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 linear-in-T form, which is a good approximation for every realistic case, we extract the spherical solutions of the theory. Using these spherical solutions to describe the Sun's gravitational field, we use recently determined supplementary advances of planetary perihelia, to infer upper bounds on the allowed f (T) corrections. We find that the maximal allowed divergence of the gravitational potential in f (T) gravity from that in the teleparallel equivalent of General Relativity is of the order of 6.2 × 10 −10 , in the applicability region of our analysis. This is much smaller than the corresponding (significantly small too) divergence that is predicted from cosmological observations, as expected. Such a tiny allowed divergence from the linear form should be taken into account in f (T) model building.

Recent years have seen increasing efforts to directly measure some aspects of the general relativistic gravitomagnetic interaction in several astronomical scenarios in the solar system. After briefly overviewing the concept of gravitomagnetism from a theoretical point of view, we review the performed or proposed attempts to detect the Lense-Thirring effect affecting the orbital motions of natural and artificial bodies in the gravitational fields of the Sun, Earth, Mars and Jupiter. In particular, we will focus on the evaluation of the impact of several sources of systematic uncertainties of dynamical origin to realistically elucidate the present and future perspectives in directly measuring such an elusive relativistic effect.

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. general relativity and gravitation; classical general relativity; gravitational waves; quantum gravity; cosmology; experimental studies of gravity PACS classifications: 04.; 04.20.-q; 04.30.-w; 04.60.-m; 98.80.-k; 04.80.-y

In the original LARES mission the general relativistic Lense-Thirring effect would be detected by using as observable the sum of the residuals of the nodes of the existing passive geodetic laser-ranged LAGEOS satellite and of its proposed twin LARES. The proposed nominal orbital configuration of the latter one would reduce the systematic error due to the mismodelling in the even zonal harmonics of the geopotential, which is the main source of error, to 0.3%, according to the most recent Earth gravity model EGM96. This observable turns out to be sensitive to possible departures of the LARES orbital parameters from their nominal values due to the orbital injection errors. By adopting a suitable combination of the orbital residuals of the nodes of LAGEOS, LAGEOS II and LARES and the perigees of LAGEOS II and LARES it should be possible to reduce the error due to the geopotential by one order of magnitude, according to the EGM96 gravity model. Moreover, the sensitivity to the orbital injection errors should be greatly reduced. According to a preliminary estimate of the error budget, the total error of the experiment should be reduced to less than 1%. In the near future, when the new data of the terrestrial gravitational field from the CHAMP and GRACE missions will be available, a further increase in the accuracy should be obtained. The proposal of placing LARES in a polar 2,000 km altitude orbit and considering only its nodal rate would present the drawback that even small departures from the polar geometry would yield notable errors due to the mismodelled even zonal harmonics of the geopotential, according to the EGM96 model.

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 10 4 higher than the best current result. The mission is based on a satellite carrying cold atombased 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