Continuous-Thrust Circular Orbit Phasing Optimization of Deep Space CubeSats

The recent technology advancements in miniaturizing the primary components of spacecraft allow the classic CubeSats to be considered as a valid option in the design of a deep space scientific mission, not just to support a main typical interplanetary spacecraft. In this context, the proposed ESA M-ARGO mission, whose launch is currently planned in 2026, will use the electric thruster installed onboard of a 12U CubeSat to transfer the small satellite from the Sun-Earth second Lagrangian point to the orbit of a small and rapidly spinning asteroid. Starting from the surrogate model of the M-ARGO propulsion system proposed in the recent literature, this paper analyzes a simplified thrust vector model that can be used to study the heliocentric optimal transfer trajectory with a classical indirect approach. This simplified thrust model is a variation of the surrogate one used to complete the preliminary design of the trajectory of the M-ARGO mission, and it allows to calculate, in an analytical form, the typical Euler-Lagrange equations without singularities. The thrust model is then used to study the performance of a M-ARGO-type CubeSat (MTC) in a different scenario (compared to that of the real mission), in which the small satellite moves along a circular heliocentric orbit in the context of a classic phasing maneuver. In this regard, the work discusses a simplified study of the optimal constrained MTC transfer towards one of the two Sun-Earth triangular Lagrangian points. Therefore, the contributions of this paper are essentially two: the first is the simplified thrust model that can be used to analyze the heliocentric trajectory of a MTC; the second is a novel mission application of a CubeSat, equipped with an electric thruster, moving along a circular heliocentric orbit in a phasing maneuver.