Abstract
In this work, the artificial equilibrium points for a general two-body system are derived, visualized, and summarized as functions of the direction of the thrust, for several directions. The results for the Sun-Earth system are also presented. Planar solar sail applications are also considered.
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References
Dusek, Hermann M.: Motion in the vicinity of libration points of a generalized restricted three-body model. Prog. Astronaut. Rocket. 54, 17–37 (1966)
Tsiolkovsky, K.E.: Extension of man into outer space. In: Proceedings of Symposium on Jet Propulsion, vol. 2. United Scientific and Technical Press (1936)
Tsander, K.: From a Scientific Heritage. NASA Technical Translation No TTf-541, NASA, Washington, DC (1967)
Forward, R.L.: Statite—a spacecraft that does not orbit. J. Spacecr. Rockets 28(5), 606 (1991)
Simmons, J.F.L., McDonald, A.J.C., Brown, J.C.: The restricted 3-body problem with radiation pressure. Celest. Mech. 35, 145 (1985)
McInnes, C.R., McDonald, A.J.C., Simmons, J.F.L., MacDonald, E.W.: Solar sail parking in restricted three-body systems. J. Guid. Control Dyn. 17(2), 399 (1994)
McInnes, C.R.: Dynamics, stability, and control of displaced non-Keplerian orbits. J. Guid. Control Dyn. 21(5), 799 (1998)
Broschart, S.B., Scheeres, D.J.: Control of hovering spacecraft near small bodies: application to asteroid 25143 Itokawa. J. Guid. Control Dyn. 28(2), 343–354 (2005)
Bu, S., Li, S., Yang, H.: Artificial equilibrium points in binary asteroid systems with continuous low-thrust. Astrophys. Space Sci. 362, 137 (2017)
Bombardelli, C., Pelaez, J.: On the stability of artificial equilibrium points in the circular restricted three-body problem. Celest. Mech. Dyn. Astron. 109(1), 13–26 (2011)
Ranjana, K., Kumar, V.: On the artificial equilibrium points in a generalized restricted problem of three bodies. Int. J. Astron. Astrophys. 3, 508–516 (2013)
Aliasi, G., Mengali, G., Quarta, A.A.: Artificial equilibrium points for a generalized sail in the circular restricted three-body problem. Celest. Mech. Dyn. Astron. 110(4), 343–368 (2011)
de Almeida Jr., A.K., Prado, A.F.B.A., Sanchez, D.M., Yokoyama, T.: Searching for artificial equilibrium points to place satellites above and below \(L_3\) in the Sun–Earth system. Rev. Mex. Astron. Astrofis. 53, 349 (2017)
Baoying, H., McInnes, C.R.: Solar sail halo orbits at the sunearth artificial l1 point. Celest. Mech. Dyn. Astron. 94, 155 (2006)
Waters, T.J., McInnes, C.R.: Periodic orbits above the ecliptic in the solar-sail restricted three-body problem. J. Guid. Control Dyn. 30(3), 687 (2007)
Baig, S., McInnes, C.R.: Artificial halo orbits for low-thrust propulsion spacecraft. Celest. Mech. Dyn. Astron. 104, 321 (2009)
Farres, A., Jorba, A.: Dynamics, geometry and solar sails. Indag. Math. 27(5), 1245 (2016)
Goebel, D.M., Katz, I.: Fundamentals of Electric Propulsion, Ion and Hall Thrusters. Wiley, New Jersey (2008)
McInnes, C.R.: Solar Sailing Technology, Dynamics and Mission Applications. Springer, Berlin (2004)
Ueno, K.: Thrust measurement of pure magnetic sail. Trans. JSASS Space Tech. Jpn. 7(26), 65–69 (2009)
Zubrin, R.M., Andrews, D.G.: Magnetic sails and interplanetary travel. J. Spacecr. Rockets 28(2), 197–203 (1991). https://doi.org/10.2514/3.26230
Mengali, G., Quarta, A.A.: Non-Keplerian orbits for electric sails. Celest. Mech. Dyn. Astron. 105, 179195 (2009)
Janhunen, P.: Electric sail for spacecraft propulsion. J. Propuls. Power 20(4), 763–764 (2004)
Janhunen, P., Sandroos, A.: Simulation study of solar wind push on a charged wire: basis of solar wind electric sail propulsion. Ann. Geophys. 25, 755–767 (2007)
Yamakawa, H.: Magneto-plasma sail: an engineering satellite concept and its application for outer planet missions. Acta Astron. 59(8–11), 777 (2006)
Symon, Keith R.: Mechanics, 2nd edn. Campus Ltda, Rio de Janeiro (1986)
Luzum, Brian, et al.: The IAU 2009 system of astronomical constants: the report of the IAU working group on numerical standards for Fundamental Astronomy. Celest. Mech. Dyn. Astron. 110, 293 (2011)
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The authors wish to express their appreciation for the financial support from the Coordination for the Improvement of Higher Education Personnel (CAPES) and the support provided by Grants 406841/2016-0, 301338/2016-7, and 305834/2013-4 from the National Council for Scientific and Technological Development (CNPq), Grants 2016/24561-0 and 2016/14665-2 from São Paulo Research Foundation (FAPESP).
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de Almeida, A.K., Prado, A.F.B.A. & Yokoyama, T. Determination of thrusts to generate artificial equilibrium points in binary systems with applications to a planar solar sail. Nonlinear Dyn 95, 919–942 (2019). https://doi.org/10.1007/s11071-018-4605-3
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DOI: https://doi.org/10.1007/s11071-018-4605-3