity – An Advance from Einstein’s Relativity

Based on a postulate that photons of low frequencies (undetectable by current technology) are the gravity force carrier, the paper derives quantitative results that are the same as or very similar to those derived in the special and general relativity theories and explains experiments and observations better. These quantitative results include the mass-energy formula, the energy momentum equation, and those for relative mass, the transverse Doppler effect, gravitational red shift, planetary precession, the deflection angle of light in gravitational lensing, the orbits around a black hole, and the strength and direction of gravitational waves (orbit decay of pulsars). Moreover, the explanations are different from those in Einstein’s relativity theory, such as the explanation of the null Doppler effect of electromagnetic waves reflected from a transversely moving surface, the reason for gravitational red shift, and the size of the light sphere around a black hole. The paper claims that both the high-order Doppler effect and the gravitational red shift occur only at the point of photon emission. The paper also explains why the predicted pulsar orbit decay is close but differs from calculations based on observations.

Gravitational fields and gravitational waves

The relative velocity between objects with finite velocity affects the reaction between them. This effect is known as general Doppler effect. The Laser Interferometer Gravitational-Wave Observatory (LIGO) discovered gravitational waves and found their speed to be equal to the speed of light c. Gravitational waves are generated following a disturbance in the gravitational field; they affect the gravitational force on an object. Just as light waves are subject to the Doppler effect, so are gravitational waves. This article explores the following research questions concerning gravitational waves: Is there a linear relationship between gravity and velocity? Can the speed of a gravitational wave represent the speed of the gravitational field (the speed of the action of the gravitational field upon the object)? What is the speed of the gravitational field? What is the spatial distribution of gravitational waves? Do gravitational waves caused by the revolution of the Sun affect planetary precession? Can we modify Newton's gravitational equation through the influence of gravitational waves?

Precession shift in curvature based extended theories of gravity and quintessence fields

In this paper we constrain the sizes of hypothetical new weak forces by making use the data coming from the precession of Planets. We consider the weak field approximation of Scalar–Tensor Fourth Order Gravity (STFOG), which include several models of modified gravity. The form of the corrections to the Newtonian potential if of the form of Yukawa-like potential (5th force), i.e. V(r)=alpha frac{e^{-beta r}}{r}, where alpha is the parameter related to the strength of the potential, and beta to the range of the force. The present data on periastron advance allow to infer a constraint on the free parameter of the gravitational models. Moreover, the Non-commutative Spectral Gravity (NCSG) is also studied, being a particular case STFOG. Here we show that the precession shift of Planet allows to improve the bounds on parameter beta by several orders of magnitude. Finally such an analysis is studied to the case of power-like potential, referring in particular to deformation of the Schwarzschild geometry induced by a quintessence field, responsible of the present accelerated phase of the Universe.

Ultralight dark matter: constraints from gravitational waves and other astrophysical observations

The orbital period loss of the compact binary systems is the first indirect evidence of gravitational waves which agrees well with Einstein’s general theory of relativity to a very good accuracy. However, there is less than one percent uncertainty in the measurement of orbital period loss from the general reltivistic prediction. Perihelion precession of planets, Gravitational light bending and Shapiro delay are three other successful tests of general relativity theory. Though there are uncertainties in the measurements of those observations from the general reltivistic predictions as well. To resolve these uncertainties, we assume radiation of ultralight axions and light gauge boson particles of L i – Lj type from those systems which can be a possible candidate of fuzzy dark matter. In this article, we obtain bounds on new physics parameters from those astrophysical observations.

Constraints on long range force from perihelion precession of planets in a gauged L_e-L_{mu ,tau } scenario

The standard model leptons can be gauged in an anomaly free way by three possible gauge symmetries namely {L_e-L_mu }, {L_e-L_tau }, and {L_mu -L_tau }. Of these, {L_e-L_mu } and {L_e-L_tau } forces can mediate between the Sun and the planets and change the perihelion precession of planetary orbits. It is well known that a deviation from the 1/r^2 Newtonian force can give rise to a perihelion advancement in the planetary orbit, for instance, as in the well known case of Einstein’s gravity (GR) which was tested from the observation of the perihelion advancement of the Mercury. We consider the long range Yukawa potential which arises between the Sun and the planets if the mass of the gauge boson is M_{Z^{prime }}le mathcal {O}(10^{-19})mathrm {eV}. We derive the formula of perihelion advancement for Yukawa type fifth force due to the mediation of such U(1)_{L_e-L_{mu ,tau }} gauge bosons. The perihelion advancement for Yukawa potential is proportional to the square of the semi major axis of the orbit for small M_{Z^{prime }}, unlike GR where it is largest for the nearest planet. For higher values of M_{Z^{prime }}, an exponential suppression of the perihelion advancement occurs. We take the observational limits for all planets for which the perihelion advancement is measured and we obtain the upper bound on the gauge boson coupling g for all the planets. The Mars gives the stronger bound on g for the mass range le 10^{-19}mathrm {eV} and we obtain the exclusion plot. This mass range of gauge boson can be a possible candidate of fuzzy dark matter whose effect can therefore be observed in the precession measurement of the planetary orbits.

Extended gravitoelectromagnetism. II. Metric perturbation

This article makes the connection between the new gravitoelectromagnetic theory presented in the part I paper and general gravity in its weak formulation. The perturbation in the metric tensor is obtained in terms of the flat-space total energy–momentum tensor given by the sum of the consistent fully relativistic fluid and gravitoelectromagnetic field contributions. Expressions for the perturbed metric in the internal (fluid) and external (vacuum) regions are given in terms of the fluid and field variables. This formulation of gravitoelectromagnetism is compatible with the formation of gravitational waves. The geodesic equation is obtained in both the internal and external regions, including new terms neglected in the standard gravitomagnetic formulation. It is shown that the new terms reproduce the anomalous shift of planetary precession, which results from a balance between the gravitoelectric and gravitomagnetic forces.

Constraints on fifth forces through perihelion precession of planets

The equivalence principle is important in fundamental physics. The fifth force, as a describing formalism of the equivalence principle, may indicate the property of an unknown theory. Dark matter is one of the most mysterious objects in the current natural science. It is interesting to constrain the fifth force of dark matter. We propose a new method to use perihelion precession of planets to constrain the long-range fifth force of dark matter. Due to the high accuracy of perihelion precession observation, and the large difference of matter composition between the Sun and planets, we get one of the strongest constraints on the fifth force of dark matter. In the near future, the BepiColombo mission will be capable to improve the test by another factor of ten.

The gyroscopic frequency of metric f(R) and generalised Brans–Dicke theories: constraints from Gravity Probe–B

We confront the predicted gyroscopic precession (in particular the geodetic precession) from metric $f(R)$ theory with the data provided by the mission, Gravity Probe--B. We find the constraint, $|a_2| < 1.33\times 10^{12} \mathrm{m}^2$, where $a_2$ is the coefficient assessing the strength of the lowest order correction to the Einstein--Hilbert action for a metric $f(R)$ theory with $f$ analytic. This constraint improves over astrophysical bounds provided by massive black holes and planetary precession which are $|a_2|\gtrsim 10^{17} \mathrm{m}^2$ and $|a_2|\lesssim 1.2\times10^{18} \mathrm{m}^2$ respectively and it is complementary to the stringent ones provided by lab based experiments, like the E\"ot--Wash experiment. We also investigate the modification of our result for gyroscopic precession if the oblateness of Earth is taken into account by considering the quadrupole moment of Earth. Finally, we provide a generalisation of our result for the gyroscopic precession in the context of Brans--Dicke theories with a potential (recovering the previously derived results in the appropriate limits).

Calculation of the Uncertainties in the Planetary Precessions with the Recent EPM2017 Ephemerides and their Use in Fundamental Physics and Beyond

Abstract I tentatively compile the formal uncertainties in the secular rates of change of the orbital elements a, e, I, Ω, and ϖ of the planets of the solar system from the recently released formal errors in a and the nonsingular elements h, k, p, and q estimated for the same bodies with the EPM2017 ephemerides by E. V. Pitjeva and N. P. Pitjev. The highest accuracies occur for the inner planets and Saturn in view of the extensive use of radiotechnical data collected over the last decades. For the inclination I, node Ω and perihelion ϖ of Mercury and Mars, I obtain accuracies , while for Saturn they are . As far as the semimajor axis a is concerned, its rates for the inner planets are accurate to the level, while for Saturn I obtain . In terms of the parameterized post-Newtonian (PPN) parameters β and γ, a formal error as little as for the Hermean apsidal rate corresponds to a ≃2 × 10−7 bias in the combination parameterizing the Schwarzschild-type periehlion precession of Mercury. The realistic uncertainties of the planetary precessions may be up to one order of magnitude larger. I discuss their potential multiple uses in fundamental physics, astronomy, and planetology.

Unification of Newtonian Physics with Einstein Relativity Theory by using Generalized Metrics of Complex Spacetime and application to the Motions of Planets and Stars, eliminating Dark Matter

In this paper we unify Theories of Physics (TPs) with real or infinite Universal Speed (cI), such as Einstein Relativity Theory (ERT) and Newtonian Physics (NPs). Generalized Special Relativity (SR) relates the frames of Relativistic Inertial observers (RIOs) where the spacetime has the metric gI=diag(gI00, gI11, gI11, gI11). The parameter ξI=sqrt(-gI11/gI00) is contained in the matrix (ΛI) of the Euclidean Closed Linear Transformation of complex spacetime (ECLSTT). Besides the elements of ΛI are complex numbers. So, the corresponding spacetime is necessarily complex and there exists real cI=c/ξI. In addition, the complex Cartesian Coordinates (CCs) of the theory, may be turned to the corresponding real CCs, in order to be perceived by human senses. The new real transformation is not closed (the corresponding real matrices ΛIR do not form a group) and the successive real transformations produce Generalized Thomas Rotation. The specific value ξI=1 gives Vossos transformation (VT) endowed with Lorentz metric (for gI11=1) of complex spacetime and invariant speed of light in vacuum (cI=c), which produce the Lorentzian version of Euclidean Complex Relativistic Mechanics (ECRMs). The corresponding real matrix (ΛIR) is the matrix of Lorentz Boost (ΛIR=ΛL). The specific value ξI→0 gives Galilean Transformation (GT) with invariant time, in which any other ECLSTT is reduced, if one RIO has small velocity wrt another RIO. Thus we unify TPs such as NPs and ERT, keeping the formalism of ERT. The generalized definition of Proper Time (r) gives us the possibility to compute four-velocity, four-momentum, Relativistic Doppler Shift etc, building the whole structure of the Generalized SR and General Relativity (GR). For instance the Generalized Relativistic Energy of Rest Mass (m) is Erest=mc2/ξI2. In case of NPs, the annihilation energy becomes infinite. Thus the Lomonosov-Lavoisier Law becomes clear theorem of NPs. In addition, the case of observers with variable metric of spacetime leads to GR. Thus we produce the 1st Generalized Schwarzschild metric (1GSM) and 2nd Generalized Schwarzschild metric (2GSM), which are in accordance with Einstein field equations for any TPs. In case of 1GSM, we compute the corresponding Lagrangian, geodesics, equations of motion, precession of planets’ orbits etc, resulting formulas which are referred to any TPs. We then combine the theoretical results to the experimental data of our Solar system, producing a set of valid values of ξI. In case of 2GSM, the combination of its Galilean version with Modified Newtonian Dynamics (MOND), leads to MOND relativization. After, we pass to RIOs with ordinary flat spacetime (Minkowski space), extending MOND methods to ERT. We use Simple and Standard Interpolating Function (μ) to the Lorentzian-Einsteinian version of 2GSM for the explanation of Rotation Curves in Galaxies as well as the Solar system, eliminating Dark Matter. Generally, this approach, in non rotating black hole, planetary and star system scale, coincides to the original Schwarzschild metric, while in galactic scale, it gives MONDian results. In universal scale, the gravitational field strength becomes negative, producing slight antigravity.

GTR component of planetary precession

Even as the theory of relativity is more than a hundred years old, it is not within easy reach of undergraduate students. These students have an insatiable urge to learn more about it even if the full machinery of the tools required to study the same is not within their comfortable reach. The recent detection of gravitational waves has only augmented their enthusiasm about the General Theory of Relativity (GTR), developed just over a hundred years now, encapsulated in Einstein’s Field Equations. The GTR provided a consistent formulation of the theory of gravity, removed the anomalies in the Newtonian model, and predicted spectacular natural phenomena which eventual experiments have testified to. This pedagogical article retraces some of the major milestones that led to the GTR and presents a simple numerical simulation of the GTR advance of the perihelion of planetary motion about the sun.

Influence of Yukawa-type additions to a Newtonian gravitational potential on the perihelion precession of bodies in the solar system

The results of theoretical studies of the influence of Yukawa-type additions to a Newtonian gravitational potential on the perihelion precession of bodies in the solar system are presented. An expression for the precession angle due to such additions is obtained. It is shown that, with certain relationships between the parameters in the Yukawa potential, their contribution to the perihelion precession of the trans-Neptunian objects 2000 OO67, 2006 SQ372, 2009 FW54, 2013 BL76, and 2003 VB12 is of order 0.01″ over the period, exceeding the contribution of general relativistic terms by at least an order of magnitude. The fundamental possibility of perihelion precession of these trans-Neptunian objects in the retrograde direction is established. Observational data on the precession of planets in the solar system are used to place constraints on the parameters of the added Yukawa potential.

Anomalous precession of planets for a Weyl conformastatic solution

In this paper, we investigate the anomalous planets precession in the nearly-newtonian gravitational regime. This limit is obtained from the application of the slow motion condition to the geodesic equations without altering the geodesic deviation equations. Using a non-standard expression for the perihelion advance from the Weyl conformastatic vacuum solution as a model, we can describe the anomaly in planets precession compared with different observational data from Ephemerides of the Planets and the Moon (EPM2008 and EPM2011) and Planetary and Lunar Ephemeris (INPOP10a). As a result, using the Levenberg-Marquardt algorithm and calculating the related Chi-squared statistic, we find that the anomaly is statistical irrelevant in accordance with INPOP10a observations. As a complement to this work, we also do an application to the relativistic precession of giant planets using observational data calibrated with the EPM2011.

The deep Earth may not be cooling down

Abstract The Earth is a thermal engine generating the fundamental processes of geomagnetic field, plate tectonics and volcanism. Large amounts of heat are permanently lost at the surface yielding the classic view of the deep Earth continuously cooling down. Contrary to this conventional depiction, we propose that the temperature profile in the deep Earth has remained almost constant for the last ∼4.3 billion years. The core–mantle boundary (CMB) has reached a temperature of ∼4400 K in probably less than 1 million years after the Moon-forming impact, regardless the initial core temperature. This temperature corresponds to an abrupt increase in mantle viscosity atop the CMB, when ∼60% of partial crystallization was achieved, accompanied with a major decrease in heat flow at the CMB. Then, the deep Earth underwent a very slow cooling until it reached ∼4100 K today. This temperature at, or just below, the mantle solidus is suggested by seismological evidence of ultra-low velocity zones in the D”-layer. Such a steady thermal state of the CMB temperature excludes thermal buoyancy from being the predominant mechanism to power the geodynamo over geological time. An alternative mechanism to sustain the geodynamo is mechanical forcing by tidal distortion and planetary precession. Motions in the outer core are generated by the conversion of gravitational and rotational energies of the Earth–Moon–Sun system. Mechanical forcing remains efficient to drive the geodynamo even for a sub-adiabatic temperature gradient in the outer core. Our thermal model of the deep Earth is compatible with an average CMB heat flow of 3.0 to 4.7 TW. Furthermore, the regime of core instabilities and/or secular changes in the astronomical forces could have supplied the lowermost mantle with a heat source of variable intensity through geological time. Episodic release of large amounts of heat could have remelted the lowermost mantle, thereby inducing the dramatic volcanic events that occurred during the Earth's history. In this scenario, because the Moon is a necessary ingredient to sustain the magnetic field, the habitability on Earth appears to require the existence of a large satellite.

Gravitational mass and Newton's universal gravitational law under relativistic conditions

We discuss the predictions of Newton's universal gravitational law when using the gravitational, mg, rather than the rest masses, mo, of the attracting particles. According to the equivalence principle, the gravitational mass equals the inertial mass, mi, and the latter which can be directly computed from special relativity, is an increasing function of the Lorentz factor, γ, and thus of the particle velocity. We consider gravitationally bound rotating composite states, and we show that the ratio of the gravitational force for gravitationally bound rotational states to the force corresponding to low (γ ≈ 1) particle velocities is of the order of (mPl/mo)2 where mpi is the Planck mass (ħc/G)1/2. We also obtain a similar result, within a factor of two, by employing the derivative of the effective potential of the Schwarzschild geodesics of GR. Finally, we show that for certain macroscopic systems, such as the perihelion precession of planets, the predictions of this relativistic Newtonian gravitational law differ again by only a factor of two from the predictions of GR.

Preliminary bounds of the gravitational local position invariance from Solar system planetary precessions

In the framework of the Parameterized Post-Newtonian (PPN) formalism, we calculate the long-term Preferred Location (PL) effects, proportional to the Whitehead parameter $\xi$, affecting all the Keplerian orbital elements of a localized two-body system, apart from the semimajor axis $a$. They violate the gravitational Local Position Invariance (LPI), fulfilled by General Relativity (GR). We obtain preliminary bounds on $\xi$ by using the latest results in the field of the Solar System planetary ephemerides. The non-detection of any anomalous perihelion precession for Mars allows us to indirectly infer $|\xi|\leq 5.8\times 10^{-6}$. \textcolor{black}{Such a bound is close to the constraint, of the order of $10^{-6}$, expected from the future BepiColombo mission to Mercury. As a complementary approach, the PL effects should be explicitly included in the dynamical models fitted to planetary data sets to estimate $\xi$ in a least-square fashion in a dedicated ephemerides orbit solution.} The ratio of the anomalous perihelion precessions for Venus and Jupiter, determined with the EPM2011 ephemerides at the $<3\sigma$ level, if confirmed as genuine physical effects needing explanation by future studies, rules out the hypothesis $\xi \neq 0$. A critical discussion of the $|\xi| \lesssim 10^{-6}-10^{-7}$ upper bounds obtained in the literature from the close alignment of the Sun's spin axis and the total angular momentum of the Solar System is presented.

CONSTRAINING THE STRING GAUGE FIELD BY GALAXY ROTATION CURVES AND PERIHELION PRECESSION OF PLANETS

We discuss a cosmological model in which the string gauge field coupled universally to matter gives rise to an extra centripetal force and will have observable signatures on cosmological and astronomical observations. Several tests are performed using data including galaxy rotation curves of 22 spiral galaxies of varied luminosities and sizes, and perihelion precessions of planets in the solar system. The rotation curves of the same group of galaxies are independently fit using a dark matter model with the generalized Navarro--Frenk--White (NFW) profile and the string model. A Remarkable fit of galaxy rotation curves is achieved using the one-parameter string model as compared to the three-parameter dark matter model with the NFW profile. The average $\chi^2$ value of the NFW fit is 9\% better than that of the string model at a price of two more free parameters. Furthermore, from the string model, we can give a dynamical explanation for the phenomenological Tully-Fisher relation. We are able to derive a relation between field strength, galaxy size and luminosity, which can be verified with data from the 22 galaxies. To further test the hypothesis of the universal existence of the string gauge field, we apply our string model to the solar system. Constraint on the magnitude of the string field in the solar system is deduced from the current ranges for any anomalous perihelion precession of planets allowed by the latest observations. The field distribution resembles a dipole field originating from the Sun. The string field strength deduced from the solar system observations is of a similar magnitude as the field strength needed to sustain the rotational speed of the Sun inside the Milky Way. This hypothesis can be tested further by future observations with higher precision.