How many random observations are needed for good phase coverage of a periodic source?

The specific problem considered is the number of radial velocity measurements required to obtain good estimates of physical parameters of binary star. It is assumed that observations are made at random binary phases. The loss of information due to poor phase coverage is explored, and a suggested limit on the largest acceptable gap introduced. The statistical distribution of maximum gap lengths can then be used to specify the minimum number of velocity measurements to obtain good phase coverage with a specified confidence limit. The effects of non-zero orbital eccentricity are discussed, as are the ramifications of having multiple binary targets. The theory is also applicable to the characterisation of the radial velocity curves induced by exoplanets on their host stars, provided that the periods and eccentricities are known (from e.g. transit observations).