This paper presents a novel sensor management framework to effectively monitor Resident Space Objects (RSOs) for Space Situational Awareness (SSA) applications. The central idea of the proposed methodology is to make use of information geometry for the characterization of current state of knowledge (situational awareness), which is used for the purpose of optimal sensor management. Recently developed Conjugate Unscented Transformation (CUT) method has been exploited to accurately and efficiently propagate non-Gaussian orbit state uncertainty and compute information metrics. Finally, an optimization problem is posed to solve for optimal sensing action while accounting for orbital state uncertainty. Numerical simulations are performed which illustrate the effectiveness of the proposed methodology in comparison to conventional methods which assume orbital density function to be Gaussian.