Sun-Earth system Lagrange point spacecraft orbit computation by numerical method and deep learning technique

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In this article, the Lagrange points locations are computed in the Rotating Lagrangian Point (RLP) as well as in J2000 inertial reference frames. The well-known Sun-Earth system is considered for the circular restricted three-body problem (CRTBP). In the synodic frame, the Sun-Earth Lagrangian L1 point halo orbit is computed via Differential Correction and Lindstedt-Poincaré (LP) methods. The periodic halo orbits are expressed with respect to barycenter, heliocenter and geocenter, respectively. The deep learning-based model is further explored for the orbit accuracy obtained by the numerical method considering the third, fourth and fifth order LP method.