Phased observations are needed for a variety of purposes.  The most complicated one is the case of an eclipsing binary or an explanetary transit, shown here.

The times of the periodic phenomena are assumed to be given by an initial time, T0, a period P0, and an event number E such that the reference time of the event is given by t0 = T0+E*P0.  This could be the time of mid-eclipse/mid-transit, for instance.

One presumedly wants to start some time before the event and cover the object either for a given amount of time or until the measurement is symmetric around the reference time.  The MONET/Central portal captures this constraint in terms of the following: