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Title: Discrete restricted four-body problem: Existence of proof of equilibria and reproducibility of periodic orbits

We propose the discrete-time restricted four-body problem (d-R4BP), which approximates the orbits of the restricted four-body problem (R4BP). The d-R4BP is given as a special case of the discrete-time chain regularization of the general N-body problem published in Minesaki. Moreover, we analytically prove that the d-R4BP yields the correct orbits corresponding to the elliptic relative equilibrium solutions of the R4BP when the three primaries form an equilateral triangle at any time. Such orbits include the orbit of a relative equilibrium solution already discovered by Baltagiannis and Papadakis. Until the proof in this work, there has been no discrete analog that preserves the orbits of elliptic relative equilibrium solutions in the R4BP. For a long time interval, the d-R4BP can precisely compute some stable periodic orbits in the Sun–Jupiter–Trojan asteroid–spacecraft system that cannot necessarily be reproduced by other generic integrators.
Authors:
 [1]
  1. Tokushima Bunri University, Nishihama, Yamashiro-cho, Tokushima 770-8514 (Japan)
Publication Date:
OSTI Identifier:
22342167
Resource Type:
Journal Article
Resource Relation:
Journal Name: Astronomical Journal (New York, N.Y. Online); Journal Volume: 149; Journal Issue: 1; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; APPROXIMATIONS; ASTEROIDS; EQUILIBRIUM; FOUR-BODY PROBLEM; JUPITER PLANET; MATHEMATICAL SOLUTIONS; ORBITS; PERIODICITY; SUN