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The recent news article "What time is it on the Moon? Researchers plan to build a lunar clock", Nature 614, 13-14 (2023) claims that

"Clocks on Earth and the Moon naturally tick at different speeds, because of the differing gravitational fields of the two bodies."

and

"[A] clock’s speed would also subtly change depending on its position on the lunar surface, because of the Moon’s rotation"

and

"Satellite navigation systems for lunar settlements will require local atomic clocks. [...]
Defining a lunar standard [...] will involve installing at least three master clocks that
tick at the Moon’s natural pace, and whose output is combined by an algorithm
to generate a more accurate virtual timepiece"

The article also explicitly mentions the special general${}^{1}$ theory of relativity being relevant, but doesn't include any specific references for further research. Therefore

My question:

What is the concrete definition of "natural pace", presumably within the theory of relativity, which would supply us with a method for determining, case by case, whether a given atomic clock had "ticked at the Moon's natural pace" ?;
or more specificly, whether a given atomic clock had "ticked at the natural pace of its position on the lunar surface" ?

${}^{1}$ Edit: This wording reflects a "Correction 02 February 2023" of the linked article. (However, the phrase "the Moon's natural pace" appears unchanged in the article, and the OP question about that phrase therefore remains as before.)

user12262
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    Comments have been moved to chat; please do not continue the discussion here. Before posting a comment below this one, please review the purposes of comments. Comments that do not request clarification or suggest improvements usually belong as an answer, on [meta], or in [chat]. Comments continuing discussion may be removed. – SuperCiocia Feb 03 '23 at 20:02

1 Answers1

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I suppose you mean the gravitational redshift. This isn't related just to the moon, but can also be observed here on earth. Using modern optical atomic clocks, height differences of less than a meter can be identified due to the change in gravity. See this here for reference: https://www.nature.com/articles/s41566-020-0654-5

The moon has less mass than the earth and clocks will tick differently. This is not a problem for the physics itself, but humans need to set (time) standards to have things working together. Just imagine that an incorrect assumption about the time on the moon could lead to a collision because of wrongly timed maneuvers.

Did I answer your question?

kai90
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  • kai90: "I suppose you mean the gravitational redshift [...]" -- First: Sorry for my response coming so late. Further, I doubt very much you mean to suggest that the phrase I asked about (i.e. "natural pace") could be precisely one-to-one substituted by the phrase "gravitational redshift". Barring this possibility, I can't recognize my question being addressed by the answer you submitted. We may have to await publication of an actual "Moon SatNav" TDR document ... – user12262 Jun 21 '23 at 20:08
  • kai90: "See this here for reference: https://www.nature.com/articles/s41566-020-0654-5 " -- This: Nature Photonics volume 14, pages 408–409 (2020), is only "the PR piece" to That ("associated content"): Nature Photonics volume 14, pages 411–415 (2020); and to the latter I've submitted a question (PSE/716323) already, btw. "The moon has less mass than the earth" -- Sure. "and clocks will tick differently." -- What do mean by that exactly ?!? – user12262 Jun 21 '23 at 20:12