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Over the last few years much attention has been given to the study of modified gravity theories in order to find a more natural explanation for the late time acceleration of the Universe. Nevertheless, a comparison of the matter power…

Lunar Laser Ranging (LLR) measurements are crucial for advanced exploration of the laws of fundamental gravitational physics and geophysics. Current LLR technology allows us to measure distances to the Moon with a precision approaching 1…

We consider the problem of parametrizing modified gravity theories that include an additional vector field in the sub-Hubble regime within the quasi-static approximation. We start from the most general set of second order equations for…

In this paper the possibility of measuring some general relativistic effects in the gravitational field of the Moon via selenodetic missions, with particular emphasis to the future Japanese SELENE mission, is investigated. For a typical…

Gravitational lensing serves as a powerful probe of compact astrophysical objects and dark matter distributions. As relativistic counterparts to photons, neutrinos experiencing lensing offer a complementary means to investigate the…

A argument is described for how deformed or doubly special relativity may arise in the semiclassical limit of a quantum theory of gravity. We consider a generic quantum theory of gravity coupled to matter, from which we use only the…

A discrete and exact algorithm for obtaining planetary systems is derived in a recent article (Eur. Phys. J. Plus 2022, 137:99). Here the algorithm is used to obtain planetary systems with forces different from the Newtonian inverse square…

In gravity theories derived from a f(R) Lagrangian, matter is usually supposed to be minimally coupled to the metric, which hence defines a ``Jordan frame.'' However, since the field equations are fourth order, gravity possesses an extra…

Gravitomagnetic field is covariantly split in the {\it intrinsic} and {\it extrinsic} parts, which are generated by rotational and translational currents of matter respectively. The {\it intrinsic} component has been recently discovered in…

The effects of Horava-Lifshitz corrections to the gravito-magnetic field are analyzed. Solutions in the weak field, slow motion limit, referring to the motion of a satellite around the Earth are considered. The post-newtonian paradigm is…

In a modified gravity theory, the propagation equation of gravitational waves will be presented in a non-standard way. Therefore this tenor mode perturbation of time-space, as a complement to the scalar mode perturbation, provides a unique…

In this paper the Randall-Sundrum model with brane-localized curvature terms is considered. Within some range of parameters a compact extra dimension in this model can be astronomically large. In this case the model predicts small deviation…

We consider a long range scalar force that mainly couples to dark matter and unstable Standard Model states, like the muon, with tiny strength. Probing this type of force would present a challenge to observations. We point out that the…

In this paper, we study gravitational waves generated by binary systems within an extension of General Relativity which is described by the addition of quadratic in curvature tensor terms to the Einstein-Hilbert action. Treating quadratic…

The Mathisson-Papapetrou equations in Kerr's background are considered. The region of existence of highly relativistic planar circular orbits of a spinning particle in this background and dependence of the particle's Lorentz $\gamma$-factor…

Possible explanations of the recently reported anomalous increase of the eccentricity of the lunar orbit are sought in terms of classical Newtonian mechanics, general relativity, and long-range modifications of gravity.

Cosmologically motivated theories that explain small acceleration rate of the Universe via modification of gravity at very large, horizon or super-horizon distances, can be tested by precision gravitational measurements at much shorter…

A small mass \mu in orbit about a much more massive black hole M moves along a world line that deviates from a geodesic of the black hole geometry by O(\mu/M). This deviation is said to be caused by the gravitational self-force of the…

We consider the massive graviton phenomenological model based on the graviton's dispersion terms included into phase of gravitational wave's waveform. Such model was already considered in many works but it was based on a single…

The environment on the Moon has numerous features that make it interesting not only for the study of astrophysical phenomena, but also elementary particle physics. In fact, vacuum conditions, low gravity, and exposure to a relatively…