  Context: The bright southern Cepheid RS Pup is surrounded by a circumstellar
nebula reflecting the light from the central star. The propagation of the light
variations from the Cepheid inside the dusty nebula creates spectacular light
echoes that can be observed up to large distances from the star itself. This
phenomenon is currently unique in this class of stars. Aims: For this
relatively distant star, the trigonometric parallax available from Hipparcos
has a low accuracy. A careful observation of the light echoes has the potential
to provide a very accurate, geometric distance to RS Pup. Methods: We obtained
a series of CCD images of RS Pup with the NTT/EMMI instrument, covering the
variation period of the star (P=41.4d). This allowed us to track the
progression of the light wavefronts over the nebular features surrounding the
star. We measured precisely the phase lag of the photometric variation in
several regions of the circumstellar nebula. Results: From our phase lag
measurements, we derived a geometric distance of 1992 +/- 28 pc to RS Pup. This
distance is affected by a total uncertainty of 1.4%, and corresponds to a
parallax of pi = 0.502 +/- 0.007 mas and a distance modulus of mu = 11.50 +/-
0.03. Conclusions: The geometric distance we derived is by far the most
accurate to a Cepheid, and among the most accurate to any star. RS Pup appears
both as somewhat neglected and particularly promising to investigate the
mass-loss history of Cepheids. Thanks to its highly accurate distance, it is
also bound to become an important luminosity fiducial for the long period part
of the period-luminosity diagram.
