Skip to main content Accessibility help
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 12
  • Print publication year: 2010
  • Online publication date: December 2010

5 - Low-Thrust Trajectory Optimization Using Orbital Averaging and Control Parameterization


Introduction and Background

It is well known that spacecraft propelled by low-thrust electric propulsion (EP) can potentially deliver a greater payload fraction compared to vehicles propelled by conventional chemical propulsion. The increase in payload fraction for EP systems is due to its much higher specific impulse (Isp) or engine exhaust velocity, which is often an order of magnitude greater than the Isp for a chemical system. However, optimizing low-thrust orbit transfers is a challenging problem due to the low control authority of the EP system and the existence of long powered arcs and subsequent multiple orbital revolutions. Therefore, obtaining optimal transfers is sometimes tedious and time consuming. In his seminal paper, Edelbaum presented analytical solutions for optimizing continuous-thrust transfers between inclined circular Earth orbits. These results serve as an excellent preliminary design tool for estimating ΔV and transfer time for low-thrust missions with continuous thrust and quasi-circular transfers. Real solar electric propulsion (SEP) spacecraft, however, experience periods of zero thrust during passage through the Earth's shadow, and this major effect is not accommodated in Edelbaum's analysis. Colasurdo and Casalino have extended Edelbaum's analysis and developed an approximate analytic technique for computing optimal quasi-circular transfers with the inclusion of the Earth's shadow. Only coplanar transfers are considered, and the thrust-steering is constrained so that the orbit remains circular in the presence of the Earth's shadow.

[1] Edelbaum, T. N. (1961) Propulsion Requirements for Controllable Satellites, ARS Journal, 31, 1079–1089.
[2] Colasurdo, G., and Casalino, L. (2004) Optimal Low-Thrust Maneuvers in Presence of Earth Shadow, AIAA/AAS Astrodynamics Specialist Conference, AIAA Paper 2004-5087, Providence, RI.
[3] Kechichian, J. A. (1998) Low-Thrust Eccentricity-Constrained Orbit Raising, Journal of Spacecraft and Rockets, 35, No. 3, 327–335.
[4] Sackett, L. L., Malchow, H. L., and Edelbaum, T. N. (1975) Solar Electric Geocentric Transfer with Attitude Constraints: Analysis, NASA CR-134927.
[5] Kluever, C. A., and Oleson, S. R. (1998) Direct Approach for Computing Near-Optimal Low-Thrust Earth-Orbit Transfers, Journal of Spacecraft and Rockets, 35, No. 4, 509–515.
[6] Ilgen, M. R. (1994) Hybrid Method for Computing Optimal Low Thrust OTV Trajectories, Advances in the Astronautical Sciences, 87, No. 2, 941–958.
[7] Jenkin, A. B. (2004) Representative Mission Trade Studies for Low-Thrust Transfers to Geosynchronous Orbit, AIAA/AAS Astrodynamics Specialist Conference, AIAA Paper 2004-5086, Providence, RI.
[8] Scheel, W. A., and Conway, B. A. (1994) Optimization of Very-Low-Thrust, Many-Revolution Spacecraft Trajectories, Journal of Guidance, Control, and Dynamics, 17, No. 6, 1185–1192.
[9] Battin, R. H. (1987) An Introduction to the Mathematics and Methods of Astrodynamics, AIAA Education Series, AIAA, Washington, DC, 488–489.
[10] Vallado, D. A. (1997) Fundamentals of Astrodynamics and Applications, McGraw-Hill, New York, 579–583.
[11] Neta, B., and Vallado, D. (1998) On Satellite Umbra/Penumbra Entry and Exit Positions, Journal of the Astronautical Sciences, 46, No. 1, 91–104.
[12] Kechichian, J. A. (1997) Reformulation of Edelbaum's Low-Thrust Transfer Problem Using Optimal Control Theory, Journal of Guidance, Control, and Dynamics, 20, No. 5, 988–994.
[13] Pollard, J. E., and Janson, S. W. (1996) Spacecraft Electric Propulsion Applications, Aerospace Corporation, Report No. ATR-96 (8201)-1.
[14] Kluever, C. A. (2005) Geostationary Orbit Transfers Using Solar Electric Propulsion with Specific Impulse Modulation, Journal of Spacecraft and Rockets, 41, No. 3, 461–466.