This paper provides an analytical derivation of the observability conditions for in-orbit bearings-only navigation that can also be used to solve for the conditions under which unobservable maneuvers occur. The derivation is performed in a rigorous yet relatively simple manner by attempting to solve for the initial conditions in a discrete formulation of the problem. This newly proposed criterion is then used to derive the necessary and sufficient conditions for observability, previously established in the literature through a geometric interpretation of the problem. Moreover, the proposed scheme is used to mathematically derive this geometrical interpretation, thus providing an alternate derivation that reinforces these already established concepts. In addition, a new framework is proposed that allows solving for the unobservable maneuvers sets of a given type. This result, which can be directly applied to many maneuver types and easily extended to different maneuvering schemes, is demonstrated for the c...