TY - JOUR
T1 - Lunar close encounters compete with the circumterrestrial Lidov–Kozai effect
T2 - The dynamical demise of Luna 3
AU - Amato, Davide
AU - Malhotra, Renu
AU - Sidorenko, Vladislav
AU - Rosengren, Aaron J.
N1 - Funding Information:
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). We are grateful to Ivan Shevchenko and one anonymous reviewer for their insightful review of this article. Davide Amato thanks Jay McMahon for his indispensable support during the writing of this article, Giulio Baù for comments that improved the quality of the article, and Giovanni Valsecchi for helpful discussions at the 2019 DDA Meeting about averaged solutions in the presence of orbit crossings. Renu Malhotra acknowledges funding from NSF (Grant AST-1824869), and the Marshall Foundation of Tucson, AZ, USA. We acknowledge the use of software routines from the IAU SOFA Collection (IAU SOFA Board 2019) in the reduction of the Luna 3 ephemerides.
Funding Information:
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). We are grateful to Ivan Shevchenko and one anonymous reviewer for their insightful review of this article. Davide Amato thanks Jay McMahon for his indispensable support during the writing of this article, Giulio Baù for comments that improved the quality of the article, and Giovanni Valsecchi for helpful discussions at the 2019 DDA Meeting about averaged solutions in the presence of orbit crossings. Renu Malhotra acknowledges funding from NSF (Grant AST-1824869), and the Marshall Foundation of Tucson, AZ, USA. We acknowledge the use of software routines from the IAU SOFA Collection (IAU SOFA Board ) in the reduction of the Luna 3 ephemerides.
Publisher Copyright:
© 2020, Springer Nature B.V.
PY - 2020/6/1
Y1 - 2020/6/1
N2 - 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.
AB - 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.
KW - Averaging
KW - Close encounters
KW - Kozai
KW - Lidov
KW - Luna 3
KW - Lunisolar perturbations
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U2 - 10.1007/s10569-020-09972-6
DO - 10.1007/s10569-020-09972-6
M3 - Article
AN - SCOPUS:85088244349
VL - 132
JO - Celestial Mechanics and Dynamical Astronomy
JF - Celestial Mechanics and Dynamical Astronomy
SN - 0923-2958
IS - 6-7
M1 - 35
ER -