Modern technological developments have pushed the accuracy of astrometric measurements in the visible band down to the micro-arcsec level. This allows to test theories of gravity in the weak field limit to unprecedented level, with possible consequences spanning from the validity of fundamental physics principles, to tests of theories describing cosmological and galactic dynamics without resorting to Dark Matter and Dark Energy.This is the main goal of Astrometric Gravitation Probe (AGP) mission, which will be achieved by highly accurate astrometric determination of light deflection (as a modern rendition of the Dyson, Eddington, and Robertson eclipse experiment of 1919), aberration, and of the orbits of selected Solar System objects, with specific reference to the excess shift of the pericentre effect.The AGP concept was recently proposed for the recent call for ESA M4 missions as a collaboration among several scientists coming from many different European and US institutions. Its payload is based on a 1.15 m diameter telescope fed through a coronagraphic system by four fields, two set in symmetric positions around the Sun, and two in the opposite direction, all imaged on a CCD detector. Large parts of the instrument are common mode to all fields. The baseline operation mode is the scan of the ±1.13 deg Ecliptic strip, repeated for a minimum of 3 years and up to an optimal duration of 5 years. Operations and calibrations are simultaneous, defined in order to ensure common mode instrumental effects, identified and removed in data reduction. The astrometric and coronagraphic technologies build on the heritage of Gaia and Solar Orbiter.We review the mission concept and its science case, and discuss how this measurement concepts can be scaled to different mission implementations.