The evolution of the Line of Variations at close encounters: an analytic approach

  • G. B. ValsecchiEmail author
  • A. Del Vigna
  • M. Ceccaroni
Original Article


We study the post-encounter evolution of fictitious small bodies belonging to the so-called Line of Variations (LoV) in the framework of the analytic theory of close encounters. We show the consequences of the encounter on the local minimum of the distance between the orbit of the planet and that of the small body and get a global picture of the way in which the planetocentric velocity vector is affected by the encounter. The analytical results are compared with those of numerical integrations of the restricted three-body problem.


Close encounter Perturbation Asteroid Comet 



We are grateful to D. Farnocchia for his very useful comments.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  • G. B. Valsecchi
    • 1
    • 2
    Email author
  • A. Del Vigna
    • 3
    • 4
  • M. Ceccaroni
    • 5
  1. 1.IAPS-INAFRomeItaly
  2. 2.IFAC-CNRSesto FiorentinoItaly
  3. 3.Università di PisaPisaItaly
  4. 4.Space Dynamics Services s.r.lNavacchio di CascinaItaly
  5. 5.Cranfield UniversityCranfieldUK

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