Fifth order solution of halo orbits via Lindstedt–Poincaré technique and differential correction method

Sheth, Dhwani; Thomas, V. O.; Abouelmagd, Elbaz I.; Srivastava, Vineet K.

doi:10.1016/j.newast.2021.101585

Cited by 5 publications

(1 citation statement)

References 29 publications

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“…In our work, we propose a new way based on the Lindstedt-Poincaré method to solve the problem. The Lindstedt-Poincaré method described in Poincaré (1899) aims to find explicit solutions usually in the form of trigonometric expansions, and it is widely used to investigate periodic or quasiperiodic orbits in the restricted three-body problem (Gómez et al 1998;Jorba & Masdemont 1999;Sheth et al 2021;Tan et al 2021). The main problem of lunar orbit is solved with canonical variables in the Delaunay theory and with Cartesian coordinates in the Sun-Earth rotating frame in the Hill-Brown theory.…”

Section: Introductionmentioning

confidence: 99%

The Main Problem of Lunar Orbit Revisited

Hou

2023

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A novel algorithm based on the Lindstedt–Poincaré method is proposed to construct an analytical solution of the lunar orbit. Based on the analytical solution, a numerical fitting algorithm is proposed to improve the coefficients of the analytical solution so that its accuracy can reach the level of a few kilometers within 20 yr. By fitting our solution to the long-term JPL ephemerides, we are able to recover the receding speed of the Moon from the Earth due to tidal effects. The proposed algorithm also provides a general way to treat the third-body perturbation in rectangular coordinates.

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Section: Introductionmentioning

confidence: 99%