  Sky survey telescopes and powerful targeted telescopes play complementary
roles in astronomy. In order to investigate the nature and characteristics of
the motions of very faint objects, a flexibly-pointed instrument capable of
high astrometric accuracy is an ideal complement to current astrometric surveys
and a unique tool for precision astrophysics. Such a space-based mission will
push the frontier of precision astrometry from evidence of Earth-mass habitable
worlds around the nearest stars, to distant Milky Way objects, and out to the
Local Group of galaxies. As we enter the era of the James Webb Space Telescope
and the new ground-based, adaptive-optics-enabled giant telescopes, by
obtaining these high precision measurements on key objects that Gaia could not
reach, a mission that focuses on high precision astrometry science can
consolidate our theoretical understanding of the local Universe, enable
extrapolation of physical processes to remote redshifts, and derive a much more
consistent picture of cosmological evolution and the likely fate of our cosmos.
Already several missions have been proposed to address the science case of
faint objects in motion using high precision astrometry missions: NEAT proposed
for the ESA M3 opportunity, micro-NEAT for the S1 opportunity, and Theia for
the M4 and M5 opportunities. Additional new mission configurations adapted with
technological innovations could be envisioned to pursue accurate measurements
of these extremely small motions. The goal of this White Paper is to address
the fundamental science questions that are at stake when we focus on the
motions of faint sky objects and to briefly review instrumentation and mission
profiles.
