Armed with the geometric tools of the Greeks, we can understand some of the simple cycles of the sky. How can we understand the changing illumination of the Moon? The starting point is the idea that the Moon shines by the reflected light of the Sun. Just like the Earth, the Moon is always half illuminated by the Sun. However, the fraction of that half-lit surface that we see depends on the relative positions of the Earth, Sun, and Moon. When the Moon is near the Sun in the sky the lit side faces the Sun and we see only the dark half. This is a new moon. When the Moon is opposite the Sun in the sky the sunlit side faces us and we see a full moon. About a week after new moon, the Moon stands about 90° away from the Sun in the sky. This phase is called first quarter. About a week after full moon, the moon stands once again about 90° away from the Sun and the phase is called third quarter. Remember that the phases refer to portion of the Moon that we see; the Moon is always half-bathed in sunlight. This cycle is called the phases of the Moon.
Diagram of the phases of the Moon. Click here for original source URL.
Most people will be mystified if you ask them where to look for a full moon or a new moon. If you understand the geometry of the illumination, the answer is obvious. A new moon must rise and set with the Sun. A full moon must rise around sunset and set around sunrise. A first quarter moon rises around midday and is high in the sky around sunset, and a third (or last) quarter moon rises around midnight and is high in the sky around sunrise. We know that the Moon takes about 29.5 days to go through a cycle of phases, so it must move 360 / 29.5 or about 12° through the sky from day to day. It rises and sets 24 / 29.5 hours or about 50 minutes earlier each day. These patterns were well known to all ancient people.
Series of images of different lunar phases animated. Click here for original source URL.
You can notice something interesting about our explanation for the phases of the Moon — it makes no assumption about whether the Earth or the Sun is stationary at the center of the universe. This explanation requires only that the Sun and Moon travel on a similar path through the sky (the ecliptic) and that the Moon periodically pass between the Sun and the Earth. A model where the Sun and the Moon travel in concentric circles around the Earth can do this. In other words, the phases of the Moon provide no evidence for or against the idea of an Earth-centered universe.