Moon Day, Moon Month

We all know what a day is, and what a month is, on Earth. A day (really a synodic day, or solar day), is the time necessary for the Sun to return to the same position in the sky, as viewed by an individual from a specific location on Earth. For example, a day is how long it takes for the Sun to return to its highest point in the sky (local noon, with the Sun on your meridian).A month (really a synodic month) is the time necessary for a lunation, a sequence of phases of the Moon starting with, and returning to, a particular phase (for example New Moon to New Moon).So if you were living on the Moon, what would be a Moon day for you, and what would be a Moon month for you? Clearly, a Moon day would be the time necessary for the Sun to return to the same position in the sky. If you think about it, that would take an Earth month, or one lunation period. Here is a movie that depicts such a sequence. The blue dot is the Earth. You can also see the Milky Way rotating.

Similarly, a Moon month, would be the time needed to complete a series of phases of the illumination of Earth. Again, if you think about it, that would take an Earth month, or one lunation period. Here is a movie that depicts such a sequence. The "crazy orange thing" that goes flying by early in the movie is the Andromeda Galaxy.