Why It's So Difficult To Establish a Lunar Time Standard

Abstract and 1. Introduction

2. Clock in Orbit

   2.1 Coordinate Time

   2.2 Local Frame for the Moon

3. Clock Rate Differences Between Earth and Moon

4. 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

5. 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

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An instructive example of establishing a coordinate time on Earth is the GPS time. The constellation clocks are set to beat at the average coordinate rate corresponding to clocks at rest on the surface of the rotating Earth by applying a “factory frequency offset” to the clocks before launch, which is [4]

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\ This model is based on using an eccentric Keplerian orbit in the local inertial frame centered on Earth’s center of mass. The center of mass of the Earth and Moon approximately follows a Keplerian orbit. However, for the EarthMoon system, one cannot have a Keplerian orbit in a coordinate system centered on the Earth and a Keplerian orbit in a coordinate system centered on the Earth-Moon center of mass with the same orbit parameters. There are also relativistic effects arising from changes in time and length scales, Lorentz contraction, and changes in tidal effects.

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:::info 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]).

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:::info This paper is available on arxiv under CC0 1.0 license.

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