A Novel Initial Design for Low-Thrust Transfer Trajectories Using Gravity-Assist

Abstract

In this paper, an initial design method of low thrust transfer trajectories using gravity-assist based on exponential sinusoid function is introduced. Firstly, the exponential sinusoid function is established under polar coordinates to simulate the low thrust transfer trajectories. All the parameters of the transfer trajectories can be described by flight-path-angle and winding parameter. Secondly, the parameters of transfer trajectories are discretely processed with constraints, and then obtaining the intersection points of transfer trajectories with target's projected trajectories to get the polar angle to the target trajectory. The rest parameters based on exponential sinusoid can also be obtained, so that we can get the initial design parameters of low thrust transfer trajectory. Finally, the Earth-Jupiter low thrust transfer trajectory using gravity-assist by Mars is designed. The simulation results show that the method is able to search out the initial design parameters of low-thrust transfer trajectory quickly and accurately.

Keywords

low-thrust transfer trajectory / gravity-assist trajectory / projected trajectory / exponential sinusoid / trajectory initial design

References

[1] Broucke R A. The celestial mechanics of gravity assist[C]//Astrodynamics Conference. [S.l.]: AIAA, 1988:88-4220.
[2] Roy A E. Orbital Motion[M]. England: Adam Hilger Ltd, 1982:129-130.
[3] Dunne J A, Burgess E. The voyage of Mariner 10[J]. National Aeronautics and Space Administration SP, 1978:424.
[4] Petropoulos A E, Longuski J M, Bonfiglio E P. Trajectories to Jupiter via gravity assists from Venus, Earth, and Mars[J]. Journal of Spacecraft and Rockets, 2000,37(6):776-783.
[5] Sims J A, Staugler A J, Longuski J M. Trajectory options to Pluto via gravity assists from Venus, Mars, and Jupiter[J]. Journal of Spacecraft and Rockets, 1997,34(3):347-353.
[6] Kawaguchi J, Takiura K, Matsuo H. On the optimization and application of electric propulsion to Mars and sample and return mission[J]. Spaceflight mechanics, 1994:539-556.
[7] Thorne J D, Hall C D. Minimum-time continuous-thrust orbit transfers[J]. The Journal of the Astronautical Sciences, 1997,45(4):411-432.
[8] Kluever C A. optimal low-thrust interplanetary trajectories by direct method techniques[J]. The Journal of the Astronautical Sciences, 1997,45(3):247-262.
[9] Kechichian J A. Low-thrust trajectory optimization based on epoch eccentric longitude formulation[J]. Journal of Spacecraft and Rockets, 1999,36(4):543-553.
[10] Coverstone-Carroll V, Williams S N. Optimal low thrust trajectories using differential inclusion concepts[J]. Journal of the Astronautical Sciences, 1994,42:379-393.
[11] Betts J T. Survey of numerical methods for trajectory optimization[J]. Journal of Guidance, Control, and Dynamics, 1998,21(2):193-207.
[12] Petropoulos A E, Longuski J M, Vinh N X. Shape-based analytic representations of low-thrust trajectories for gravity-assist applications[J]. Astrodynamics 1999, 2000:563-581.
[13] McConaghy T T, Debban T J, Petropoulos A E, et al. Design and optimization of low-thrust trajectories with gravity assists[J]. Journal of Spacecraft and Rockets, 2003,40(3):380-387.
[14] Petropoulos A E, Longuski J M. Shape-based algorithm for the automated design of low-thrust, gravity assist trajectories[J]. Journal of Spacecraft and Rockets, 2004,41(5):787-796.