Direct measurement of acceleration is a key scientific goal for both cosmology and exoplanets. For cosmology, the concept of redshift drift (more than 60 years old by the 2020s) could directly establish the Friedmann-Lema{\^\i}tre-Robertson-Walker model. It would increase the dark energy figure of merit by a factor of 3 beyond Stage 4 experiments, in combination with cosmic microwave background measurements. For exoplanets, the same technology required provides unprecedented radial velocity accuracy, enabling detection of Earth mass planets in the habitable zone. Other science cases include mapping the Milky Way gravitational potential and testing its dark matter distribution.