The time interval description is a natural way to introduce finite intervals, like finite time intervals. This approach depends on results for radiation propagation from star sources, where properties relate to a propagation surface, which is finite for every realistic event and measurement. In contrast the usual vector approach like for Newton’s laws depends on introducing an infinite coordinate system. A time interval only approach necessarily has to start from scratch. Properties for time intervals have to be defined with time intervals. Where the first parts of this paper are devoted to time interval set properties, in the discussion part these are applied to quantities and measurements within astronomy. The introduction provides a survey of results.