Is there a way to calculate the time it has to be on Earth at any moment in time when a person on the Moon would say their clock reads noon (i.e. a time at which a sundial on the Moon would cast no shadow)?

I would guess it has to do with the relative angle between the planes in which the Moon orbits the Earth and the Earth orbits the Sun respectively, but then how is the Moon facing the Sun at any given moment? Any ideas?

(inspired by this Tom Lehrer song)

  • $\begingroup$ When is it noon on Earth? There is always some place where it's noon. $\endgroup$ – user2723984 May 19 at 13:48
  • $\begingroup$ I see that I need to impose some initial conditions, but I have no idea how... $\endgroup$ – JansthcirlU May 19 at 13:50

At any time there is a place on the Moon where the Sun is at the Zenith. Of course, during a lunar eclipse Earth is blocking its rays.

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  • $\begingroup$ Noon happens not only when the Sun is at the zenith. Noon is simultaneously on the whole meridian. $\endgroup$ – Ruslan May 19 at 10:07
  • $\begingroup$ What if we imagined the Earth to be transparent for the sake of having a functional sundial on the Moon? What kind of initial conditions would we need in order to relate the time on Earth to the time on the Moon? $\endgroup$ – JansthcirlU May 19 at 10:49

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