Decay-optimal lift-based adjustments of the orbital plane in Very Low Earth Orbits

Very Low Earth Orbits (VLEOs) present a compelling trade-off between the benefits of high-resolution imaging and low-latency communication, and the challenge of rapid orbital decay from atmospheric drag. While propellant-less orbital plane adjustments using aerodynamic lift are possible, mission duration depends critically on executing these manoeuvres efficiently, i.e., with minimal altitude loss. Existing analytical guidance laws for lift-based adjustments fail to adequately account for this decay, often necessitating computationally expensive numerical optimization. This article presents novel, decay-optimal analytical guidance laws derived with Pontryagin’s Minimum Principle, assuming a quadratic drag polar. The optimal control profile for the lift coefficient is shown to be a simple trigonometric function of the argument of latitude, with its shape being independent of atmospheric density and aerodynamic characteristics. Comparison with high-fidelity numerical optimization validates the analytical laws, showing high accuracy for manoeuvres involving small sideslip angles. Deviations grow with control effort as the practical quadratic drag polar assumption becomes less precise. Further, coupling effects between secular drifts induced by the J 2 perturbation and the achievable changes in RAAN are revealed. The analytical formulation provides crucial physical insight, revealing the control’s direct dependence on geometric efficiency. It promises to be a practical tool for efficient mission planning and a valuable initial guess for numerical solvers. • An analytic decay-optimal control law for aerodynamic inclination and RAAN changes in VLEO is derived using Pontryagin’s Maximum Principle. • Advantages in terms of decay reduction over existing constant-lift strategies are demonstrated. • The guidance laws are compared to results obtained via numerical optimization. • Critical insights into the practicality of relevant application scenarios are obtained.