Two-Faced Janus

On the Motion of Janus and Epimetheus

Authors

  • Nikolay Kondratyev Institute of Astronomy of the Russian Academy of Sciences

Keywords:

olympiad problems, celestial mechanics, co-orbital satellites, conservation laws, approximate calculations

Abstract

The solution to an olympiad problem often hinges on one or more key ideas, without which further calculations are impossible. This article examines Problem 11.6 from the final round of the 2026 Russian National Astronomy Olympiad, concerning the motion of Saturn's moons Janus and Epimetheus. Several methods are presented for estimating the satellites' semimajor axes and orbital periods, as well as the minimum distance between them: expansion in a small parameter, binary search, direct integration of the forces, and application of conservation laws in inertial and non-inertial reference frames. The article shows which approximations allow the orbits to be regarded as nearly coincident and why Saturn's influence cannot be neglected when estimating the close approach. A comparison of the solutions demonstrates the importance of checking orders of magnitude and the range of validity of the chosen physical model.

Author Biography

Nikolay Kondratyev, Institute of Astronomy of the Russian Academy of Sciences

Junior Research Fellow, Department of Stellar Systems Physics, Institute of Astronomy, Russian Academy of Sciences; Graduate Student, Sternberg State Astronomical Institute

References

Кондратьев Н. Е. 11 класс, задача № 6 // Всероссийская олимпиада школьников по астрономии. Заключительный этап. 2026. URL: https://vos.astroedu.ru.

How Janus’ Orbital Swap Affects the Edge of Saturn’s A Ring? / M. El Moutamid [и др.] // Icarus. 2016. Нояб. Т. 279. С. 125—140. ISSN 0019-1035. DOI: 10.1016/j.icarus.2015.10.025.

Theoretical Competition : Problem 12. Co-orbital Satellites // International Olympiad on Astronomy and Astrophysics. 2022. URL: https://ioaastrophysics.org.

Downloads

Published

2026-08-12

How to Cite

[1]
Kondratyev, N. 2026. Two-Faced Janus: On the Motion of Janus and Epimetheus. Astronomy Education. 1, 2 (Aug. 2026), 11–18.

Issue

No. 2 (2026)

Section

Astronomical Etudes

License

Copyright (c) 2026 Nikolay Kondratiev

Creative Commons License

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Materials are published under the Creative Commons Attribution-ShareAlike 4.0 International (CC BY-SA 4.0) license.

You are free to:

  • Share — copy and redistribute the material in any medium or format for any purpose, even commercially.

  • Adapt — remix, transform, and build upon the material for any purpose, even commercially.

Under the following terms:

  • Attribution — You must give appropriate credit , provide a link to the license, and indicate if changes were made . You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.

  • ShareAlike — If you remix, transform, or build upon the material, you must distribute your contributions under the same license as the original.