Ah. I think I may be compelled to contribute here...

Rayleigh scattering is named for Lord Rayleigh, a 19thC British physicist who first published papers describing the phenomenon. “Red sky at...” - sunrises, the glowing, setting sun, moons tinted in increasing shades of orange & red (this happens when they are relatively low to the horizon, as with sunrise & sunset). Even the everyday (alright, in Britain most, alright, some days!) blue of the sky. It's all down to Rayleigh scattering. Not being a scientist, I'm not absolutely certain, but if you do see a genuinely blue moon, my understanding is that it's due to particulate scattering (smoke, dust), which is not the same thing. If you want to get more technical than that, something for you to investigate for yourselves.

Then there's phases of the moon...

There are actually several “months”. The two primary ones are the sidereal & synodic. The sidereal (“pertaining to the stars”, mid 17thC from Latin; possibly from a PIE root meaning “to shine”) is the actual time it takes the moon to complete one orbit; it's (roughly) 27.3 days.

The synodic is 29.5 days. It's the “visible to the naked eye” cycle, the time it takes for an Earth-bound observer to see the same phase of the moon recur. All down to the vagaries of the orbit of the Earth around the Sun. Simply, by the time the Moon completes its sidereal orbit, the Earth has moved about 27° around the Sun. Therefore, it takes that extra 2.2 days to appear in the same phase.

As for 'Harvest' & 'Hunter's' moons...

There has long been a tradition, in American almanacs, of giving the full moon of each month a name, these being ascribed to the First Peoples i.e. Native Americans Some of those names may or may not genuinely be from their traditions, but two of them are known in Britain from the first decade of the 18thC at the latest & were likely taken over there by settlers from here.

You will find the counter-claim out there, most likely from an American source. I find this most unlikely. The second of these names is specifically mentioned in 1710 as “The Country People call this...”, which implies it had been in use for several generations. The first colony, Virginia, was scarcely a century old then, and the foundation was fraught with difficulties & hostility with the native population. How, then, and why would our “country people” be adopting terms from a colony few probably even knew existed in such a short space of time? And the claims that I've seen that we adopted it from the US offer no evidence at all.

“Harvest” & “Hunter's” are consecutive moons in autumn. The Harvest moon is the full moon nearest the autumn equinox. Since it can be 2 weeks either way, it usually falls in September, sometimes in October. Equally, the Hunter's moon is usually in October, sometimes in November.

Why should either moon be so called? The same theory covers both, but it seems one of those “because everyone says” reasons that is offered without thought, let alone evidence. It amounts to - a full moon is really bright which gives you light to work by.

I suggest this can be discounted for the Harvest moon. Whether, ultimately, the seasonal name derives from the activity or vice versa, you can only gather in your crops, sown or wild, when they are ready, and then you must before they spoil. The days are still long (most of it, if not all, will be done by the equinox at the latest) and the work is hard enough in daylight. In extremis, you might be compelled to work by moonlight, but ordinarily?

I suggest that the Harvest moon is so named not from any moonlit labouring, but simply because that was the principal work of the day for most folk at that time of year (remembering that in centuries past, farming absorbed a far greater part of labour than now). The light of a full moon would certainly assist a hunter but, again, I suggest the origin of the name is rather more prosaic.

Your crops are gathered, the demands that the land makes on your time is at a much lower ebb now. Wild animals have gorged themselves on summer's bounty, and are as fat & fit as they will be at any point in the year. If you are free to do so & have the opportunity, then post-harvest is the time to fill the larder with game, whether you do so at dawn, dusk, or somewhere in between!

I hope these thoughts are of some interest to you folkies! ;-)