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Lovely words yiur grandpa's!
Actually they are still rainbows, but they call them moonbows just to distinguish them from the ones we see in daytime.

He used to tell me that all rainbows have double rainbows. And triples for that matter. It's just whether or not you can detect them with your eye. Most of the time they are simply too dim to be visible. Which I found was true once I grown up.

Your grandpa must have taught you so much, he sounds like a great man.