We use recent observations of Solar system orbital motions in order to constrain f(T) gravity. In particular, imposing a quadratic f(T) correction to

The present Editorial introduces the Special Issue dedicated by the journal Universe to the General Theory of Relativity, the beautiful theory of gravitation of Einstein, a century after its birth. It reviews some of its key features in a historical perspective, and, in welcoming distinguished researchers from all over the world to contribute it, some of the main topics at the forefront of the current research are outlined.

The Einstein Gravity Explorer mission (EGE) is devoted to a precise measurement of the properties of space-time using atomic clocks. It tests one of the most fundamental predictions of Einstein’s Theory of General Relativity, the gravitational redshift, and thereby searches for hints of quantum effects in gravity, exploring one of the most important and challenging frontiers in fundamental physics. The primary mission goal is the measurement of the gravitational redshift with an accuracy up to a factor 10⁴ higher than the best current result. The mission is based on a satellite carrying cold atom-based clocks. The payload includes a cesium microwave clock (PHARAO), an optical clock, a femtosecond frequency comb, as well as precise microwave time transfer systems between space and ground. The tick rates of the clocks are continuously compared with each other, and nearly continuously with clocks on earth, during the course of the 3-year mission. The highly elliptic orbit of the satellite is optimized for the scientific goals, providing a large variation in the gravitational potential between perigee and apogee. Besides the fundamental physics results, as secondary goals EGE will establish a global reference frame for the Earth’s gravitational potential and will allow a new approach to mapping Earth’s gravity field with very high spatial resolution. The mission was proposed as a class-M mission to ESA’s Cosmic Vision Program 2015–2025.

Empirically determining the averaged variations of the orbital parameters of the stars orbiting the Supermassive Black Hole (SBH) hosted by the Galactic center (GC) in Sgr ${\mathrm{A}}^{*}$ is, in principle, a valuable tool to test the General Theory of Relativity (GTR), in regimes far stronger than those tested so far, and certain key predictions of it like the “no-hair” theorems. We analytically work out the long-term variations of all the six osculating Keplerian orbital elements of a test particle orbiting a nonspherical, rotating body with quadrupole moment $Q_2$ and angular momentum $\mathit{S}$ for a generic spatial orientation of its spin axis $\widehat{\mathit{k}}$. This choice is motivated by the fact that, basically, we do not know the position in the sky of the spin axis of the SBH in Sgr ${\mathrm{A}}^{*}$ with sufficient accuracy. We apply our results to S2, which is the closest star discovered so far having an orbital period $P_{\mathrm{b}}=15.98\mathrm{yr}$, and to a hypothetical closer star $X$ with $P_{\mathrm{b}}=0.5\mathrm{yr}$. Our calculations are quite general, not being related to any specific parameterization of $\widehat{\mathit{k}}$, and can be applied also to astrophysical binary systems, stellar planetary systems, and planetary satellite geodesy in which different reference frames, generally not aligned with the primary’s rotational axis, are routinely used.