Analytical Planet-Centred Solar-Sail Trajectory Prediction with the Stark Model

Abstract

Planet-centred solar sailing offers a propellantless way of sustaining non-Keplerian motion for Earth-centred missions. For preliminary mission design and broad trade-space exploration, rapid yet accurate trajectory propagation tools are required. This work evaluates the performance of the Stark model, an analytical formulation that represents the dynamics as two-body motion subject to a uniform perturbing acceleration, applied to controlled solar-sail trajectories and benchmarked against classical numerical integration. Two control strategies for the sail are considered: (i) constant cone-angle laws, for which the Stark solution enables direct state evaluation, and (ii) time-varying locally optimal steering laws designed to target individual Keplerian elements. Performance is assessed in terms of positional accuracy and computational cost over representative one-day propagations. For constant control laws, accuracy is shown to improve with increasing perturbation magnitude, corresponding to larger sail lightness numbers and smaller cone angles. Sensitivity analyses reveal that smaller semi-major axes and larger eccentricities lead to faster dynamical regimes, resulting in increased position error and higher computational cost. For time-varying control laws, the Stark model’s performance depends strongly on the smoothness of the control law: smooth profiles (semi-major axis-, eccentricity-, and argument of periapsis-raising) yield broader regions of superiority in the accuracy-cost trade space compared to numerical integration, whereas abrupt profiles (inclination- and right ascension of the ascending node-raising) significantly reduce these regions. Furthermore, larger lightness numbers diminish the model’s ability to capture rapid dynamics, owing to the restriction of fixed step sizes. Overall, the results demonstrate that the Stark model provides a computationally efficient alternative for preliminary planet-centred solar-sail trajectory design, with advantages over classical numerical integration methods in specific regions of the accuracy-cost trade-off space, particularly for smooth control regimes.