Abstract
Orbits about the Sun–Earth libration points are perturbed by the Moon, and orbits about the Earth–Moon libration points are perturbed by the Sun. We study both situations in the framework of a single, coherent model, the Hill restricted four-body problem. This model is presented in a Sun–Earth rotating reference frame to complement its earlier Earth–Moon frame formulation. We provide an overview of the planar quasi-periodic orbits that originate from the L 1 and L 2 Lyapunov periodic orbits in Hill’s problem and the circular restricted three-body problem. The role of resonances is also discussed.
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Notes
- 1.
The Earth–Moon HR4BP equations of motion in fact have a minimal period π due to symmetry, but this is not essential for the discussion.
- 2.
As m varies, the dimensional time unit is scaled by (1 + m). When m = 0 (Earth–Moon CR3BP), 2π time units corresponds to a sidereal month (27.32 days). When m = 0. 0808 (Sun–Earth–Moon HR4BP), 2π time units is a synodic month (29.53 days). See Scheeres (1998) for more details.
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Acknowledgements
This work was supported by the Marie Curie Initial Training Network PITN-GA-2011-289240, AstroNet-II.
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Olikara, Z.P., Gómez, G., Masdemont, J.J. (2016). A Note on Dynamics About the Coherent Sun–Earth–Moon Collinear Libration Points. In: Gómez, G., Masdemont, J. (eds) Astrodynamics Network AstroNet-II. Astrophysics and Space Science Proceedings, vol 44. Springer, Cham. https://doi.org/10.1007/978-3-319-23986-6_13
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DOI: https://doi.org/10.1007/978-3-319-23986-6_13
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