Abstract: A telescope or other viewing instrument is controlled to optimally observe objects based on continuous or periodic determinations of whether geometrical or physical constraints are satisfied over specific intervals of time, including a cumulative determination of background light. A program stores results in data structures for algorithm matching and for simplified adjustment of constraint parameters. Preliminary visibility intervals are determined using geometrical or physical constraints to restrict the computation. Other constraints such as limiting cumulative background light flux are used to determine the resulting visibility intervals based on the preliminary visibility intervals. A device for scheduling observations based on the visibility intervals is described. A method for determining calibration of the off-axis attenuation of background light is defined.