  In this paper we develop an analytical expression relating the sensitivity to
a periodic signal to the duration and accuracy of a given set of data. The
effects of windowing are explored, and also the sensitivity to periods longer
than the total length of observations. As specific examples, we outline the
performance of our technique on large amplitude and large eccentricity radial
velocity signals recently discussed in the literature and we delineate the
region explored by the measurements of 14 single stars made over a twelve year
period by Walker et al. (1995). Had any of these stars shown motion like that
caused by the exo-planets recently detected, it would have been easily
detected. Finally, we suggest an observing strategy for future large radial
velocity surveys which, if implemented, will allow coverage of the largest
range of parameter space with the smallest amount of observing time per star.
We suggest that about 10-15 measurements be made of each star in the first two
years of the survey, then 2--3 measurements per year thereafter, provided no
(or slow) variation is observed. More frequent observations would of course be
indicated if such variations were present.
