1. Gonzalo: "You are gentlemen of brave metal; you would lift the
moon out of
her sphere, if
she would continue in it five weeks without changing."
2. Antonio: "The man i' the moon's too slow..."
3. Stephano: "How camest thou to be the siege of this moon-calf?"
4. Trinculo: "I hid me under the dead moon-calf's gaberdine for fear of the storm."
5. Sephano: "How now, moon-calf! How does thine ague?"
6. Stephano: "Out o' the moon, I do assure thee: I was the man i' the
moon when time was."
7. By this good light, this is a very shallow monster! I afeard of him! A very weak monster! The man i' the moon!"
Here are a few things that I found with a good amount of Google-Searching:
"Elizabethans believed the earth was flat...There was a sharp division between everything beneath the sphere of the moon, and all the rest of the universe."
Moon-calf actually refers to an aborted fetus, "abortive, shapeless, fleshy mass" attributed to the influence of the moon.
According to the Oxford Companion to the Body, the moon is thought of as the most "human" in the heavens (probably because many people found people or faces in the craters of the moon), and as a result of its phases, it has been linked to many other life cycles. Its three most common connotations are: the feminine principle, controlling menstruation, and cause madness, (the term lunacy is derived from the Latin luna, which means moon!).
With all of this information, I think that Shakespeare is using the
"man in the moon" and "moon-calf" so often because in this act, one, because there is a lot of lunacy going on, but also for the other moon connotations that an Elizabethan audience would have caught. Caliban, for one, does not have a distinctive human or animal form, so it makes sense for the stranded men to call him "moon-calf." Plus, he is driven by natural human vices, such as alcohol consumption... Shakespeare refers to the female using the moon, cycles of life, as well as madness with mentions of "moon" in Act 2.