It's pretty simple, actually. The time zones are on average 1 hour apart. So there should be about 24*28=672 time zones on the Moon. SIMPLE.
Or we invent 24 lunar hours and then we're back to 24 timezones.
However I don't think keeping the sun overhead at noon is the goal here. That stuff is only important to humans. The real issue is figuring out how to count time on the moon in such a way that it doesn't run out of sync with how we count time on earth because of relativistic effects.
The relativistic effects would be so small in human terms that the clock could just be synchronized with Earth time once daily and nobody would ever notice.
It's pretty simple, actually. The time zones are on average 1 hour apart. So there should be about 24*28=672 time zones on the Moon. SIMPLE.
Or we invent 24 lunar hours and then we're back to 24 timezones.
However I don't think keeping the sun overhead at noon is the goal here. That stuff is only important to humans. The real issue is figuring out how to count time on the moon in such a way that it doesn't run out of sync with how we count time on earth because of relativistic effects.
The relativistic effects would be so small in human terms that the clock could just be synchronized with Earth time once daily and nobody would ever notice.