Abstract
Low-thrust transfers between preset orbits are considered in the presence of perturbations of different origin. A simple method of finding the transfer trajectory is suggested, based on linearization of motion near reference orbits. The required accuracy of calculations is achieved by way of increasing the number of reference orbits. The method can also be used in the case of a large number of revolutions around the attracting center: no averaging of motion is required in this case. The suggested method is applicable as well, when the final orbit is specified partially and when there are constraints on the thrust direction. The optimal solution to the linearized problem is not optimal for the original problem; closeness of solutions to these two problems is estimated using a numerical example. Capabilities of the method are also illustrated by examples.
Similar content being viewed by others
References
Gobetz, F.W., Optimal Variable-Thrust Transfer of a Power-Limited Rocket between Neighboring Circular Orbits, AIAA J., 1964, vol. 2, no. 2, pp. 339–343.
Edelbaum, T.N., Optimum Power-Limited Orbit Transfer in Strong Gravity Fields, AIAA J., 1965, vol. 3, no. 5, pp. 921–925.
Marec, J.-P. and Vinh, N.X., Optimal Low-Thrust, Limited Power Transfers between Arbitrary Elliptical Orbits, Acta Astronaut., 1977, vol. 4, nos. 5–6, pp. 511–540.
Hassig, C.M., Mease, K.D., and Vinh, N.X., Minimum-Fuel Power-Limited Transfer between Coplanar Elliptical Orbits, Acta Astronaut., 1993, vol. 29, no. 1, pp. 1–15.
Kiforenko, B.N., Optimal Low-Thrust Orbital Transfers in a Central Gravity Field, International Applied Mechanics, 2005, vol. 41, no. 11, pp. 1211–1238.
Fernandes, S. da Silva and Golfetto, W.A., Numerical Computation of Optimal Low-Thrust Limited-Power Trajectories-Transfers between Coplanar Circular Orbits, J. Brazilian Society of Mechanical Sciences and Engineering, 2005, vol. 27, no. 2, pp. 178–185.
Fernandes, S. da Silva and Golfetto, W.A., Numerical and Analytical Study of Optimal Low-Thrust Limited-Power Transfers between Close Circular Coplanar Orbits, Mathematical Problems in Engineering, 2007, ID 59372. doi: 10.1155/2007/59372.
Beletskii, V.V. and Egorov, V.A., Interplanetary Flights with Engines of Constant Power, Kosm. Issled., 1964, vol. 2, no. 3, pp. 360–391. [Cosmic Research, pp. 303–330.]
Sukhanov, A.A., Optimization of Flights with Low Thrust, Kosm. Issled., 1999, vol. 37, no. 2, pp. 182–191. [Cosmic Research, pp. 171–181.]
Sukhanov, A.A., Optimization of Low-Thrust Interplanetary Transfers, Kosm. Issled., 2000, vol. 38, no. 6, pp. 624–627. [Cosmic Research, pp. 584–587.]
Sukhanov, A.A. and Prado, A.F.B. de A., A Modification of the Method of Transporting Trajectory, Kosm. Issled., 2004, vol. 42, no. 1, pp. 107–112. [Cosmic Research, pp. 103–108.]
Sukhanov, A.A. and Prado, A.F.B. de A., Optimization of Low-Thrust Transfers in the Three-Body Problem, Kosm. Issled., 2008, vol. 46, no. 5, pp. 440–451. [Cosmic Research, pp. 413–424.]
Sukhanov, A.A. and Prado, A.F.B. de A., Optimization of Transfers under Constraints on the Thrust Direction: I, Kosm. Issled., 2007, vol. 45, no. 5, pp. 443–449. [Cosmic Research, pp. 417–423.]
Sukhanov, A.A. and Prado, A.F.B. de A. Optimization of Transfers under Constraints on the Thrust Direction: II, Kosm. Issl., 2008, vol. 46, no. 1, pp. 51–60. [Cosmic Research, pp. 49–59.]
Spravochnoe rukovodstvo po nebesnoi mekhanike i astrodinamike (Handbook on Celestial Mechanics and Astrodynamics), Duboshin, G.N, Ed., Moscow: Nauka, 1976.
Bakhshiyan, B.Ts. and Sukhanov, A.A., Isochronous Derivatives of the First and Second Order in the Two-Body Problem, Kosm. Issled., 1978, vol. 16, no. 4, pp. 481–491. [Cosmic Research, p. 391.]
Sukhanov, A.A., Isochronous Derivatives in the Two-Body Problem, Kosm. Issled., 1990, vol. 28, no. 2, pp. 304–306. [Cosmic Research, p. 264.]
Pontryagin, L.S., Boltyanskii, V.G., Gamkrelidze, R.V., and Mishchenko, E.F., Matematicheskaya teoriya optimal’nykh protsessov (Mathematical Theory of Optimal Processes), Moscow: Nauka, 1969.
Jacobson, R.A. and Powers, W.F., Asymptotic Solution to the Problem of Optimal Low-Thrust Energy Increase, AIAA J., 1972, vol. 10, no. 12, pp. 1679–1680.
Petukhov, V.G., Optimization of Interplanetary Trajectories for Spacecraft with Ideally Regulated Engines Using the Continuation Method, Kosm. Issled., 2008, vol. 46, no. 3, pp. 224–237. [Cosmic Research, pp. 219–232].
Beletskii, V.V., Ocherki o dvizhenii kosmicheskikh tel. 2-e izd. (Essays on Motion of Celestial Bodies, Second Edition), Moscow: Nauka, 1977.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © A.A. Sukhanov, A.F.B. de A. Prado, 2013, published in Kosmicheskie Issledovaniya, 2013, Vol. 51, No. 2, pp. 159–175.
Rights and permissions
About this article
Cite this article
Sukhanov, A.A., de A. Prado, A.F.B. Inter-orbital low-thrust transfers in an arbitrary field of forces. Cosmic Res 51, 147–163 (2013). https://doi.org/10.1134/S0010952513020056
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0010952513020056