How Keplerian Orbits Help Define Time on the Moon

Written by exoplanetology | Published 2025/02/25
Tech Story Tags: space-exploration | space-navigation-clocks | earth-moon-time-difference | cislunar-navigation-system | lagrange-point-clock-rates | einstein-relativity-in-space | relativistic-time-dilation | time-transfer-in-space

TLDRThis study introduces a Keplerian orbit-based model for defining time on the Moon and at Earth-Moon Lagrange points. Accurate timekeeping is essential for navigation, synchronization, and future lunar missions.via the TL;DR App

Table of Links

Abstract and 1. Introduction

  1. Clock in Orbit

    2.1 Coordinate Time

    2.2 Local Frame for the Moon

  2. Clock Rate Differences Between Earth and Moon

  3. Clocks at Earth-Moon Lagrance Points

    4.1 Clock at Lagrange point L1

    4.2. Clock at Lagrange point L2

    4.3. Clock at Lagrange point L4 or L5

  4. Conclusions

Appendix 1: Fermi Coordinates with Origin at the Center of the Moon

Appendix 2: Construction of Freely Falling Center of Mass Frame

Appendix 3: Equations of Motion of Earth and Moon

Appendix 4: Comparing Results in Rotating and Non-Rotating Coordinate Systems

Acknowledgments and References

5. CONCLUSION

We presented a model based on Keplerian orbits for establishing coordinate time on the Moon and rates of clocks at Lagrange points in cislunar space. We have used values for Keplerian orbit parameters that can be looked up; the only parameters that fit were the times of periapsis passage. The main numerical results obtained using our approach are given in Table II. We assumed a fixed eccentricity and fixed value for the semi-major axis for the Moon’s orbit around the Earth, as the present-day values for these parameters are very slowly varying [13].

Authors:

(1) Neil Ashby, National Institute of Standards and Technology, Boulder, CO 80305 ([email protected]);

(2) Bijunath R. Patla, National Institute of Standards and Technology, Boulder, CO 80305 ([email protected]).


This paper is available on arxiv under CC0 1.0 license.


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Published by HackerNoon on 2025/02/25