This paper presents a multi-objective trajectory optimisation under uncertainty for the ascent and descent flight paths for the first stage of a two-stage, semi-reusable space launch system. Using Orbital Access' Orbital 500-R launcher as a test case, within the preliminary design phase, robust multi-disciplinary design optimisation is being used to analyse the tradeoffs with both the vehicle and system design and operation. An area of focus is on the predicted aerodynamic performance, and its impact on the design and planned mission scenarios. The model uncertainties are quantified for the atmospheric model and aerodynamic surrogate models and integrated into the optimal control solver MODHOC extended by the addition of an unscented transformation to handle the uncertainties. A multi-objective optimisation under uncertainty is run, examining the Pareto-optimal sets for the ascent and descent trajectories of the first stage spaceplane.