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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 has the capability to account for the Pioneer anomaly while preserving the compatibility of other gravity tests with general relativity.

We study the modification of Newton's second law, upto first order in the deformation parameter a, in the κ-spacetime. We derive the deformed Hamiltonian, expressed in terms of the commutative phase space variables, describing the particle moving in a central potential in the κ-spacetime. Using this, we find the modified equations of motion and show that there is an additional force along the radial direction. Using Pioneer anomaly data, we set a bound for a. We also analyze the violation of equivalence principle predicted by the modified Newton's equation, valid up to first order in a and use this also to set an upper bound on a.

Experimental tests of Newton law put stringent constraints on potential deviations from standard theory with ranges from the millimeter to the size of planetary orbits. Windows however remain open for short range deviations, below the millimeter, as well as long range ones, of the order of or larger than the size of the solar system. We discuss here the relation between long range tests of the Newton law and the anomaly recorded on Pioneer 10/11 probes.

Results from an almost twenty years study of radiometric data from Pioneer 10/11, Galileo and Ulysses spacecraft indicate an anomalous time depending blueshift^{1, 2} which bares hardly prosaic explanations. Local manifestation of the expansion of the universe or new force terms are not favored either by the observational data. So, we explore the possibility that the reported anomaly, referred to as the "Pioneer anomaly", does not result from a real change in velocity. It turns out that the main Pioneer anomaly may be looked at as a new validation of general relativity (GR) in the weak field and low velocity limit on account of the "machian" behavior of quintessence like dark energy.

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 nonlinearity 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.

The Pioneer 10/11 spacecraft yielded the most precise navigation in deep space to date. However, their radiometric 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 × 10^-9Hz/s and can be interpreted as a constant sunward acceleration of each particular spacecraft of a_P = (8.74±1.33) × 10^-10m/s² (or, alternatively, a time acceleration of a_t = (2.92±0.44) × 10^-18s/s²). This signal has become known as the Pioneer anomaly; the nature of this anomaly remains unexplained. We discuss the current state of the efforts to retrieve the entire data sets of the Pioneer 10 and 11 radiometric Doppler data. We also report on the availability of recently recovered telemetry files that may be used to reconstruct the engineering history of both spacecraft using original project documentation and newly developed software tools. We discuss possible ways to further investigate the discovered effect using these telemetry files in conjunction with the analysis of the much extended Pioneer Doppler data. In preparation for this new upcoming investigation, we summarize the current knowledge of the Pioneer anomaly and review some of the mechanisms proposed for its explanation. We emphasize the main objectives of this new study, namely (i) analysis of the early data that could yield the true direction of the anomaly and thus, its origin, (ii) analysis of planetary encounters, which should say more about the onset of the anomaly (e.g. Pioneer 11's Saturn flyby), (iii) analysis of the entire dataset, which should lead to a better determination of the temporal behavior of the anomaly, (iv) comparative analysis of individual anomalous accelerations for the two Pioneers with the data taken from similar heliocentric distances, (v) the detailed study of on-board systematics, and (vi) development of a thermal-electric-dynamical model using on-board telemetry. The outlined strategy may allow for a higher accuracy solution for the anomalous acceleration of the Pioneer spacecraft and, possibly, will lead to an unambiguous determination of the origin of the Pioneer anomaly.

In this work, we study the gravitational influence of the material extending from Uranus orbit to the Kuiper belt and beyond on objects moving within these regions. We conclude that a density distribution given by generates a constant acceleration towards the Sun on those objects, which, with the proper amount of mass, accounts for the blue shift detected on the Pioneers space crafts. We also discuss the effect of this gravitational pull on Neptune, and comment on the possible origin of such a matter distribution.

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.

Concept considerations for a space mission with the objective of precisely testing the gravitational motion of a small test mass in the solar system environment are presented. In particular, the mission goal is an unambiguous experimental verification or falsification of the Pioneer anomaly effect. A promising concept is featuring a passive reference mass, shielded or well modeled with respect to nongravitational accelerations and formation flying with a rather standard deep space probe. The probe provides laser ranging and angular tracking to the reference mass, ranging to Earth via the radio-communication link and shielding from light pressure in the early parts of the mission. State-of-the-art ranging equipment can be used throughout, but requires in part optimization to meet the stringent physical budget constraints of a deep space mission. Mission operation aspects are briefly addressed.

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 the capability to preserve compatibility with existing gravity tests while opening free space for the Pioneer anomaly. They constitute arguments for new mission designs and new space technologies as well as for having a new look at data of already-performed experiments.

Independently developed orbit determination software is employed to analyze the orbits of Pioneer 10 and 11 using Doppler data. The analysis takes into account the gravitational fields of the Sun and planets using the latest JPL ephemerides, accurate station locations, signal propagation delays (e.g. the Shapiro delay, atmospheric effects), the spacecraft's spin, and maneuvers. New to this analysis is the ability to utilize telemetry data for spin, maneuvers, and other on-board systematic effects. Using data that were analyzed in prior JPL studies,^1,2 the anomalous acceleration of the two spacecraft is confirmed. We are also able to put limits on any secondary acceleration (i.e. jerk) terms. The tools that were developed will be used in the upcoming analysis of recently recovered Pioneer 10 and 11 Doppler data files.

Given some assumptions, it is possible to derive the most general post-general relativistic theory of gravity for the distant field of a point mass. The force law derived from this theory contains a Rindler term in addition to well-known contributions, a Schwarzschild mass and a cosmological constant. The same force law recently was confronted with solar system precision data. The Rindler force, if present in Nature, has intriguing consequences for gravity at large distances. In particular, the Rindler force is capable of explaining about 10% of the Pioneer anomaly and simultaneously ameliorates the shape of galactic rotation curves.

Validity of general relativity has been confirmed at distance scales ranging from the millimeter to the size of planetary orbits. But windows remain open for potential violations at shorter or longer scales. The anomalous acceleration recorded on Pioneer 10/11 probes on their escape trajectories outwards the solar system might constitute a first hint that gravity laws should be modified at large scales.

The anomalous acceleration recorded on Pioneer 10/11 probes on their escape trajectories outwards the solar system might constitute a first hint that gravity laws should be modified at large scales. But the modification needed to accomodate the Pioneer anomaly has to remain compatible with other gravity tests in the solar system. This question is discussed in the framework of metric extensions of General Relativity.

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 the capability to preserve compatibility with existing gravity tests while opening free space for the Pioneer anomaly. They constitute arguments for new mission designs and new space technologies as well as for having a new look at data of already-performed experiments.

Concept considerations for a space mission with the objective of precisely testing the gravitational motion of a small test mass in the solar system environment are presented. In particular, the mission goal is an unambiguous experimental verification or falsification of the Pioneer anomaly effect. A promising concept is featuring a passive reference mass, shielded or well modeled with respect to nongravitational accelerations and formation flying with a rather standard deep space probe. The probe provides laser ranging and angular tracking to the reference mass, ranging to Earth via the radio-communication link and shielding from light pressure in the early parts of the mission. State-of-the-art ranging equipment can be used throughout, but requires in part optimization to meet the stringent physical budget constraints of a deep space mission. Mission operation aspects are briefly addressed.

General relativity is not yet consistent. Pauli has misinterpreted Einstein’s 1916 equivalence principle that can derive a valid field equation. The Wheeler School has distorted Einstein’s 1916 principle to be his 1911 assumption of equivalence, and created new errors. Moreover, errors on dynamic solutions have allowed the implicit assumption of a unique coupling sign that violates the principle of causality. This leads to the space-time singularity theorems of Hawking and Penrose who “refute” applications for microscopic phenomena, and obstruct efforts to obtain a valid equation for the dynamic case. These errors also explain the mistakes in the press release of the 1993 Nobel Committee, who was unaware of the non-existence of dynamic solutions. To illustrate the damages to education, the MIT Open Course Phys. 8.033 is chosen. Rectification of errors confirms that E = mc² is only conditionally valid, and leads to the discovery of the charge-mass interaction that is experimentally confirmed and subsequently the unification of gravitation and electromagnetism. The charge-mass interaction together with the unification predicts the weight reduction (instead of increment) of charged capacitors and heated metals, and helps to explain NASA’s Pioneer anomaly and potentially other anomalies as well.

The formula for periastron advance/perihelion advance of Mercury is not original nor unique to GR. It was first derived, and shown to work for the Mercury example, by Paul Gerber in 1898 and his follow-up paper of 1902 (republished 1917), on the basis of gravitational communication being at velocity c. This physical view differs importantly from that espoused in General Relativity, so its incorporation, unacknowledged, by Einstein into his GR equations of 1915 constitutes an omission for GR, questioning its vaunted status as a physically consistent body of theory. However Einstein himself said GR was ‘just a convenient stopping place.’ Continuum Theory (CT) on the other hand, finds that gravitation is one of the electromagnetic family of forces, with the expectation that its communication is at velocity c or a simple multiple thereof.