Abstract
We use the numerical continuation package AUTO to investigate families of periodic orbits in the solar sail circular restricted three-body problem. For a sail orientated perpendicular to the Sun-line we find significant differences to the classical case for some families near the Earth, including the L Halo family and retrograde satellite family. Specifically, we expand on existing results and find that the change in the Halo family H1 is associated with a bifurcation of a branch point in the retrograde satellite family, which splits H1 in half. We also track regions of stability within the family, and find some large amplitude stable orbits. For a sail tilted relative to the Earth-Sun line only we find large amplitude families with some stable orbits. Interestingly there is also a small range of parameters for which L 1 bifurcates into three separate points in this system.
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References
McInnes, C. R., Solar sailing, Springer-Praxis, Chichester, UK, 1999
Devaney, R. L., “Reversible Diffeomorphisms and Flows”, Transactions of the American Mathematical Society, Vol. 218, 1976, pp. 89-113
Sevryuk, M.B., Reversible Systems, Lecture Notes in Mathematics, Springer-Verlag, New York, 1986, Chap. 6
Doedel, E. J. et al., “Elemental Periodic Orbits associated with the Libration Points in the Circular Restricted 3-Body Problem”, International Journal of Bifurcation and Chaos, Vol. 17, No. 8, 2007, pp. 2625-2677 doi: 10.1142/S0218127407018671
Doedel, E. J., Keller, H. B., and Kernévez, J. P., “Numerical analysis and control of bifurcation problems I: bifurcation in finite dimension”, International Journal of Bifurcation and Chaos, Vol. 1, No. 3, 1991, pp. 493-520 doi: 10.1142/S0218127491000397
Doedel, E. J. et al., “Continuation of periodic solutions in conservative systems with application to the 3-body problem”, International Journal of Bifurcation and Chaos, Vol. 13, No. 6, 2003, pp. 1353-1381 doi: 10.1142/S0218127403007291
Doedel, E. J., Govaerts, W., Kuznetsov, Y. A., and Dhooge, A., “Numerical continuation of branch points of equilibria and periodic orbits”, International Journal of Bifurcation and Chaos, Vol. 15, No. 3, 2005, pp. 841-860 doi: 10.1142/S0218127405012491
Calleja, R. C., Doedel, E. J., Humphries, A. R., Lemus-Rodríguez, A., and Oldeman, E. B., “Boundary-value problem formulations for computing invariant manifolds and connecting orbits in the circular restricted three body problem”, Celestial Mechanics and Dynamical Astronomy, Vol. 114, No. 1-2, 2012, pp. 77-106 doi: 10.1007/s10569-012-9434-y
Munõz-Almaraz, F. J., Freire, E., Galán, J., Doedel, E., and Vanderbauwhede, A., “Continuation of periodic orbits in conservative and Hamiltonian systems”, Physica D Nonlinear Phenomena, Vol. 181, No. 1-2, 2003, pp. 1-38 doi: 10.1016/S0167-2789(03)00097-6
Farrés, A., and Jorba, À., “Periodic and quasi-periodic motions of a solar sail close to SL1 in the Earth–Sun system”, Celestial Mechanics and Dynamical Astronomy, Vol. 107, No. 1-2, 2010, pp. 233-253 doi: 10.1007/s10569-010-9268-4
Farrés, A., and Jorba, À., “Dynamics of a solar sail near a Halo orbit”, Acta Astronautica, Vol. 67, No. 7-8, 2010, pp. 979-990 doi: 10.1016/j.actaastro.2010.05.022
McInnes, A., “Strategies for solar sail mission design in the circular restricted three-body problem”, M.S. Dissertation, School of Aeronautics and Astronautics, Purdue University, West Lafayette, IN, 2000
Baoyin, H., and McInnes, C. R., “Solar Sail Halo Orbits at the Sun–Earth Artificial L1 Point”, Celestial Mechanics and Dynamical Astronomy, Vol. 94, No. 2, 2006, pp. 155-171 doi: 10.1007/s10569-005-4626-3
Hénon, M. “Numerical exploration of the restricted problem, V”, Astronomy and Astrophysics, Vol. 1, Feb. 1969, pp. 223-238
Strömgren, E., “Connaissance actuelle des orbites dans le problème des trois corps”, Bulletin Astronomique, Vol. 9, No. 2, 1935, pp. 87-130
Howell, K.C., and Campbell, E.T., “Three-dimensional periodic solutions that bifurcate from Halo families in the circular restricted three-body problem”, Spaceflight Mechanics 1999, AAS 99-161, AAS, San Diego, CA, 1999, pp. 891-910
Howell, K. C., “Three-Dimensional Periodic Halo Orbits”, Celestial Mechanics, Vol. 32, No. 1, 1984, pp. 53-71 doi: 10.1007/BF01358403
Waters, T. and McInnes, C.R., “Periodic Orbits Above the Ecliptic in the Solar-Sail Restricted Three-Body Problem”, Journal of Guidance, Control, and Dynamics, Vol. 30, No. 3, 2007, pp. 687-693 doi: 10.2514/1.26232
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This work was funded by the University of Portsmouth’s Faculty of Technology.
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Verrier, P., Waters, T., Sieber, J. (2014). Families of Periodic Orbits for Solar Sails in the CRBTP. In: Macdonald, M. (eds) Advances in Solar Sailing. Springer Praxis Books(). Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34907-2_52
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DOI: https://doi.org/10.1007/978-3-642-34907-2_52
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