This thesis presents a framework to solve optimal control problems for hypersonic mission design and to perform sensitivity analyses of the optimal trajectory. The framework discretizes the optimal control problem using Radau pseudospectral collocation and solves the resulting nonlinear program using an interior-point method. This discretization enables accurate approximation of continuous Lagrange multipliers via a costate mapping, which is important for discretization error and sensitivity analysis. An atmospheric re-entry problem in two-dimensional flight with pointwise state constraints, path constraints, and control via angle of attack is solved. Models for lift, drag, etc. in the dynamics are vehicle-dependent and ultimately need to be extracted from large-scale CFD simulations at suitably chosen flight configurations. Because these models are not exact, optimality sensitivity studies are performed. The framework is designed to support the ultimate goal of computing hypersonic vehicle mission designs with more complex surrogate models and using optimality sensitivity to construct surrogates.