Abstract:
Applying Newtonian dynamics in five dimensions rather than four, to a universe that is closed, isotropic and expanding,suggests that under certain circumstances an additional and previously unidentified acceleration, a_A, can arise affecting the four dimensional motion of spacecraft. The two cases of this acceleration being either real or virtual are considered. In the real case, simple estimates of a_A are shown to be in partial agreement with reported acceleration anomalies from several Earth flybys and from the Pioneer spacecraft. However, these estimates do not fully reconcile with radio Doppler tracking data. The virtual case, by contrast, appears to overcome these and other difficulties with the real case, and is discussed in an addendum. Furthermore, the virtual case has an altitude dependence which makes detection of any anomaly unlikely above ~2000 km. Equations governing this additional acceleration have been derived from first principles, without the introduction of free parameters or new constants and without amendment to the law of gravity.

Abstract:
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 spacecrafts, 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. By using our model, we explain the numerical coincidence between the value of the anomalous acceleration and the Hubble constant at the present epoch and also confirm our previous determination of the cosmological parameters ？ and . New Pioneer data are expected to be publicly available in the near future, which might enable more precise evaluations of these parameters. 1. Introduction The Pioneer 10 and 11 spacecrafts were launched in the early 1970s, to conduct explorations in the region of the solar system beyond the orbit of Mars and to perform close observations of Jupiter. They were also the first spacecraft to explore the outer solar system and to send back to Earth their navigational signals for almost thirty years (for a review see [1] and references therein). In recent years, the orbits of Pioneer 10 and 11 were reconstructed very accurately, by using the original radiometric Doppler tracking data, based on the signals exchanged between the spacecraft and NASA’s terrestrial tracking stations. This reconstruction yielded a persistent discrepancy between the observed and predicted data, equivalent to an unexplained small acceleration of the spacecraft in the direction of the Sun. This effect is evidenced by measuring a small frequency shift (toward higher frequencies, i.e., a “blueshift”) of the signal reaching us from the spacecraft. The nature of this anomalous acceleration or of the related blueshift remains unexplained; this effect has become known as the “Pioneer anomaly” ([2–4]). This is not the only known gravitational anomaly in the solar system, since several others are currently under investigation (for general reviews see [5, 6]), such as the secular increase of the astronomical unit [7], the anomalies in planetary flybys ([8–10]), the anomalous perihelion precession of Saturn ([11, 12]), the increase in the eccentricity of the Moon’s orbit ([13, 14]), and other effects related in general with ephemerides of planets and the Moon ([15, 16]). The importance of all these effects is not related to how they affect the spacecraft navigation, since they all produce very

Abstract:
We show that the anomalous acceleration of the Pioneer 10/11 spacecraft can be explained if there is some mirror gas or mirror dust in our solar system.

Abstract:
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% improvement in the residuals compared to a constant acceleration model; ii) although the direction of the acceleration remains imprecisely determined, we find no support in favor of a Sun-pointing direction over the Earth-pointing or along the spin-axis directions, and iii) support for an early "onset" of the acceleration remains weak in the pre-Saturn Pioneer 11 tracking data. We present these new findings and discuss their implications for the nature of the Pioneer anomaly.

Abstract:
The Pioneer anomaly stands for unexplained frequency shifts of the Doppler radio-tracking signals received at the ground stations from the Pioneer 10 and 11 spacecraft in disagreement with expectations based on model calculations. We consider here observations of Pioneer 10 at heliocentric distances between 40 ua and 70.5 ua over a time interval of 11.55 years from 1987 to 1998. The anomaly has been interpreted in the literature either as a Doppler shift caused by an apparent spacecraft deceleration not accounted for by known effects, or as an unexpected clock acceleration of the frequency standards at the ground stations. The reasons for the anomalous behaviour are not understood in both cases. Based on a gravitational impact model – requiring a secular mass increase of all massive bodies – a solution is proposed that implies a clock acceleration with a value close to that of the Hubble constant.

Abstract:
Doppler shift observations of spacecraft, such as Galileo, NEAR, Cassini, Rosetta and MESSENGER in earth flybys, have all revealed unexplained speed `anomalies' - that the doppler-shift determined speeds are inconsistent with expected speeds. Here it is shown that these speed anomalies are not real and are actually the result of using an incorrect relationship between the observed doppler shift and the speed of the spacecraft - a relationship based on the assumption that the speed of light is isotropic in all frames, i.e. invariant. Taking account of the repeatedly measured light-speed anisotropy the anomalies are resolved. The Pioneer 10/11 anomalies are discussed, but not resolved. The spacecraft observations demonstrate again that the speed of light is not invariant, and is isotropic only with respect to a dynamical 3-space. The existing doppler shift data also offers a resource to characterise a new form of gravitational waves, the dynamical 3-space turbulence, that has also been detected by other techniques.

Abstract:
The detected anomalous frequency drift acceleration in Pioneer's radar data finds its explanation in a Berry phase that obtains the quantum state of a photon that propagates within an expanding space-time. The clock acceleration is just the adiabatic expansion rate and an analogy between the effect and Foucault's experiment is fully suggested. In this sense, light rays play a similar role in the expanding space than Foucault's Pendulum does while determining Earth's rotation. On the other hand, one could speculate about a suitable future experiment at "laboratory" scales able to measure the local cosmological expansion rate using the procedure outlined in this paper.

Abstract:
Mindful of the anomalous perihelion precession of Mercury discovered by U. Le Verrier in the second half of the nineteenth century and its successful explanation by A. 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 bodies 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 cumulative science, as shown to us by the discovery of Neptune in the first half of the nineteenth century. 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; and h) The anomalous secular increase of the astronomical unit

Abstract:
The study of post-Einsteinian metric extensions of general relativity (GR), which preserve the metric interpretation of gravity while considering metrics which may differ from that predicted by GR, is pushed one step further. We give a complete description of radar ranging and Doppler tracking in terms of the time delay affecting an electromagnetic signal travelling between the Earth and a remote probe. Results of previous publications concerning the Pioneer anomaly are corrected and an annually modulated anomaly is predicted besides the secular anomaly. Their correlation is shown to play an important role when extracting reliable information from Pioneer observations. The formalism developed here provides a basis for a quantitative analysis of the Pioneer data, in order to assess whether extended metric theories can be the appropriate description of gravity in the solar system.

Abstract:
Doppler shift observations of spacecraft, such as Galileo, NEAR, Cassini, Rosetta and MESSENGER in earth flybys, have all revealed unexplained speed "anomalies" - that the Doppler-shift determined speeds are inconsistent with expected speeds. Here it is shown that these speed anomalies are not real and are actually the result of using an incorrect relationship between the observed Doppler shift and the speed of the spacecraft - a relationship based on the assumption that the speed of light is isotropic in all frames, viz invariant. Taking account of the repeatedly measured light-speed anisotropy the anomalies are resolved ab initio. The Pioneer 10/11 anomalies are discussed, but not resolved. The spacecraft observations demonstrate again that the speed of light is not invariant, and is isotropic only with respect to a dynamical 3-space. The existing Doppler shift data also offers a resource to characterise a new form of gravitational waves, the dynamical 3-space turbulence, that has also been detected by other techniques. The Einstein spacetime formalism uses a special definition of space and time coordinates that mandates light speed invariance for all observers, but which is easily misunderstood and misapplied.