AbstractA new technique is proposed, leading to two closely related instruments, the solar and stellar accelerometers. The principal fields of application are solar/stellar seismology and the search for extrasolar planets. The technique is fully specific: it cannot give the velocities themselves. The results are absolute : the measured accelerations are directly related to primary length and frequency standards. Essentially one makes use of a variable path Fabry-Pérot interferometer whose channelled spectrum is constrained by a servo loop to track the Doppler shifted astronomical spectrum. Then a tunable laser tracks the interferometer. The ultimately measured quantity is the beat frequency between the tunable laser and a stabilized one.A fundamental limit to the precision of radial velocity measurements, set by photon counts and the spectral profile itself, is established, and it is shown that the proposed technique closely approaches that limit. Hence it is considerably more sensitive than any other used so far, and holds the promise of making both planetary searches and the study of oscillations practical for a large number of stars.