Lunar close encounters compete with the circumterrestrial Lidov-Kozai effect
Abstract
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.
- Publication:
-
Celestial Mechanics and Dynamical Astronomy
- Pub Date:
- July 2020
- DOI:
- 10.1007/s10569-020-09972-6
- arXiv:
- arXiv:2006.08827
- Bibcode:
- 2020CeMDA.132...35A
- Keywords:
-
- Luna 3;
- Averaging;
- Lunisolar perturbations;
- Close encounters;
- Lidov;
- Kozai;
- Astrophysics - Earth and Planetary Astrophysics;
- Astrophysics - Instrumentation and Methods for Astrophysics;
- 70F15
- E-Print:
- 17 pages, 7 figures. Accepted for publication in Celestial Mechanics and Dynamical Astronomy, topical collection "Toward the Moon and Beyond." Parts of this work were presented at the 2018 John L. Junkins Dynamical Systems Symposium and at the 2019 Meeting of the AAS Division on Dynamical Astronomy (DDA)