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<p>The circular restricted three-body problem is used as an approximate model in space mission planning. Its periodic solutions around equilibrium points, which are referred to as the libration points, are utilized for exploration of possible spacecraft trajectories in the preliminary stages of mission design. In this paper, a numerical methodology for periodic libration point orbits (LPOs) computation is introduced and applied to the construction and study of <i>N</i>-periodic (up to <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(N=6\)</EquationSource> </InlineEquation>) quasi-planar orbit families in the Earth-Moon system. The stability and the bifurcation points of these families are determined. The proposed method is based on an iterative algorithm searching for the initial state vector of periodic LPOs, which allows computing unstable long-periodic and large-amplitude orbits. The method is suited to perform a straightforward switch to bifurcating branches of periodic orbits.</p>

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Computation of Periodic Libration Point Orbits in the Circular Restricted Three-Body Problem

  • 期刊论文

  • 发表日期：

    2025年9月25日

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  • Daniella Gafurova,
  • Sergey Aksenov

摘要

The circular restricted three-body problem is used as an approximate model in space mission planning. Its periodic solutions around equilibrium points, which are referred to as the libration points, are utilized for exploration of possible spacecraft trajectories in the preliminary stages of mission design. In this paper, a numerical methodology for periodic libration point orbits (LPOs) computation is introduced and applied to the construction and study of N-periodic (up to \(N=6\) ) quasi-planar orbit families in the Earth-Moon system. The stability and the bifurcation points of these families are determined. The proposed method is based on an iterative algorithm searching for the initial state vector of periodic LPOs, which allows computing unstable long-periodic and large-amplitude orbits. The method is suited to perform a straightforward switch to bifurcating branches of periodic orbits.