How Keplerian Orbits Help Define Time on the Moon

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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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].

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:::info Authors:

(1) Neil Ashby, National Institute of Standards and Technology, Boulder, CO 80305 (Neil.Ashby@Colorado.Edu);

(2) Bijunath R. Patla, National Institute of Standards and Technology, Boulder, CO 80305 (bijunath.patla@nist.gov).

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

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