how would you exaplain how and why each of the four moon phases appear to look like they do to us here on earth?

Sure! The four moon phases that appear to us here on Earth are New Moon, First Quarter Moon, Full Moon, and Last Quarter Moon. The appearance of these moon phases is influenced by the relative positions of the Earth, Sun, and Moon.

To understand how and why each moon phase looks the way it does, here's a step-by-step explanation:

1. New Moon: During a New Moon, the moon is located between the Earth and the Sun. The side of the moon that is illuminated by the Sun faces away from Earth, resulting in the moon appearing completely dark to us. To observe a New Moon, you would need to imagine a line connecting the Sun, Earth, and the Moon, and you would be looking at the unilluminated side of the moon.

2. First Quarter Moon: About a week after a New Moon, we observe the First Quarter Moon. At this point, the moon has completed about a quarter of its orbit around the Earth. From our perspective on Earth, we see half of the moon illuminated and half in darkness. The line connecting the Earth, Moon, and Sun forms a right angle, with the illuminated half facing toward us.

3. Full Moon: A Full Moon occurs when the Earth is positioned between the Sun and the Moon. This arrangement causes the entire side of the moon facing Earth to be illuminated by the Sun. As a result, we see the moon as a complete circle or disk. During this phase, the line connecting the Sun, Earth, and Moon is straight, and all the illuminated portion is visible to us.

4. Last Quarter Moon: Approximately a week after the Full Moon, we observe the Last Quarter Moon. Similar to the First Quarter Moon, half of the moon is illuminated and half is in darkness. However, this time the illuminated half is facing away from us. The line connecting the Earth, Moon, and Sun again forms a right angle, but now the illuminated side is facing away from us.

In summary, the varying appearance of the moon phases is due to the changing positions of the Earth, Moon, and Sun. These relative positions determine how much of the moon's surface is illuminated and which part is facing towards or away from us on Earth.