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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…

The anomalous acceleration of Pioneer 10 is presented as a calculation using a simple optical model. The model is based on the bending of background gravity behind the Sun in the same way that light is bent by the Sun. Structures of…

Relationship between the speed of gravity c_g and the speed of light c_e in the bi-metric theory of gravity is discussed. We reveal that the speed of light is a function of the speed of gravity which is a primary fundamental constant. Thus,…

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…

We develop a new model for the Universe based on two key assumptions: first, the inertial energy of the Universe is a constant, and second, the total energy of a particle, the inertial plus the gravitational potential energy produced by the…

Anderson, et al. find the measured trajectories of Pioneer 10 and 11 spacecraft deviate from the trajectories computed from known forces acting on them. This unmodelled acceleration (and the less well known, but similar, unmodelled torque)…

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…

The OPERA collaboration has announced to have observed superluminal neutrinos with a mean energy 17.5 GeV, but afterward the superluminal interpretation of the OPERA results has been refuted theoretically by Cherenkov-like radiation and…

The invariance of the speed of light in all inertial frames is shown to be an inevitable consequence of the relativity principle of special relativity contrary to the view held by Hsu and Hsu in taiji relativity where the speed of light is…

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…

It is proposed that the recently reported anomalous acceleration acting on the Pioneers spacecrafts should be a consequence of the existence of some local curvature in light geodesics when using the coordinate speed of light in an expanding…

We show that the Supernovae results, implying evidence for an accelerating Universe, may be closely related to the recent discovery of redshift dependence in the fine structure constant $\alpha$. The link is a class of varying speed of…

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…

Testing the constancy of the gravitational constant G has been a longstanding fundamental question in natural science. As first suggested by Jofr\'{e}, Reisenegger and Fern\'{a}ndez [1], Dirac's hypothesis of a decreasing gravitational…

Recently, Jaekel and Reynaud put forth a metric linear extension of general relativity which, in the intentions of its proponents, would be able, among other things, to provide a gravitational mechanism for explaining the Pioneer anomaly…

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…

The analysis of the data from the distant supernovae (A.Riess et al, Astron.J. {\bf 116}, 1009, (1988)) for acceleration of the expending Universe from the viewpoint of the gravitation equations proposed by one of the authors (Phys.Lett.…

A collection is made of presently unexplained phenomena within our Solar system and in the universe. These phenomena are (i) the Pioneer anomaly, (ii) the flyby anomaly, (iii) the increase of the Astronomical Unit, (iv) the quadrupole and…

Current constraints on photon velocity variability are summarized and displayed in terms of an energy dependent vacuum refraction index. It is shown that the energy-momentum balance of high energy Compton scattering is very sensitive to the…

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…