Improved Edelbaum's Approach to Optimize Low Earth/Geostationary Orbits Low-Thrust Transfers

Abstract

Edelbaum's approach to the optimization of low-thrust transfers is revisited and some simplifications are removed. The variation of the spacecraft mass due to the propellant consumption is considered in the case of constant thrust, and the corresponding numerical result is compared with Edelbaum's solution. The approach is then extended to consider variable specific impulse and thrust magnitude with constant power level. The payload increment is first computed maintaining Edelbaum's suboptimal control strategy (i.e., constant-thrust direction during each half-revolution). An analytical solution of the quasi-circular one-revolution transfer is then found using the optimal control of both the thrust direction and magnitude. The very-low-thrust multirevolution problem is easily solved by assembling many one-revolution basic trajectories; in particular, the transfer from a 28.5 deg inclined low Earth orbit to the equatorial geostationary orbit is considered. Exact numerical solutions for both constant and variable specific impulse have also been obtained using an indirect optimization method: the accuracy of the solution based on the quasi-circular approximation has been verified.

Closed form optimal continuous guidance scheme for new dynamic of electrical propulsion plane change transfers

“…In reference [9], the original Edelbum theory is revisited by extending, completing, and deriving the yaw steering expressions without ambiguity and recasting the theory within the framework of optimal control for minimum time. In reference [10], the authors reexamine Edelbum's approach and some improvements are introduced, while maintaining the assumption of quasi-circular orbits. Also, trajectories with variable thrust and specific impulse at constant power are analysed.…”

Combined high and low-thrust geostationary orbit insertion with radiation constraint

“…The use of low-thrust electric propulsion (EP) on-board telecommunications spacecraft in Geostationary orbit (GEO) for station-keeping is well-established. Similarly, GEO orbit insertion using only low-thrust electric propulsion has been extensively studied [1][2][3][4][5][6][7][8][9][10][11][12][13]. In the frame of Horizon 2020 project HYPROGEO, which aims to develop synergies between electrical and hybrid propulsion (solid polyethylene fuel with high concentration liquid H2O2 oxidizer) systems, in this paper the use of the EP systems is considered in combination with a high-thrust propulsion system for application to the propellant-optimal GEO insertion problem, whilst considering both temporal and radiation flux constraints.…”

Design and optimization of low-thrust orbital phasing maneuver

“…Edelbaum suggested that changing station using tangential thrust is the most effective approach [4]. On the basis of Edelbaum's approach, the trajectory from one circular orbit to another is optimized under the assumption of quasi-circular orbits [2,10,13]. In addition, the phasing mission between different orbits has been investigated by many researchers.…”