What is the origin of the phrase "blue moon"? Any alternate phrase for it?

Was just wondering how this phrase came into being? Was it inspired from some natural or astronomical observation? or is it the result of poetic imagination?

The Online Etymology Dictionary gives the following origin:

blue moon
1821 as a specific term in the sense "very rarely," perhaps suggesting something that, in fact, never happens (cf. at the Greek calends); suggested earliest in this couplet from 1528:

Yf they say the mone is blewe,
We must beleve that it is true.

Though this might refer to calendrical calculations by the Church, so that the general sense of the term and the specific one (commonly misinterpreted as "second full moon in a calendar month," but actually a quarterly calculation) are difficult to disentangle. In either case, the sense of blue is obscure. Literal blue moons do occasionally occur under extreme atmospheric conditions.

So as you suggest, its origin could be either poetic or astronomical. Perhaps the latter inspired the former? A lot older than I would have guessed, in any case!

As for alternatives, the most obvious one is simply "[very] rarely". A more interesting one is "black swan", which can be used to describe a very infrequent event.

A Blue moon is the second full moon in the same month.

As a full moon appears every 28 days the chances of a full moon happening twice in the same month are very rare.

This brings us to the common expression:

Once in a blue moon.

Meaning it happens very rarely.

Though Dr Hiscock in one of his books noted this is a modern interpretation of the term "Blue Moon"; Historically it has probably been related to the moon changing colour because of atmospheric conditions (which was even more rare).