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<p>In the spatial Circular, Restricted Three-Body Problem (CR3BP) there exist quasi-periodic orbits that undergo long duration periodic changes in the shape of the orbit. These long duration transformations may initially appear as though the motion is chaotic; however, over time these transformations repeat with a predictable pattern. Similar to any periodic orbit in the CR3BP, these transforming orbits can be defined by a position and velocity vector, but these six terms do not allow one to easily visualize and understand the transformation of the orbit. An efficient way of describing the motion of a transforming orbit is necessary in order for these orbits to be evaluated for their usefulness for conducting different mission types. This paper introduces two new variables called the Scaled Position Difference and Transformation Indicator to analyze the behavior of transforming orbits. This paper presents a standardized method for describing transforming orbits to enable them to be more easily discussed and considered for future missions. This paper also uses a chaos indicator to analyze these transforming orbits. The chaos indicator can provide additional insight into how the orientation of the orbit changes over time.</p>

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Methods for analyzing transforming orbits

  • 期刊论文

  • 发表日期：

    2025年1月28日

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  • Tyler J. Kapolka,
  • Robert A. Bettinger,
  • Kerry D. Hicks

摘要

In the spatial Circular, Restricted Three-Body Problem (CR3BP) there exist quasi-periodic orbits that undergo long duration periodic changes in the shape of the orbit. These long duration transformations may initially appear as though the motion is chaotic; however, over time these transformations repeat with a predictable pattern. Similar to any periodic orbit in the CR3BP, these transforming orbits can be defined by a position and velocity vector, but these six terms do not allow one to easily visualize and understand the transformation of the orbit. An efficient way of describing the motion of a transforming orbit is necessary in order for these orbits to be evaluated for their usefulness for conducting different mission types. This paper introduces two new variables called the Scaled Position Difference and Transformation Indicator to analyze the behavior of transforming orbits. This paper presents a standardized method for describing transforming orbits to enable them to be more easily discussed and considered for future missions. This paper also uses a chaos indicator to analyze these transforming orbits. The chaos indicator can provide additional insight into how the orientation of the orbit changes over time.