Pioneer Anomaly Research Articles

Calculation of Macroscopic Effects of Quantum Gravity in General Static Isotropic Gravitational Fields

In this paper we calculated the self-interaction of the gravitational field in coordinate space by approximate method, and find the functional relationship between gravitational source and distance and self-interaction of quantum gravity. The calculation result shows that the self-interaction of quantum gravity can explain the gravitational effects of dark matter. In the solar system, the self-interaction is extremely weak, but it is enough to explain the the Pioneer anomaly.

Ether Gravity

Mass does not create Gravity. Ether Energy Flow is Gravity. Ether fills the Universe and ether envelopes the Sun. High energy ether transfers some of its energy to the Sun, creating an energy density gradient in ether. The resulting Ether Energy River flows from the far corners of the Universe into the Sun. It is a “surround” river like a globe. This ether energy flow is Gravity. It is pushing the Planets, including our Earth toward the Sun. In addition, the Energy carried by this River of ether to the Sun causes the Sun to heat up and glow. The Sun and every celestial body is powered from the outside by Ether’s Energy. This ether energy river also caused the Pioneer Anomaly.

The Descartes Code (Spin Orbital Rotation of Photons)–II. The Gravitational Redshift

A new alternative model to the Schwarzschild’s solution of the Einstein's gravitational theory is presented. Descartes’s code is the old color theory (published in 1637) based on the rotation of “light globules”, however, it was rejected by Newton in 1672. In this model, the photon spin-orbital speed is modified by the gravitational field. The formulae for the wavelength, frequency, local time, momentum, energy, and temperature of photons in the gravitational field are identical in the first order both for the Schwarzschild solution and Descartes’ code. To experimentally determine the predictions of Descartes’ photon model we have to search for the experiments in the second order or for the situations where the standard model has to postulate some hidden elements (e.g., the dark matter). Some examples are presented here. The new interpretations of the bending of light by the Sun and the Shapiro time delay are given. The Anderson acceleration constant known as the Pioneer anomaly was derived as the effect of the Earth’s gravitational field on photons. Similar acceleration could be found in invaluable data from the Laser Lunar Ranging experiment. Stellar photons are modified by the Solar gravitational field at the distance of 1 AU and the acceleration constant identical to the Milgrom acceleration (MOND gravitational model) was derived. Therefore, we should study in more detail the influence of the Solar, Earth’s, and Moon’s gravitational fields on photons to avoid traps with false gravitational models.

Noncommutative Quantum Gravity and Dark Matter

According to the theory of noncommutative quantum gravity[1][2], we calculate the self-interaction of gravitons in momentum space. It shows that the self-interaction of gravitons makes the gravitational field deviate from the inverse square law. By calculating the metric, it can be obtained that the stronger the gravitational source, the stronger the energy momentum of the excited gravitons, and the stronger the gravitational effect produced by the self-interaction of gravitons. Maybe be it can be used to explain dark matter and the Pioneer anomaly.

Comment: A Solution to the Pioneer Anomalous Annual and Diurnal Residuals by E. D. Greaves, et al., 2021 Progress in Physics, vol. 17, 2, p. 168

A comparison is made between Greaves, E. D., Bracho, C., Gift, S., and Rodrigues, A. N., 2021. A Solution to the Pioneer Anomalous Annual and Diurnal Residuals, Progress in Physics, vol. 17, 2, p. 168. and Hodge, J. C. 2006. Scalar potential model of the Pioneer Anomaly.arXiv: astro-ph/0612567v1. Both papers suggest the Pioneer Anomaly obser- vation is due to the signal being modified by a characteristic of space that is influenced by the Sun and Earth. The papers differ by what that characteristic is and how it influences the signal. The former paper uses “energy density” (a scalar) which is proportional to distance (r-4) from bodies. All the characteristics of the former paper were accounted in the original calculation of the Pioneer Anomaly. The latter paper used a vector proportional to r-2, a gravitational force exerted on photons that was not accounted. The different treatment of r by the latter provides a more accurate treatment of the periodicities and all 10 anomalous characteristics of the Pioneer Anomaly. The conclusions of the former that the velocity of light is Galilean additive and the use of the “gravitational density” are not supported.

The NOW of time and the Pioneer Anomaly

The NOW of time and the Pioneer Anomaly

Solar Gravitational Radiation Reflected on the Hydrogen Wall might explain the Pioneer Anomaly: Do Mirrors for Gravitational Radiation Exist?

The Hydrogen wall found in the Voyager 1 data was modeled as the spherical mirror reflecting the Solar gravitational radiation back to the Solar System. A similar proposal appeared in the forgotten publication of Jaumann in 1912. The formula describing the anomalous acceleration of Pioneer 10 and 11 towards the Sun was derived. The decreasing temperature in the Solar System decreases slightly the mass of both Pioneers 10 and 11 as it was predicted by Einstein in 1907. The experimental value for both Pioneers was published as ap = (8.74 ± 1.33) * 10-10 ms-2. This new model predicts the value of the anomalous acceleration towards the Sun as ap = (8.50 – 0.0106 * x) * 10-10 ms-2 AU-1 where x is the distance of Pioneers from the Sun in astronomical unit AU. The annual amplitude visible in the Pioneer data (~ 1.6 *10-10 ms-2) was interpreted as the reflection of the Earth´s gravitational radiation from the surface of the Sun – the Earth´s self-gravitational effect with the predicted value 1.49 * 10-10 ms-2. The diurnal amplitude visible in the Pioneer anomaly (~ 3 * 10-12 ms-2) was interpreted as the result of Newton´s third law – for every action, there is an equal and opposite reaction between the Sun and the Earth: the diurnal amplitude was derived as 3.05 * 10-12 ms-2. It will be very helpful to get more experimental data from the next missions towards the Termination shock, the Hydrogen wall using the spacecraft of the type Voyager and Pioneer.

On The Nature of Tachyons and The Pioneer Anomaly

One considers tachyon repulsive force f from intergalactic space, by Takaaki Musha, as responsible for the rotation speed of galaxies, as not due to dark matter. Comparisons are made between this tachyon force f and dark energy, as an possible explanation for the pioneer anomaly, and considering the inertial effects of tachyon force f being nonlocal upon the pioneer spacecraft, arising from the vacuum zero point field ZPF, and introduce Mach’s principle as an effect of tachyon force f having an effect on the pioneer spacecraft from the future, because tachyons are regarded as travelling into the past. One considers various papers by other authors, and come to the conclusion that the reason tachyons may be undetected, as due to relativistic effects where an observer reference frame sees tachyons as ordinary particles, and that because tachyons also travel into the past, in a region of spacetime inaccessible to an co-moving observer, as why tachyons are not observed. But I also present experimental evidence of the detection of tachyons.

Is the Growth of the Astronomical Unit Caused by the Allais Eclipse Effect?

In addition to the Pioneer anomaly and the Earth flyby anomaly for spacecraft, other unexplained anomalies disrupt the solar system dynamics, like the astronomical unit. We show in this paper that the Allais eclipse effect causes the major part of the growth of the length scale for the entire solar system. It is the rough disturbance on the barycenter Earth-Moon implying the Sun that was recorded in the movement of the paraconical pendulum. Earth and Moon revolve around their common center of gravity, which in turn orbits the Sun, and the perturbation of the eclipse hits this double, coupled Kepler’s movements. The thesis of the tidal friction supports that oceanic tidal friction transfers the angular momentum of the Earth to the Moon and slows down the rotation of the Earth while taking away the Moon. However, we think that there are not enough shallow seas to sanction this interpretation. The Earth-Moon tidal system might be inaccurate or unreliable in determining the Earth’s actual rotational spin-down rate. Our assertion is that the change in the Earth’s rotation is caused by a repulsive gravitational interaction during solar eclipse. The perturbation would submit to variations and distortions the region of the barycenter of the Earth-Moon system which revolves around the Sun, with the dual secular effects that the Moon spirals outwards and that the Earth-Moon system goes away from the Sun.

The misunderstood Sagnac effect

The Sagnac effect of first order (in one-way light) is shown to explain the aberration observed in the very long base interferometry tests. This fact is also consistent with Sagnac’s results and with the observed stellar aberration. The Sagnac effect of second order (in two-way light) is shown to be real, but not observable, in the experiments that were done by Michelson and Morley. However, it is also shown that the same second order effect is observable in the Pioneer anomaly. The Doppler effect of second order is also demonstrated to explain the cosmic red shift, due to a radial ether wind.

Squeezing of the Super-Elastic Double-Helix Photon in the Gravitational Field (Hidden in Very-Well Known Old Formulae). Pound - Rebka - Snider Effect Studied by the Advanced LIGO Instrument, Pioneer Anomaly and CMB (Cosmic Microwave Background) (23.11.201

In our approach we have combined knowledge of Old Masters (working in this field before the year 1905), New Masters (working in this field after the year 1905) and Dissidents under the guidance of Louis de Broglie and David Bohm. Based on the great experimental work of Robert Pound, Glen A. Rebka and J.L. Snider we have proposed a squeezing of the super-elastic double-helix photon in the gravitational field. We have newly defined the squeeze rate of that photon particle on the helical path. We have inserted this squeeze rate into the very-well old formulae of Newton, Soldner, Gerber and Einstein and might glimpse traces of the quantum gravity. The squeeze rate of photons can be studied in details using the Great instrument - the Advanced LIGO - located on the surface of the Earth (USA, Italy, Japan). The observed strains on the level 5*10-19 should be caused by the gravitational field of our Earth. The observed strains on the level 5*10-22 should be caused by the gravitational fields of the Moon and the Sun. We estimate that the experimental value of the gravitational constant G studied by the LIGO instrument can achieve the accuracy to the level of ppb (parts per billion) after the removal of those strains from the measured signal and the removal of the gravitational influences of the Earth, the Moon, the Sun, Venus and Jupiter. To study the squeeze effect on a bigger scale we propose to analyze the Pioneer anomaly where Pioneer´s photons have been flying around the planets in our Solar system causing the squeeze effect - the anomalous blueshift. Similarly, we can study cosmic microwave photons flying around the objects in our Solar system that might create “the axis of evil” - temperature fluctuations in the CMB map (Wien displacement law). Can we prepare in our Solar system “tired” light by frequent blueshift - redshift transitions? Can it be that Nature cleverly inserted the squeeze rate into our very-well known Old Formulae? We want to pass this concept into the hands of Readers of this Journal better educated in the Mathematics and Physics.

STOE Explains "Planet 9"

Planet 9 is a hypothetical mass in the Kuiper Belt that causes the trans--Neptunian bodies to have unexplained orbits. The Scalar Theory of Everything (STOE) suggests the rotation curve anomalies of spiral galaxies, the Pioneer Anomaly, and the hypothetical Planet 9 phenomena are linked by a common cause, another application of the STOE Universal Equation.

Varying Physical Constants, Astrometric Anomalies, Redshift and Hubble Units

We have developed a cosmological model by allowing the speed of light c, gravitational constant G and cosmological constant Λ in the Einstein filed equation to vary in time, and solved them for Robertson-Walker metric. Assuming the universe is flat and matter dominant at present, we obtain a simple model that can fit the supernovae 1a data with a single parameter almost as well as the standard ΛCDM model with two parameters, and which has the predictive capability superior to the latter. The model, together with the null results for the variation of G from the analysis of lunar laser ranging data determines that at the current time G and c both increase as dG/dt = 5.4GH0 and dc/dt = 1.8cH0 with H0 as the Hubble constant, and Λ decreases as dΛ/dt = −1.2ΛH0. This variation of G and c is all what is needed to account for the Pioneer anomaly, the anomalous secular increase of the moon eccentricity, and the anomalous secular increase of the astronomical unit. We also show that the Planck’s constant ħ increases as dħ/dt = 1.8ħH0 and the ratio D of any Hubble unit to the corresponding Planck unit increases as dD/dt = 1.5DH0. We have shown that it is essential to consider the variation of all the physical constants that may be involved directly or indirectly in a measurement rather than only the one whose variation is of interest.

Relativistic mass due to a dilatant vacuum leads to a quantum reformulation of the relativistic kinetic energy

Relativistic mass change with speed is considered here as the effect of a viscous, dilatant vacuum, whose apparent viscosity is related to the Lorentz factor. Transient solid-like vacuum due to shear stress is presented as the reason why vacuum prevents the speed of massive objects from being indefinitely increased. Such a vacuum – that in a previous study allowed to exactly calculate the Pioneer anomaly, Mercury’s perihelion precession, and was shown to be compatible with stable planetary orbits – leads here to a quantum formula for the relativistic kinetic energy. A formula which distinguishes between the case of accelerated charges in a vacuum, for which a Stokes–Einstein radius comes into play, and the case of accelerated macroscopic bodies, for which the quantum potential term vanishes. In this way, incidentally, one obtains again correct results for the Pioneer 10, confirming the role of vacuum’s viscous force. This description of a quantum mechanism underlying the relativistic kinetic energy may be also helpful in constructing a theory of quantum relativity and may even tell us more about the interactions of matter with the Higgs field and the dark sector: two issues which can be themselves linked to a dilatant vacuum.

Physical vacuum as a dilatant fluid yields exact solutions to Pioneer anomaly and Mercury’s perihelion precession

By using the Lorentz factor as a viscosity term in Stokes’ law for objects traveling in a vacuum, Mercury’s perihelion precession and the Pioneer anomaly are directly and exactly solved, demonstrating that physical vacuum is a shear-thickening (dilatant) fluid. The modified Stokes’ equation also correctly indicates that planetary orbits are stable (over trillions of years). This unexpected feature of physical vacuum may help in achieving quantum relativity and implies interesting consequences for various fields of modern physics.

Principle of Constancy and Finiteness of the Speed of Gravitational Interaction and Dark Matter.

It can be shown that the anomalously high rates of rotation of the outer regions of galaxies follow from the constancy and finiteness of the rate of gravitational interaction, which is equal to the speed of light in accordance with general relativity of A. Einstein. Since the speed of propagation of the gravitational interaction is constant and equal to the speed of light, then for compensation of lag of the gravitational field, an increase in the mass velocity will always be used, since the metric tensor according to general relativity of A. Einstein is depends on to both geometry and kinematics of masses.

The Pioneer anomaly in covariant theory of gravitation

The difference of equations of motion in the covariant theory of gravitation and in the general theory of relativity is used to explain the Pioneer anomaly. Calculation shows that the velocities of a spacecraft in both theories at equal distances can differ by several centimetres per second. This leads also to a possible explanation of the flyby anomaly and comet disturbances, which are not taken into account by the general theory of relativity.

On the possible onset of the Pioneer anomaly

We explore the possibility that the observed onset of the Pioneer anomaly after Saturn encounter by Pioneer 11 is not necessarily due to mismodeling of solar radiation pressure but instead reflects a physically relevant characteristic of the anomaly itself. We employ the principles of a recently proposed cosmological model termed "the theory of inertial centers" along with an understanding of the fundamental assumptions taken by the Deep Space Network (DSN) to attempt to model this sudden onset. Due to an ambiguity that arises from the difference in the DSN definition of expected light-time with light-time according to the theory of inertial centers, we are forced to adopt a seemingly arbitrary convention to relate DSN-assumed clock-rates to physical clock-rates for this model. We offer a possible reason for adopting the convention employed in our analysis; however, we remain skeptical. Nevertheless, with this convention, one finds that this theory is able to replicate the previously reported Hubble-like behavior of the "clock acceleration" for the Pioneer anomaly as well as the sudden onset of the anomalous acceleration after Pioneer 11 Saturn encounter. While oscillatory behavior with a yearly period is also predicted for the anomalous clock accelerations of both Pioneer 10 and Pioneer 11, the predicted amplitude is an order of magnitude too small when compared with that reported for Pioneer 10.

Gravitational anomalies in the solar system?

Mindful of the anomalous perihelion precession of Mercury discovered by Le Verrier in the second half of the nineteenth century and its successful explanation by Einstein with his General Theory of Relativity in the early years of the twentieth century, discrepancies among observed effects in our Solar system and their theoretical predictions on the basis of the currently accepted laws of gravitation applied to known matter-energy distributions have the potential of paving the way for remarkable advances in fundamental physics. This is particularly important now more than ever, given that most of the universe seems to be made of unknown substances dubbed Dark Matter and Dark Energy. Should this not be directly the case, Solar system's anomalies could anyhow lead to advancements in either cumulative science, as shown to us by the discovery of Neptune in the first half of the nineteenth century, and technology itself. Moreover, investigations in one of such directions can serendipitously enrich the other one as well. The current status of some alleged gravitational anomalies in the Solar system is critically reviewed. They are: (a) Possible anomalous advances of planetary perihelia. (b) Unexplained orbital residuals of a recently discovered moon of Uranus (Mab). (c) The lingering unexplained secular increase of the eccentricity of the orbit of the Moon. (d) The so-called Faint Young Sun Paradox. (e) The secular decrease of the mass parameter of the Sun. (f) The Flyby Anomaly. (g) The Pioneer Anomaly. (h) The anomalous secular increase of the astronomical unit.

On the Trigonometric Correction of One Powerful Formula

An attempt is presented for the description of the magnitude of Newton’s gravitational force in the experiments with a horizontal torsion balance. There were developed many experimental arrangements in order to find experimentally the value of big G – the Newtonian gravitational constant – after the Michell-Cavendish experiment in 1798. The geometrical configurations of test and source masses play a very important role in these experiments. The old trigonometric function “sagitta” used by Johannes Kepler and Isaac Newton was newly employed as the trigonometric tool for the determination of the magnitude of Newton’s gravitational force between the source mass and the test mass. Based on the known experimental configurations with the horizontal torsion balance we have found that the “true” Michell-Cavendish configuration is not dependent on the space orientation. This “sagitta” function can be experimentally tested in the Karagioz-Izmailov configuration and the Karagioz-Izmailov-Gillies-Gershteyn configuration with the technology available at begin of our century. A proposal for the decomposition of the big G was presented. This concept could not be experimentally tested before the discoveries of the dipole in the cosmic microwave background radiation and the Pioneer anomaly.