ABSTRACT. In the present work, we define the concept of a “moon”, which is a generalization of the fundamental notion of a sun. We are especially interested in determining those normed linear spaces in which every moon is a sun. Knowledge of such spaces is often quite useful in practice since it is generally much easier to verify that a given set is a moon than verify it is a sun. Our approach to this problem is via certain geometric properties of the points of the unit sphere, in particular being “nonlunar”, “strongly nonlunar”, or “quasi-polyhedral” (in order of decreasing generality).