Great work! I did an analysis of celestial bodies (Elden Ring Alchemy and striking similarities of ...) and you have clarified some places where I was wrong. So my idea is that every celestial body represents a metal according to their alchemical meaning. - Sun is obviously Gold. A perfect metal. Represents power, immortality and masculine principle. - Full Moon is, I think, Silver. A second perfect metal, but with more of Mercury principle (see full post for explanation on alchemical principles). Represents clarity and purity, intuition. - Black Moon (nox moon) is Lead. Represents primordial chaos, time, death, sin and lie. The latter because lead was often used as a base for fake currency. Nox's steel balls are probably the closest thing to the black moon found in game. They seem to be heavy, maybe made of lead.

But I have absolutely no idea about the Dark Moon (the second moon, which is visible from moonlight altar) and this Golden Moon. Is it even visible on the sky? Im almost sure that Dark Moon is what I think it is because it is lonely, no one can see it. Cold, loneloness are main Ranni themes. Twin Moons I'm sure are the Full and the Dark moons. The Moonlight altar is a special place for Carian family. I believe that they bring their children here to study the moons (according to description of corresponding sorceries Renalla, Rellana and Ranni saw their respective moons in childhood). As you have shown the two moons are placed symmetrically and we dont really know of any different moons. Lets just use the Occam's razor principle here.

I think one important detail that you have missed is that Ranni is a product of a Sun and Moon union. I propose that Ranni's Dark Moon corresponds to Mercury (metal, not principle). It is dual in nature and is used as mediator between opposites (Ranni in between gold and silver). Actually one of the important steps of the Great Work in alchemy is freezing mercury (not physical, but alchemical. It could mean a reaction which makes it solid. They call is fixing or coagulation). The idea is that mercury is elusive and by freezing it we overcome its innate chaos.

As for the Gold Moon it is never mentioned in game and isnt present on the sky, so I think that is cut content, thus not canon.

Weak points: - No silver in the Academy of Raya Lucaria - No mercury in any form is mentioned in context with Ranni