Perihelion Advance Research Articles

Anomalous Sun Flyby of 1I/2017 U1 (`Oumuamua)

The findings of Micheli et al. (Nature2018, 559, 223–226) that 1I/2017 U1 (`Oumuamua) showed anomalous orbital accelerations have motivated us to apply an impact model of gravity in search for an explanation. A small deviation from the 1/r potential, where r is the heliocentric distance, is expected for the gravitational interaction of extended bodies as a consequence of this model. This modification of the potential results from an offset of the effective gravitational centre from the geometric centre of a spherically symmetric body. Applied to anomalous Earth flybys, the model accounts for energy gains relative to an exact Kepler orbit and an increased speed of several spacecraft. In addition, the flat rotation profiles of eight disk galaxies could be explained, as well as the anomalous perihelion advances of the inner planets and the asteroid Icarus. The solution in the case of `Oumuamua is also based on the proposal that the offset leads to an approach and flyby trajectory different from a Kepler orbit without postulating cometary activity. As a consequence, an adjustment of the potential and centrifugal orbital energies can be envisaged outside the narrow uncertainty ranges of the published post-perihelion data without a need to re-analyse the original data. The observed anomalous acceleration has been modelled with respect to the orbit solutions JPL 16 and “Pseudo-MPEC” for 1I/`Oumuamua.

Perihelion Advance and Trajectory of Charged Test Particles in Reissner-Nordstrom Field via the Higher-Order Geodesic Deviations

By using the higher-order geodesic deviation equations for charged particles, we apply the method described by Kerner et.al. to calculate the perihelion advance and trajectory of charged test particles in the Reissner-Nordstrom space-time. The effect of charge on the perihelion advance is studied and we compared the results with those obtained earlier via the perturbation method. The advantage of this approximation method is to provide a way to calculate the perihelion advance and orbit of planets in the vicinity of massive and compact objects without considering Newtonian and post-Newtonian approximations.

On some Aspects of Gravitomagnetism and Correction for Perihelion Advance

In 1918 Joseph Lense and Hans Thirring, discovered the gravitomagnetic effect when studied solutions to the Einstein field equations using the weak field and slow motion approximation of rotating systems. They noted that when a body falls towards a massive object in rotation it feels a force perpendicular to its movement. The equations that they obtained were similar to Maxwell’s equations of electromagnetism, now known as Maxwell’s equations for gravitomagnetism. Some authors affirm that the gravitomagnetic effect can cause precession then in this paper we calculate the precession that gravitomagnetic effect cause in Mercury’s perihelion advance. To make this we calculate the field between dipoles to measure the influence that the Sun has on Mercury, taking into account the gravitomagnetic field that the Sun and Mercury produces when they rotate around themselves. In addition, we calculate the ratio of the dipole force (of all solar system planet’s) and the Newton’s gravitational force to see how much is smaller.

Comment on Perihelion Advance Due to Cosmological Constant

We comment on the recent paper "Note on the perihelion/periastron advance due to cosmological constant" by H. Arakida (Int. J. Theor. Phys. 52 (2013) 1408-1414, arXiv:1212.6289) and provide simple derivations both of the main result of this paper and of the Adkins-McDonnell's precession formula, on which this main result is based.

Solar System tests of a scalar-tensor gravity with a general potential: Insensitivity of light deflection and Cassini tracking

In the work of Hohmann et al. [Phys. Rev. D 88, 084054 (2013)], the authors worked out the parametrized post-Newtonian (PPN) parameters $\ensuremath{\gamma}$ and $\ensuremath{\beta}$ of a scalar-tensor theory with an arbitrary coupling function and a generic potential, and they found that these two PPN parameters depend on the radial distance $r$ from the Sun, $\ensuremath{\gamma}(r)$ and $\ensuremath{\beta}(r)$. Based on the assumption that measurements on the PPN parameters can be characterized by the shortest distance to the Sun, the authors obtained their best constraints on the model parameters of the scalar-tenor theory by light deflection observation and the Cassini tracking experiment. However, as the authors stated, this approach might not be rigorous. In the present work, we physically model astronomical observations and physical experiments by calculating the null and timelike geodesics in the scalar-tensor theory. We show that, contrary to the results in the previous work, the light deflection and the Cassini tracking cannot distinguish the scalar-tensor theory from general relativity. We also investigate the additional advances in perihelia caused by the largest correction of the scalar field on the Newtonian potential. Since this correction has a Yukawa-like form, we obtain very much improved lower bounds on the model parameters by using current upper limits on the Yukawa parameters.

Effective Perihelion Advance and Potentials in a Conformastatic Background with Magnetic Field

Exact solutions of the Einstein-Maxwell field equations for a conformastatic metric with magnetized sources are investigated. In this context, effective potentials are studied in order to understand the dynamics of the magnetic field in galaxies. We derive the equations of motion for neutral and charged particles in a spacetime background characterized by this class of solutions. In this particular case, we investigate the main physical properties of the equatorial circular orbits and related effective potentials. In addition, we obtain an effective analytic expression for the perihelion advance of test particles. Our theoretical predictions are compared with the observational data calibrated with the ephemerides of the planets of the solar system and the Moon (EPM2011). In general, we show that the magnetic punctual mass predicts values that are in better agreement with observations than the values predicted in Einstein’s gravity alone.

Anomalous Earth flybys of spacecraft

A small deviation from the $1/r$ potential is expected for the gravitational interaction of extended bodies. It is explained as a consequence of a recently proposed gravitational impact model (Wilhelm et al. in Astrophys. Space Sci. 343:135–144, 2013) and has been applied to anomalous perihelion advances by Wilhelm and Dwivedi (New Astron. 31:51–55, 2014). The effect—an offset of the effective gravitational centre from the geometric centre of a spherical symmetric body—might also be responsible for the observed anomalous orbital energy gains and speed increases during Earth flybys of several spacecraft. However, close flybys would require detailed considerations of the orbit geometry. In this study, an attempt is made to explain the anomalous Earth flybys of the Galileo, NEAR Shoemaker and Rosetta spacecraft.

Perihelion advances for the orbits of Mercury, Earth, and Pluto from extended theory of general relativity (ETGR)

We explore the geodesic movement on an effective four-dimensional hypersurface that is embedded in a five-dimensional Ricci-flat manifold described by a canonical metric, to applying to planetary orbits in our solar system. Some important solutions are given, which provide the standard solutions of general relativity without any extra force component. We study the perihelion advances of Mercury, the Earth, and Pluto using the extended theory of general relativity. Our results are in very good agreement with observations and show how the foliation is determinant to the value of the perihelion’s advances. Possible applications are not limited to these kinds of orbits.

Secular perihelion advances of the inner planets and asteroid Icarus

A small effect expected from a recently proposed gravitational impact model (Wilhelm et al., 2013) is used to explain the remaining secular perihelion advance rates of the planets Mercury, Venus, Earth, Mars, and the asteroid (1566) Icarus—after taking into account the disturbances related to Newton’s Theory of Gravity. Such a rate was discovered by Le Verrier (1859) for Mercury and calculated by Einstein (1915, 1916) in the framework of his General Theory of Relativity (GTR). Accurate observations are now available for the inner Solar System objects with different orbital parameters. This is important, because it allowed us to demonstrate that the quantitative amount of the deviation from an 1/r potential is—under certain conditions—only dependent on the specific mass distribution of the Sun and not on the characteristics of the orbiting objects and their orbits. A displacement of the effective gravitational from the geometric centre of the Sun by about 4400m towards each object is consistent with the observations and explains the secular perihelion advance rates.

New upper limits on deviation from the inverse-square law of gravity in the solar system: a Yukawa parameterization

New physics beyond the standard model of particles might cause deviation from the inverse-square law of gravity. In many theoretical models of modified gravity, it is parameterized by the Yukawa correction to the Newtonian gravitational force in terms of two parameters α and λ. Here α is a dimensionless strength parameter and λ is a length scale. Using the supplementary advances in perihelia provided by INPOP10a and EPM2011 ephemerides, we obtain new upper limits on the deviation from the inverse-square law when the uncertainty of the Sun's quadrupole moment is taken into account. We find that INPOP10a yields the upper limits as α = 3.1 × 10−11 and λ = 0.15 au, and EPM2011 gives α = 5.2 × 10−11 and λ = 0.21 au. In both of them, α is at least 10 times less than the previous results.

Many-body problem in Kaluza–Klein models with toroidal compactification

In this paper, we consider a system of gravitating bodies in Kaluza–Klein models with toroidal compactification of the extra dimensions. To simulate the astrophysical objects (e.g., our Sun and pulsars) with energy density much greater than the pressure, we assume that these bodies are pressureless in the external space, i.e., the space we inhabit. At the same time, they may have nonzero parameters $$\omega _{({\bar{\alpha }} -3)} \, ({\bar{\alpha }} =4,\ldots , D)$$ in the equations of state in the extra dimensions. We construct the Lagrange function of this many-body system for any value of $$\Sigma =\sum _{{\bar{\alpha }}} \omega _{({\bar{\alpha }} -3)}$$ . Moreover, the gravitational tests (PPN parameters, perihelion and periastron advances) require a negligible deviation from the latent soliton value $$\Sigma =-(D-3)/2$$ . However, the presence of pressure/tension in the internal space results necessarily in the smearing of the gravitating masses over the internal space and in the absence of KK modes. This looks very unnatural from the point of view of quantum physics.

Advance of perihelion

The advance of perihelion, in particular for Mercury, is regarded as a classical test of general relativity, but a number of other (in some cases much larger) contributions to this phenomenon are seldom discussed in detail in textbooks. This paper presents a unified framework for evaluating the advance of perihelion due to (a) general relativity, (b) the solar quadrupole moment, and (c) planetary perturbations, the last in a ring model where the mass of each perturbing planet is “smeared out” into a coplanar circular orbit. The exact solution of the ring model agrees to within 4% with the usually quoted figure. Time-dependent contributions beyond the ring model contain some surprising features: they are not small, and some with long periods could mimic a secular advance.

F (T) gravity: effects on astronomical observations and Solar system experiments and upper bounds

The effects of the f (T) gravity have previously been investigated and constrained by using perihelion advances. As an extension of previous work and as an attempt to find more stringent constraints on its parameters, we investigate here its effects on astronomical observations and on experiments conducted in the Solar system. The expression for f (T) contains a quadratic correction of α*T2 (where α is a model parameter) and the cosmological constant Λ. Using a spherical solution describing the Sun's gravitational field, the resulting secular evolution of planetary orbital motions, in addition to the light deflection, gravitational time delay and frequency shift are calculated up to the leading contribution. From these results, we find qualitatively that the light deflection provides a unique bound on α, without dependence on Λ, and that the time delay experiments during inferior conjunction impose a clean constraint on Λ, regardless of α. Based on observations and experiments, especially the supplementary advances in the perihelia provided by the INPOP10a ephemeris, we obtain the upper bounds quantitatively: |α| ≤ 1.2 × 102 m2 and |Λ| ≤ 1.8 × 10−43 m−2, which are at least 10 times tighter than the previous results.

Exact Analytical Solution to Equations of Perihelion Advance in General Relativity

Previously the perihelion advance in binary system was computed approximately. We will present an exact analytical solution to nonlinear differential equation of perihelion advance by method of Jacobian elliptic function and the advanced angle between successive perihelions.

EPM ephemerides and relativity

AbstractIn the seventies of the last century the EPM ephemerides (Ephemerides of Planets and the Moon) of IAA RAS originated and have been developed since that time. These ephemerides are based upon relativistic equations of motion of celestial bodies and light rays and upon relativistic time scales. The updated model of EPM2008 includes the new values of planet masses and other constants, the improved dynamical model with adding Trans–Neptunian Objects and the expanded database (1913–2008). More than 260 parameters have been determined while improving the planetary part of EPM2008 to 550000 observations. EPM2008 have been oriented to ICRF by including into the total solution the VLBI data of spacecraft near the planets. The real uncertainty of EPM ephemerides has been checked by comparison with the JPL's DE ephemerides. Some estimates of the post–model parameters have been obtained: |1−β| < 0.0002, |1−γ| < 0.0002, /G = (−5.9±4.4) ⋅ 10−14 per year, the statistic zero corrections to the planet perihelion advances.

Physics of symplectic integrators: Perihelion advances and symplectic corrector algorithms

Symplectic integrators evolve dynamical systems according to modified Hamiltonians whose error terms are also well-defined Hamiltonians. The error of the algorithm is the sum of each error Hamiltonian's perturbation on the exact solution. When symplectic integrators are applied to the Kepler problem, these error terms cause the orbit to precess. In this work, by developing a general method of computing the perihelion advance via the Laplace-Runge-Lenz vector even for nonseparable Hamiltonians, I show that the precession error in symplectic integrators can be computed analytically. It is found that at leading order, each paired error Hamiltonians cause the orbit to precess oppositely by exactly the same amount after each period. Hence, symplectic corrector, or process integrators, which have equal coefficients for these paired error terms, will have their precession errors cancel at that order after each period. With the use of correctable algorithms, both the energy and precession error are of effective order n+2 where n is the nominal order of the algorithm. Thus the physics of symplectic integrators determines the optimal algorithm for integrating long-time periodic motions.

CAN SOLAR SYSTEM OBSERVATIONS TELL US SOMETHING ABOUT THE COSMOLOGICAL CONSTANT?

In this note, we show that the latest determinations of the residual perihelion advances [Formula: see text] of the inner planets of the Solar System, obtained by accounting for almost all known Newtonian and post-Newtonian orbital effects, yield only very broad constraints on the cosmological constant Λ. Indeed, from, e.g., [Formula: see text] arcseconds per century for Mercury, one gets -2 × 10-34 km -2 < Λ < 4 × 10-35 km -2. The currently accepted value for Λ, obtained from many independent cosmological and large-scale measurements, amounts to almost 10-46 km -2.

Exploring Black Holes: Introduction to General Relativity

1. Speeding (Review of Special Relativity). 2. Curving (Spacetime Near a Non-Rotating Black Hole). Project A: The Global Positioning System. 3. Plunging (Diving Toward a Black Hole). Project B: Inside The Black Hole. 4. Orbiting (Zooming Around a Black Hole). Project C: Advance of Mercury's Perihelion. 5. Seeing (Bending and Orbiting Light). Project D: Einstein Rings. Project E: Light Slowed Near Sun. Project F: The Spinning Black Hole. Project G: The Friedmann Universe. Readings in General Relativity. Glossaries of Symbols and Terms. Index. Selected Formulas. Selected Physical Constants.

A measurement of the shape of the solar disk: The solar quadrupole moment, the solar octopole moment, and the advance of perihelion of the planet Mercury.

The Solar Disk Sextant experiment has measured the solar angular diameter for a variety of solar latitudes. Combined with solar surface angular rotation data, the solar quadrupole moment ${J}_{2}$ and the solar octopole moment ${J}_{4}$ have been derived first by assuming constant internal angular rotation on cylinders and then by assuming constant internal angular rotation on cones. We have derived values of $1.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$ for ${J}_{2}$ and $9.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$ for ${J}_{4}$. We conclude with a discussion of errors and address the prediction of general relativity for the rate of advance of perihelion of the planet Mercury.

On the perihelion precesion as a Machian effect

A Lagrangian is constructed which gives Newtonian gravity in the lowest-order approximation in an isotropic universe and also predicts the correct advance of the perihelion with the proper choice of a constant governing the ratio of inertial to gravitational mass. The situation considered is that of a test particle orbiting a central body with external mass at rest and distributed isotropically at large distances from the central body. In the theory developed, the perihelion advance is due to a small contribution to the test-particle inertial mass by the central attracting body rather than to a failure of the inverse-square law of attraction. Some interesting Machian features of this theory are that: (1) the local value of the gravitational constant is determined by the mass distribution of the external matter; (2) the orbits are fixed, and the perihelion advances unambiguously with respect to the external-mass distribution; (3) there are no vestiges of absolute space; (4) the perihelion precession arises from the inertial interaction of the test particle with the central mass; (5) the local rest mass is really determined by the mass distribution of the rest of the universe; and (6) a limited form of the equivalence principle is inherent in one of the equations.