Thomas L. Wilson, Hans-Joachim Blome
Based upon a simple cosmological model with no expansion, we find that the rotational terms appearing in the G/"odel universe are too small to explain the Pioneer anomaly. Although it contributes, universal rotation is not the cause of the Pioneer effect.
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In this paper an explanation of the Pioneer anomaly is given, using the hypothesis of the time dependent gravitational potential. The implications of this hypothesis on the planetary orbits and orbital periods are given in section 2. In sections 3 and 4 we give a detailed explanation of the Pioneer anomaly, which corresponds to the observed phenomena.
We examine the Pioneer anomaly - a reported anomalous acceleration affecting the Pioneer 10/11, Galileo and Ulysses spacecrafts - in the context of a braneworld scenario. We show that effects due to the radion field cannot account for the anomaly, but that a scalar field with an appropriate potential is able to explain the phenomena. Implications and features of our solution are analyzed.
In a previous work we showed that massive test particles exhibit a non-geodesic acceleration in a modified theory of gravity obtained by a non-commutative deformation of General Relativity (so-called Matrix Gravity). We propose that this non-geodesic acceleration might be the origin of the anomalous acceleration experienced by the Pioneer 10 and Pioneer 11 spacecrafts.
The Pioneer anomaly is a small sunward anomalous acceleration found in the trajectory analysis of the Pioneer 10 and 11 spacecraft. As part of the investigation of the effect, analysis of recently recovered Doppler data for both spacecraft has been completed. The presence of a small anomalous acceleration is confirmed using data spans more than twice as long as those that were previously analyzed. We examine the constancy and direction of the Pioneer anomaly, and conclude that: i) the data favor a temporally decaying anomalous acceleration (~2\times 10^{-11} m/s^2/yr) with an over 10% improvem…
Thermal modeling of complex systems faces the problems of an effective digitalization of the detailed geometry and properties of the system, calculation of the thermal flows and temperature maps, treatment of the thermal radiation including possible multiple reflections, inclusion of additional external influences, extraction of the radiation pressure from calculated surface data, and computational effectiveness. In previous publications the solution to these problems have been outlined and a first application to the Pioneer spacecraft have been shown. Here we like to present the application o…
The effect of the expanding universe on planetary motion is considered to first order in the Hubble constant H. Orbital elements are shown to be unaffected, but there is a small change in the connection between planetary proper time and coordinate time. This can produce an apparent anomalous acceleration in velocities inferred from echo-ranging, but the effect is too small by many orders of magnitude to account for the Pioneer 10/11 anomaly.
The weak field approximation of geodesics in Randers-Finsler space is investigated. We show that a Finsler structure of Randers space corresponds to the constant and sunward anomalous acceleration demonstrated by the Pioneer 10 and 11 data. The additional term in the geodesic equation acts as "electric force", which provides the anomalous acceleration.
We estimate the main systematic effects relevant in a mission to test and characterize the Pioneer anomaly through the flight formation concept, by launching probing spheres from a mother spacecraft and tracking their motion via laser ranging.
In this paper we discuss a model which can be considered as a generalization of the well-known scalar-tensor Brans-Dicke theory. This model possesses an interesting feature: due to Born-Infeld type non-linearity of the scalar field the properties of the interaction between two test bodies depend significantly on their masses. It is shown that the model can be interesting in view of the Pioneer 10, 11 spacecraft anomaly.
We build up a new phenomenological framework associated with a minimal generalization of Einsteinian gravitation theory. When linearity, stationarity and isotropy are assumed, tests in the solar system are characterized by two potentials which generalize respectively the Newton potential and the parameter $γ$ of parametrized post-Newtonian formalism. The new framework seems to have the capability to account for the Pioneer anomaly besides other gravity tests.
The Pioneer 10 and 11 spacecraft yielded the most precise navigation in deep space to date. However, while at heliocentric distance of $\sim$ 20--70 AU, the accuracies of their orbit reconstructions were limited by a small, anomalous, Doppler frequency drift. This drift can be interpreted as a sunward constant acceleration of $a_P = (8.74 \pm 1.33)\times 10^{-8}$ cm/s$^2$ which is now commonly known as the Pioneer anomaly. Here we discuss the Pioneer anomaly and present the next steps towards understanding of its origin. They are: 1) Analysis of the entire set of existing Pioneer 10 and 11 dat…
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 wi…
The radio-metric tracking data received from the Pioneer 10 and 11 spacecraft from the distances between 20-70 astronomical units from the Sun has consistently indicated the presence of a small, anomalous, blue-shifted Doppler frequency drift that limited the accuracy of the orbit reconstruction for these vehicles. This drift was interpreted as a sunward acceleration of a_P = (8.74+/-1.33)x10^{-10} m/s^2 for each particular spacecraft. This signal has become known as the Pioneer anomaly; the nature of this anomaly is still being investigated. Recently new Pioneer 10 and 11 radio-metric Doppler…
Radiometric tracking data from Pioneer 10 and 11 spacecraft has consistently indicated the presence of a small, anomalous, Doppler frequency drift, uniformly changing with a rate of ~6 x 10^{-9} Hz/s; the drift can be interpreted as a constant sunward acceleration of each particular spacecraft of a_P = (8.74 \pm 1.33) x 10^{-10} m/s^2. This signal is known as the Pioneer anomaly; the nature of this anomaly remains unexplained. We discuss the efforts to retrieve the entire data sets of the Pioneer 10/11 radiometric Doppler data. We also report on the recently recovered telemetry files that may …
The Doppler tracking data from two deep-space spacecraft, Pioneer 10 and 11, show an anomalous blueshift, which has been dubbed the "Pioneer anomaly". The effect is most commonly interpreted as a real deceleration of the spacecraft - an interpretation that faces serious challenges from planetary ephemerides. The Pioneer anomaly could as well indicate an unknown effect on the radio signal itself. Several authors have made suggestions how such a blueshift could be related to cosmology. We consider this interpretation of the Pioneer anomaly and study the impact of an anomalous blueshift on the La…
The Pioneer 10/11 missions, launched in 1972 and 1973, and their navigation are reviewed. Beginning in about 1980 an unmodeled force of ~ 8 x 10^{-8} cm/s^2 appeared in the tracking data, it later being verified. The cause remains unknown, although radiant heat remains a likely origin. A set of efforts to find the solution are underway: a) analyzing in detail all available data, b) using data from the New Horizons mission, and c) considering an ESA dedicated mission.
The data from Pioneer 10 and 11 shows an anomalous, constant, Doppler frequency drift that can be interpreted as an acceleration directed towards the Sun of a_P = (8.74 \pm 1.33) x 10^{-8} cm/s^2. Although one can consider a new physical origin for the anomaly, one first must investigate the contributions of the prime candidates, which are systematics generated on board. Here we expand upon previous analyses of thermal systematics. We demonstrate that thermal models put forth so far are not supported by the analyzed data. Possible ways to further investigate the nature of the anomaly are propo…
Experimental tests of gravity performed in the solar system show a good agreement with general relativity. The latter is however challenged by the Pioneer anomaly which might be pointing at some modification of gravity law at ranges of the order of the size of the solar system. As this question could be related to the puzzles of ``dark matter'' or ``dark energy'', it is important to test it with care. There exist metric extensions of general relativity which preserve the well verified equivalence principle while possibly changing the metric solution in the solar system. Such extensions have th…
The Pioneer 10 and 11 spacecraft yielded very accurate navigation that was limited only by a small, anomalous frequency drift of their carrier signals received by the NASA Deep Space Network (DSN). This discrepancy, evident in the data for both spacecraft, was interpreted as an approximately constant acceleration and has become known as the Pioneer anomaly. The origin of this anomaly is yet unknown. Recent efforts to explain the effect included a search for independent confirmation, analyses of conventional mechanisms, even ideas rooted in new physics, and proposals for a dedicated mission. We…
The 1972 and 1973 launched Pioneer 10 and 11 were the first missions to explore the outer solar system. They achieved stunning breakthroughs in deep-space exploration. But around 1980 an unmodeled force of \sim 8 \times 10^{-8} cm/s^2, directed approximately towards the Sun, appeared in the tracking data. It later was unambiguously verified as not being an artifact. The origin remains unknown (although radiant heat remains a likely cause). Increasing effort has gone into understanding this anomaly. We review the situation and describe programs to resolve the issue.
Einstein-Infeld-Hoffmann method is used to solve the problem of motion of two bodies when the equations of general relativity are of the generalized form: they have been reduced to a form invariant under conformal transformations. It is proved that not only metric degrees of freedom, but also derivatives of vector $A_α$ appearing in the generalized equations can exert influence on the motion of bodies in a certain space-time domain. This influence can account for the recently observed anomalous acceleration of spacecrafts Pioneer 10, Pioneer 11. The impact of vector $A_α$ on the motion of bodi…
In 1972 and 1973 the Pioneer 10 and 11 missions were launched. They were the first to explore the outer solar system and achieved stunning breakthroughs in deep-space exploration. But beginning in about 1980 an unmodeled force of \sim 8 \times 10^{-8} cm/s^2, directed approximately towards the Sun, appeared in the tracking data. It later was unambiguously verified as being in the data and not an artifact. The cause remains unknown (although radiant heat remains a likely origin). With time more and more effort has gone into understanding this anomaly (and also possibly related effects). We revi…
The Pioneer 10/11 spacecraft yielded the most precise navigation in deep space to date. However, their radio-metric tracking data received from the distances between 20--70 astronomical units from the Sun consistently indicated the presence of a small, anomalous, Doppler frequency drift. The drift is a blue frequency shift that can be interpreted as a sunward acceleration of a_P = (8.74 +/- 1.33) x 10^(-10) m/s^2 for each particular spacecraft. This signal has become known as the Pioneer anomaly; the nature of this anomaly remains unexplained. New Pioneer 10 and 11 radio-metric Doppler data re…
A model is presented in which the Pioneer anomaly is not related to the motion of the spaceship, but is a consequence of the acceleration of the cosmological proper time $τ$ with respect to the coordinate parametric time $t$, what is an effect of the background gravitational potential of the entire universe. The light speed, while being constant if defined with respect to $τ$ ({\it i. e.} as ${\rm d}\ell /{\rm d} τ$), would suffer an adiabatic secular acceleration, $a_\ell={\rm d}c/{\rm d}t >0$, if defined in terms of $t$ ({\it i. e.} as ${\rm d}\ell /{\rm d} t$). Such an adiabatic acceleratio…
Radio-metric Doppler tracking data received from the Pioneer 10 and 11 spacecraft from heliocentric distances of 20-70 AU has consistently indicated the presence of a small, anomalous, blue-shifted frequency drift uniformly changing with a rate of ~6 x 10^{-9} Hz/s. Ultimately, the drift was interpreted as a constant sunward deceleration of each particular spacecraft at the level of a_P = (8.74 +/- 1.33) x 10^{-10} m/s^2. This apparent violation of the Newton's gravitational inverse-square law has become known as the Pioneer anomaly; the nature of this anomaly remains unexplained. In this revi…
Experimental tests of gravity performed in the solar system show a good agreement with general relativity. The latter is however challenged by the Pioneer anomaly which might be pointing at some modification of gravity law at ranges of the order of the size of the solar system. We introduce a metric extension of general relativity which, while preserving the equivalence principle, modifies the coupling between curvature and stress tensors and, therefore, the metric solution in the solar system. The ``post-Einsteinian extension'' replaces Newton gravitation constant by two running coupling cons…
The Pioneer 10/11 spacecraft yielded the most precise navigation in deep space to date. However, their radio-metric tracking data has consistently indicated the presence of a small, anomalous, Doppler frequency drift. The drift is a blue-shift, uniformly changing with a rate of ~6 x 10^{-9} Hz/s and can be interpreted as a constant sunward acceleration of each particular spacecraft of a_P =(8.74 +/- 1.33) x 10^{-10} m/s^2. The nature of this anomaly remains unexplained. Here we summarize our current knowledge of the discovered effect and review some of the mechanisms proposed for its explanati…
Analysis of the radio tracking data from the Pioneer 10/11 spacecraft has consistently indicated the presence of an anomalous small Doppler frequency drift. The drift can be interpreted as being due to a constant acceleration of a_P= (8.74 +/- 1.33) x 10^{-8} cm/s^2 directed towards the Sun. Although it is suspected that there is a systematic origin to the effect, none has been found. The nature of this anomaly has become of growing interest in the fields of relativistic cosmology, astro- and gravitational physics as well as in the areas of spacecraft design and high-precision navigation. We p…
The trajectories of test particles moving in the gravitational field of a non-spherically symmetric mass distribution become affected by the presence of multipole moments. In the case of hyperbolic trajectories, the quadrupole moment of an oblate mass induces a displacement of the trajectory towards the mass source, an effect that can be interpreted as an additional acceleration directed towards the source. Although this additional acceleration is not constant, we perform a general relativistic analysis in order to evaluate the possibility of explaining Pioneer's anomalous acceleration by mean…
Analysis of the radio tracking data from the Pioneer 10/11 spacecraft at distances between about 20 - 70 AU from the Sun has consistently indicated the presence of an unmodeled, small, constant, Doppler blue shift drift of order 6 \times 10^{-9} Hz/s. After accounting for systematics, this drift can be interpreted as a constant acceleration of a_P= (8.74 \pm 1.33) \times 10^{-8} cm/s^2 directed towards the Sun, or perhaps as a time acceleration of a_t = (2.92 \pm 0.44)\times 10^{-18} s/s^2. Although it is suspected that there is a systematic origin to this anomaly, none has been unambiguously …
The radio-metric Doppler tracking data from the Pioneer 10/11 spacecraft, from between 20-70 AU, yields an unambiguous and independently confirmed anomalous blue shift drift of a_t = (2.92 \pm 0.44)\times 10^{-18} s/s^2. It can be interpreted as being due to a constant acceleration of a_P = (8.74 \pm 1.33) \times 10^{-8} cm/s^2 directed towards the Sun. No systematic effect has been able to explain the anomaly, even though such an origin is an obvious candidate. We discuss what has been learned (and what might still be learned) from the data about the anomaly, its origin, and the mission desig…
We present source code for the computer algebra system Mathematica that analyzes the motion of the Pioneer spacecraft using the public available ephemeris data from JPL's website. Within 15 minutes, the reader can verify that the Pioneer anomalous acceleration a_p (1) exists in the order of magnitude of c H_0, (2) is not due to mismodeling of gravitational attraction, solar pressure or spacecraft attitude maneuvers. The simple code of about 100 lines may easily be extended by the reader to include further tests. Due to the limitations of our approach, we do not know (1) whether the unknown raw…
In addition to its long-term constancy, the Pioneer (spacecraft) anomaly appears to only exist for bodies whose mass is less than that of: planets, moons, comets, and heavy asteroids of known mass. Assuming the observational evidence is reliable, and not the result of an unknown systematic effect, a violation of the Weak Principle of Equivalence is implied. To propose an additional force fails to satisfy this constraint. This paper presents a new hypothesis involving additional field energy in the form of: a finite number of lunar sourced constant amplitude (Lorentz invariant) wave-like undula…
Analysis of the radio tracking data from the Pioneer 10/11 spacecraft at distances between about 20 - 70 AU from the Sun has indicated the presence of an unmodeled, small, constant, Doppler blue shift which can be interpreted as a constant acceleration of a_P= (8.74 \pm 1.33) \times 10^{-8} cm/s^2 directed approximately towards the Sun. In addition, there is early (roughly modeled) data from as close in as 5 AU which indicates there may have been an onset of the anomaly near Saturn. We observe that the data now arriving from the New Horizons mission to Pluto and the Kuiper Belt could allow a r…
The modification of the Doppler effect due to the coupling of the helicity of the radiation with the rotation of the source/receiver is considered in the case of the Pioneer 10/11 spacecraft. We explain why the Pioneer anomaly is not influenced by the helicity-rotation coupling.
In this manuscript, it is shown that the Pioneer anomaly is the local evidence for an expanding universe. In other words, its value is a direct measure of the Hubble constant while its sign shows the expanding behavior of the dynamics of the universe. This analysis is obtained by studying the radial geodesic deviation of the light rays in the perturbed Friedmann-Robertson-Walker metric in the Newtonian gauge.
The reported anomalous acceleration acting on the Pioneers spacecrafts could be seen as a consequence of the existence of some local curvature in light geodesics when using the coordinate speed of light in an expanding space-time. The effect is related with the non synchronous character of the underlying metric and therefore, planets closed orbits can not reveal it. It is shown that the cosmic expansion rate -the Hubble parameter H- has been indeed detected. Additionally, a relation for an existing annual term is obtained which depends on the cosine of the ecliptic latitude of the spacecraft, …
It is shown that the Pioneer anomaly is a natural consequence of variable speed of light cosmological models wherein the speed of light is assumed to be a power-law function of the scale factor (or cosmic time). In other words, the Pioneer anomaly can be regarded as a non-gravitational effect of the continuously decreasing speed of light which indicates itself as an anomalous light propagation time delay in local frames. This time delay is accordingly interpreted as an additional Doppler blue shift.
Analysis of radio-metric tracking data from the Pioneer 10/11 spacecraft at distances between 20 - 70 astronomical units (AU) from the Sun has consistently indicated the presence of an anomalous, small, constant Doppler frequency drift. The drift can be interpreted as being due to a constant acceleration of a_P= (8.74 \pm 1.33) x 10^{-8} cm/s^2 directed towards the Sun. Although it is suspected that there is a systematic origin to the effect, none has been found. As a result, the nature of this anomaly has become of growing interest. Here we present a concept for a deep-space experiment that w…
The Pioneer 10 and 11 spacecraft yielded the most precise navigation in deep space to date. These spacecraft had exceptional acceleration sensitivity. However, analysis of their radio-metric tracking data has consistently indicated that at heliocentric distances of $\sim 20-70$ astronomical units, the orbit determinations indicated the presence of a small, anomalous, Doppler frequency drift. The drift is a blue-shift, uniformly changing with a rate of $\sim(5.99 \pm 0.01)\times 10^{-9}$ Hz/s, which can be interpreted as a constant sunward acceleration of each particular spacecraft of $a_P = (8…
In the context of a parametric theory (with the time being a dynamical variable) we consider the coupling between the quantum vacuum and the background gravitation that pervades the universe (unavoidable because of the universality of gravity). In our model the fourth Heisenberg relation introduces a possible source of discrepancy between the marches of atomic and gravitational clocks, which accelerate with respect to one another. This produces in its turn another discrepancy between the observations, performed with atomic time, and the theoretical analysis, which uses parametric astronomical …
The anomalous time depending blueshift, the so-called "Pioneer anomaly", that was detected in the radio-metric data from Pioneer 10/11, Ulysses and Galileo spacecraft may not result from a real change of velocity. Rather, the Pioneer anomaly may be understood within the framework of general relativity as a time depending gravitational frequency shift accounting for the time dependence of the density of the dark energy when the latter is identified with quintessence. Thus, instead of being in conflict with Einstein equivalence principle, the main Pioneer anomaly appears merely as a new validati…
The description of the cosmological expansion and its possible local manifestations via treating the proper conformal transformations as a coordinate transformation from a comoving Lorentz reference frame to an uniformly accelerated one is given. The explicit form of the conformal time inhomogeneity is established. The expression defining the location cosmological distance in the form of simple function on the red shift is obtained. By coupling it with the relativistic formula for the longitudinal Doppler effect, the explicit expression for the Hubble law is obtained, which gives rise to the c…
From Doppler tracking data and data on circular motion of astronomical objects we obtain a metric of the Pioneer Anomaly. The metric resolves the issue of manifest absence of anomaly acceleration in orbits of the outer planets and extra-Pluto objects of the Solar system. However, it turns out that the energy-momentum tensor of matter, which generates such a gravitational field in GR, violates energy dominance conditions. At the same time the equation of state derived from the energy-momentum tensor is that of dark energy with $w=-1/3$. So the model proposed must be carefully studied by "Grand-…
We analyze here the reasons why an explanation of the Pioneer anomaly proposed by the authors is fully compatible with the cartography of the solar system. First, this proposal posits that the phenomenon is an apparent acceleration, not a real one, caused by a progressive desynchronization of the astronomical and the atomic clock-times, after they had been synchronized at a previous instant. The desynchronization could be caused by a coupling between the background gravitation and the quantum vacuum. Therefore, the standard argument for the incompatibility of the Pioneer acceleration and the v…
This work proposes an explanation of the Pioneer anomaly, the unmodelled and as yet unexplained blueshift detected in the microwave signal of the Pioneer 10 and other spaceships by Anderson {\it et al} in 1998. What they observed is similar to the effect that would have either (i) an anomalous acceleration $a_{\rm P}$ of the ship towards the Sun or (ii) an acceleration of the clocks $a_{\rm t}=a_{\rm P}/c$. The second alternative is investigated here, with a phenomenological model in which the anomaly is an effect of the background gravitational potential $Ψ(t)$ that pervades all the universe …
Precision navigation of spacecraft requires accurate knowledge of small forces, including the recoil force due to anisotropies of thermal radiation emitted by spacecraft systems. We develop a formalism to derive the thermal recoil force from the basic principles of radiative heat exchange and energy-momentum conservation. The thermal power emitted by the spacecraft can be computed from engineering data obtained from flight telemetry, which yields a practical approach to incorporate the thermal recoil force into precision spacecraft navigation. Alternatively, orbit determination can be used to …
We present a methodology based on point-like Lambertian sources that enables one to perform a reliable and comprehensive estimate of the overall thermally induced acceleration of the Pioneer 10 and 11 spacecraft. We show, by developing a sensitivity analysis of the several parameters of the model, that one may achieve a valuable insight on the possible thermal origin of the so-called Pioneer anomaly.
We propose here an explanation of the Pioneer anomaly which is not in conflict with the cartography of the solar system. In our model, the spaceship does not suffer any extra acceleration but follows the trajectory predicted by standard gravitational theory. The observed acceleration is not real but apparent and has the same observational footprint as a deceleration of astronomical time with respect to atomic time. The details can be summarized as follows: i) as we argued in a recent paper, there is an unavoidable coupling between the background gravitation that pervades the universe and the q…
The description of the cosmological expansion and its possible local manifestations via treating the proper conformal transformations as a coordinate transformation from a comoving Lorentz reference frame (RF) to an uniformly accelerated RF is given. The explicit form of the conformal deformation of time is established. The expression defining the location cosmological distance in the form of simple function on the red shift is obtained. By coupling it with the well known relativistic formula defining the relative velocity of the mutually moving apart source and receiver of the signal, the exp…
Analysis of the radio-metric tracking data from the Pioneer 10/11 spacecraft at distances between 20--70 astronomical units (AU) from the Sun has consistently indicated the presence of an anomalous, small, constant Doppler frequency drift. The drift is a blue-shift, uniformly changing with rate a_t = (2.92 +/- 0.44) x 10^(-18) s/s^2. It can also be interpreted as a constant acceleration of a_P = (8.74 +/- 1.33) x 10^(-8) cm/s^2 directed towards the Sun. Although it is suspected that there is a systematic origin to the effect, none has been found. As a result, the nature of this anomaly has bec…
On the basis of the nonisometric transformations subgroup of the SO(4.2) group, the nonlinear time inhomogeneity one-parameter conformal transformations are constructed. The connection between the group parameter and the Hubble constant H0 is established. It is shown that the existence of an anomalous blue-shifted frequency drift is a pure kinematic manifestation of the time inhomogeneity induced by the Universe expansion. This conclusion is confirmed via a generalization of the standard Special Relativity clock synchronization procedure to the space expanding case. The obtained formulae are i…
Recently, Brownstein and Moffat proposed a gravitational mechanism to explain the Pioneer anomaly based on their scalar-tensor-vector (STVG) metric theory of gravity. In this paper we show that their model, fitted to the presently available data for the anomalous Pioneer 10/11 acceleration, is in contrast with the latest determinations of the perihelion extra-rates of Jupiter, Saturn and Uranus.
A methodology based on point-like sources is discussed, enabling a reliable estimate of the acceleration of the Pioneer 10 and 11 probes caused by thermal effects. A sensitivity analysis of the several parameters of the model allows for a clear indication of the possible thermal origin of the so-called Pioneer anomaly.
We review the fundamental results of a new cosmological model, based on conformal gravity, and apply them to the analysis of the early data of the Pioneer anomaly. We show that our conformal cosmology can naturally explain the anomalous acceleration of the Pioneer 10 and 11 spacecraft, in terms of a local blueshift region extending around the solar system and therefore affecting the frequencies of the navigational radio signals exchanged between Earth and the spacecraft. On the contrary, conformal gravity corrections alone would not be able to account for dynamical effects of such magnitude to…
If the Pioneer anomaly has a gravitational origin, it would, according to the equivalence principle, distort the motions of the planets in the Solar System. Since no anomalous motion of the planets has been detected, it is generally believed that the Pioneer anomaly can not originate from a gravitational source in the Solar System. However, this conclusion becomes less obvious when considering models that either imply modifications to gravity at long range or gravitational sources localized to the outer Solar System, given the uncertainty in the orbital parameters of the outer planets. Followi…
We use metric formalism in $f(R)$ modified gravity to study the dynamics of various systems from the solar system to the cosmological scale. we assume an ansatz for the derivative of action as a function of distance and describe the Pioneer anomaly and the flat rotation curve of the spiral galaxies. Having the asymptotic behavior of action, we propose the action of $f(R) = (R + Λ)(1 + \ln(R/R_c)/(R/R_0 + 2/α))$ where in galactic and solar system scales it can recover our desired form. The vacuum solution of this action also results in a positive late time acceleration for the universe. We fix …
The Hubble law is extended to massive particles based on the de Broglie wavelength. Due to the expansion of the universe the wavelength of an unbound particle would increase according to its cosmological redshift. Based on the navigation anomalies of the Pioneer 10 & 11 spacecraft it is postulated that an unbound massive particle has a cosmological redshift z = (c / v_0) H_0 t, where c is the speed of light in vacuum, v_0 is the initial velocity of the particle, H_0 is Hubble's constant and t is the duration of time that the particle has been unbound. The increase in wavelength of the particle…
In this paper we test the hypothesis that the Pioneer anomaly can be of gravitational origin by comparing the predicted model-independent shifts Delta a/a for the semimajor axis of Uranus and Neptune with the Voyager 2 radio-technical distance measurements performed at JPL-NASA. As in the case of other tests based on different methods and data sets (secular perihelion advance, right ascension/declination residuals over about one century), the orbits of the investigated planets are not affected by any anomalous acceleration like that experienced by the Pioneer 10/11 spacecraft.
The occurrence of the phenomenon known as photon acceleration is a natural prediction of nonlinear electrodynamics (NLED). This would appear as an anomalous frequency shift in any modeling of the electromagnetic field that only takes into account the classical Maxwell theory. Thus, it is tempting to address the unresolved anomalous, steady; but time-dependent, blueshift of the Pioneer 10/11 spacecrafts within the framework of NLED. Here we show that astrophysical data on the strength of the magnetic field in both the Galaxy and the local (super)cluster of galaxies support the view on the major…
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