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Acknowledgments and References

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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

Acknowledgments

We would like to acknowledge the funding we received from the NASA grant NNH12AT81I. We are grateful to Elizabeth Donley, who carefully and critically reviewed the manuscript and provided valuable suggestions. We would also like to express our gratitude to Cheryl Gramling for initiating discussions on lunar time. We extend our sincere thanks to Roger Brown, Thomas Heavner, Judah Levine, Jeffrey Sherman, and Daniel Slichter for their review of the manuscript. This work is a contribution of NIST and is not subject to US copyright.




[1] Artemis Plan: NASA’s Lunar Exploration Program Overview, https://www.nasa.gov/sites/default/files/atoms/files/ artemis plan-20200921.pdf, Sept. 2020


[2] Einstein, A. The Collected Papers of Albert Einstein, Volume 6: The Berlin Years: Writings, 1914-1917 Princeton University Press, 1996.


[3] Park RS, Folkner WM, Williams JG, and Boggs DH, The JPL Planetary and lunar Ephemerides DE440 and DE441, AJ. 161 105, 2021


[4] Ashby N, Relativity in the Global Positioning System, Liv. Rev. Relativity 6, [Online Article]: cited Sept. 14, 2023, http://www.livingreviews.org/lrr-2003-1.


[5] International Astronomical Union (IAU), Proceedings of the Twenty-Fourth General Assembly,” Transactions of the IAU, XXIVB,pp. 34-57,2000


[6] Ashby N and Bertotti B, Relativistic effects in local inertial frames, Phys. Rev. D 14(8), 1986 (Appendix), 2246-2259.


[7] Ashby N and Allan D, Practical Implications of Relativity for a Global Time Scale, Radio Science 14, 1979, pp 649-669.


[8] Bertone, S, Arnold, D, Girardin, V, Lasser, M, Meyer, U, J¨aggi, A, Assessing Reduced-Dynamic Parametrizations for GRAIL Orbit Determination and the Recovery of Independent lunar Gravity Field Solutions, Earth and Space Science, 2021, https://doi.org/10.1029/2020EA001454.


[9] Ries JC, Eanes RJ, Shum CK, Watkins MM (20 March 1992). ”Progress in the determination of the gravitational coefficient of the Earth”. Geophysical Research Letters. 19 (6): 529–531.


[10] CODATA 2006, physics.nist.gov/cuu/Constants


[11] Mohr PJ, Taylor BN, and Newell DB, The CODATA recommended values of the fundamental physical constants: 2006, Rev. Mod. Phys., 80, pp. 633-730, 2008


[12] Konopliv AS, et al., The JPL lunar gravity field to spherical harmonic degree 660 from the GRAIL Primary Mission, J. Geophys. Res. Planets, 118, 1415–1434, 2013, doi:10.1002/jgre.20097


[13] Daher, H et al., Long-Term Earth-Moon Evolution With High-Level Orbit and Ocean Tide Models, Journal of Geophysical Research: Planets, 126(12), 2021, e2021JE006875. https://doi.org/10.1029/2021JE006875


[14] Petit G and Wolf P, Relativistic theory for time comparisons: a review Metrologia, 42 (3), 2005, S138


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).


This paper is available on arxiv under CC0 1.0 license.


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