Lunar close encounters compete with the circumterrestrial Lidov–Kozai effect: The dynamical demise of Luna 3

Davide Amato, Renu Malhotra, Vladislav Sidorenko, Aaron J. Rosengren

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


Luna 3 (or Lunik 3 in Russian sources) was the first spacecraft to perform a flyby of the Moon. Launched in October 1959 on a translunar trajectory with large semimajor axis and eccentricity, it collided with the Earth in late March 1960. The short, 6-month dynamical lifetime has often been explained through an increase in eccentricity due to the Lidov–Kozai effect. However, the classical Lidov–Kozai solution is only valid in the limit of small semi-major axis ratio, a condition that is satisfied only for solar (but not for lunar) perturbations. We undertook a study of the dynamics of Luna 3 with the aim of assessing the principal mechanisms affecting its evolution. We analyze the Luna 3 trajectory by generating accurate osculating solutions, and by comparing them to integrations of singly and doubly averaged equations of motion in vectorial form. Lunar close encounters, which cannot be reproduced in an averaging approach, decisively affect the trajectory and break the doubly averaged dynamics. Solar perturbations induce oscillations of intermediate period that affect the geometry of the close encounters and cause the singly averaged and osculating inclinations to change quadrants (the orbital plane “flips”). We find that the peculiar evolution of Luna 3 can only be explained by taking into account lunar close encounters and intermediate-period terms; such terms are averaged out in the Lidov–Kozai solution, which is not adequate to describe translunar or cislunar trajectories. Understanding the limits of the Lidov–Kozai solution is of particular significance for the motion of objects in the Earth–Moon environment and of exoplanetary systems.

Original languageEnglish (US)
Article number35
Issue number6-7
StatePublished - Jun 1 2020


  • Averaging
  • Close encounters
  • Kozai
  • Lidov
  • Luna 3
  • Lunisolar perturbations

ASJC Scopus subject areas

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


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