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About a month ago I concieved the following "lunar theorem":

Whenever the moon is visible at dusk (strictly speaking, to an equatorial observer, if eg. the planet is very large compared to the distance to its moon), it is waxing.

This is because at dusk, the observer standing on the Earth and looking up is facing against the direction of the Earth's motion, and if the moon is then visible, it is therefore exactly in the semicircle where it is waxing.

I suspect the probability that it is already known is rather high. Pity!

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    $\begingroup$ It's probably not absolutely true, due to the moon's five degree incline to the the ecliptic, but it's probably been known for as long as people have kept records of the moon. So. good work for working this out, but I don't think it could be published as a new discovery... $\endgroup$
    – James K
    Commented Sep 2, 2023 at 21:40
  • $\begingroup$ @JamesK That's what I thought, and actually, it's far worse due to the Earth's axial tilt ( commons.wikimedia.org/wiki/… ). But still, I thought it was funny. Probably the Greeks did observe this. $\endgroup$
    – AlgebraicsAnonymous
    Commented Sep 2, 2023 at 21:45
  • $\begingroup$ @JamesK By the way, the proof does use some facts about the Earth's motion that are not trivial and were not accepted in Classical Greece as correct (due to people dissing Aristarchus). $\endgroup$
    – AlgebraicsAnonymous
    Commented Sep 2, 2023 at 21:48
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    $\begingroup$ not related to equatorial observations, but you may find the answers to these interesting/helpful: How does the Moon move in the "night" sky as seen from the poles? and How is this picture of the moon possible? $\endgroup$
    – uhoh
    Commented Sep 2, 2023 at 23:15

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