Analysis of medium-energy transfers to the Moon

Kenta Oshima, Francesco Topputo*, Stefano Campagnola, Tomohiro Yanao

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


This study analyzes a recently discovered class of exterior transfers to the Moon. These transfers terminate in retrograde ballistic capture orbits, i.e., orbits with negative Keplerian energy and angular momentum with respect to the Moon. Yet, their Jacobi constant is relatively low, for which no forbidden regions exist, and the trajectories do not appear to mimic the dynamics of the invariant manifolds of the Lagrange points. This paper shows that these orbits shadow instead lunar collision orbits. We investigate the dynamics of singular, lunar collision orbits in the Earth–Moon planar circular restricted three-body problem, and reveal their rich phase space structure in the medium-energy regime, where invariant manifolds of the Lagrange point orbits break up. We show that lunar retrograde ballistic capture trajectories lie inside the tube structure of collision orbits. We also develop a method to compute medium-energy transfers by patching together orbits inside the collision tube and those whose apogees are located in the appropriate quadrant in the Sun–Earth system. The method yields the novel family of transfers as well as those ending in direct capture orbits, under particular energetic and geometrical conditions.

Original languageEnglish
Pages (from-to)285-300
Number of pages16
JournalCelestial Mechanics and Dynamical Astronomy
Issue number3
Publication statusPublished - 2017 Mar 1


  • Bicircular restricted four-body problem
  • Circular restricted three-body problem
  • Collision orbits
  • Levi-Civita regularization
  • Medium-energy transfer
  • Retrograde ballistic capture orbits

ASJC Scopus subject areas

  • Modelling and Simulation
  • Mathematical Physics
  • Astronomy and Astrophysics
  • Space and Planetary Science
  • Computational Mathematics
  • Applied Mathematics


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