Multiscale gravitational astronomy in the Gaia era. The Milky Way and its constituents as Einstein's paradigm.

Highly accurate astrometric measurements in space force fundamental astronomy to move from the classical paradigm, responding to Newton's gravity, to that of Einstein's General Relativity, the current theory of gravity. As a matter of fact, general relativistic models at the very core of Gaia data analysis guarantee the quality of the scientific products that span from the fraction-of-a-parsec scale of the Solar System to the two tens of kpc of that of the Milky Way to comprise, among many others, even fundamental physics tests. With a relativistic-compliant astrometry delivered by Gaia, the question before us is to what extent the reconstruction of our Galaxy, $i.e.$, Gaia's main goal, is dictated by General Relativity or Newton dynamics. The answer would assure a coherent local cosmological laboratory for the predictions of the Lambda-CDM model at the Milky Way scale. Besides that, at the observer's scale, gravitational astrometry offers new tools to observe tiny variations in the fabric of space-time induced by passing gravitational waves, to infer their strength and pinpoint ---with unprecedented precision--- the direction to the gravitational source for a complete multi-length profile.