Engineering design problems often contain correlations and tradeoffs that may or may not be obvious or well-understood. As design problem complexity increases, decision makers find it more and more difficult to grasp these trade-offs effectively. The rapid growth of computing power now allows the simulation of millions of design alternatives, and the ability to effectively visualize these alternatives and understand the tradeoffs associated with them has never been more important. Trade space visualization tools are designed to aid decision makers by allowing them to effectively explore a design space and grasp the underlying tradeoffs and nuances particular to their specific problem. These tools provide great potential in evaluating complex dynamical systems in the aerospace industry, among others. In this paper, we apply our trade space visualization software, the Applied Research Lab Trade Space Visualizer (ATSV), to search for optimal constant thrust and constant acceleration orbit transfers. This problem is formulated as a multiobjective optimization problem where it is desirable to explore various competing objectives. First, we identify a known opti mal solution and explore the input space to search for other optimal or near-optimal trajectories. The problem is then modified to include the discrete hardware-side design variable, engine type, and optimal solutions are found for each corresponding design variable option. Finally, a study is performed to understand the sensitivity of found optimal trajectories to perturbations of the initial orbit.