When in its orbit is the Moon visible to the fewest number of people on Earth?

It is surprisingly difficult to persuade some people of this fact, though you’d think it would be trivially easy. I blame Genesis.

Yeah. The remarkable part isn’t that the Moon is visible during the day–that much is obvious to anyone with a 3rd-grade understanding of the solar system–it’s that so many people fail to appreciate the fact. Do people simply not look up from time to time? Is the Moon like those apocryphal sailing ships that were “invisible” to the ignorant natives? I couldn’t say.

You’re saying the point where the moon is visible to the least number of people is the antipode to the point where it is visible to most people? I don’t think that’s a logical conclusion.

I love the link in the XKCD article to the highly dangerous, but available to anyone with $300 (now $349), 1 watt laser. It has a disclaimer that it is not a toy. OK, I guess its resemblance to a light saber is purely unintentional.

OK, on consideration, I take that back. If the moon really is visible to exactly half the globe, then the antipodal thing makes sense. Sorry about that. Carry on!

Actually John DiFool has given a very good answer. There is a period of about 30 hours every month when no-one on Earth can see the Moon, even with a very good telescole, because of the glare of the Sun.

This website gives data on when the Moon will become visible again after the next New Moon; this data is interesting for observers, some of whom try to see it when it is very small, and useful for Muslims, who use the first sighting to calculate their calendar;

This is certainly mostly true, but I wonder if it’s 100% true. Someone above the atmosphere should be able to see a new Moon; it will have strong Earthshine (since someone on the Moon would see a “full Earth”), and it should be possible to block all glare from the Sun.

Too much atmosphere makes this impossible, but I wonder if a high mountain peak would be above just enough air to make it work. Pressure at the top of Everest is 1/3 that at sea level. Might be enough.

The band or the Star Trek MacGuffin?

I expect someone on the ISS could block the Sun sufficiently well to see the Moon most of the time, although the OP did specify on Earth.

This would only reduce the invisibility period by a calculable fraction, not remove it altogether.

Here’s an image of the New Moon, only 3 hours 27 minutes old;
as Dr Strangelove expected, it was taken from a mountain; to reduce glare from the sky even further, it was taken in the infrared.

Where can I get a very good telescole, anyway?

Except, I don’t believe that’s what the OP was asking for, given that he frames the question in terms of angles and populations.

I went through the exact same thought process as you, except that I haven’t quite convinced myself of the second part (although all my clever thought experiments to try to find an exception have failed).

However, I think that bit of the question deserves its own thread.