Planar low-energy asteroid and comet transit analysis using isolating blocks

  • Rodney L. AndersonEmail author
  • Paul W. Chodas
  • Robert W. Easton
  • Martin W. Lo
Original Article


Asteroids and comets often capture and sometimes transit near a planet by traveling through the \(\hbox {L}_1\) and \(\hbox {L}_2\) libration point gateways, and these regions are therefore key to understanding the mechanism by which captures, transits, and some potential impacts of these bodies occur. Isolating blocks have recently been used to provide a theoretically rigorous method for computing the invariant manifolds of libration point periodic orbits in the circular restricted three-body problem (CRTBP), and for an appropriate energy range, they can allow us to compute all possible transit trajectories at a particular Jacobi constant in the CRTBP. In this study, both \(\hbox {L}_1\) and \(\hbox {L}_2\) isolating blocks are found for the Sun–Earth and Sun–Jupiter CRTBP systems to rigorously compute trajectories transiting near the Earth and Jupiter in the low-energy regime common for asteroids and comets. The characteristics of these transit trajectories are explored, and individual trajectory solutions are analyzed in more detail. The transit trajectories are also characterized using their orbital elements and compared to known comets and asteroids.


Asteroid Comet Isolating block Transit 



The research presented in this paper has been carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. This material is also based upon work supported by the National Science Foundation under Grant No. DMS-1440140, while the first author was in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the Fall, 2018 semester.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  • Rodney L. Anderson
    • 1
    Email author
  • Paul W. Chodas
    • 1
  • Robert W. Easton
    • 2
  • Martin W. Lo
    • 1
  1. 1.Jet Propulsion LaboratoryCalifornia Institute of TechnologyPasadenaUSA
  2. 2.Applied MathematicsUniversity of Colorado at BoulderBoulderUSA

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