[brothrock]

The phases of the moon and the shadow cast on the moon during a lunar eclipse are not related. The phases of the moon are caused by the position of the moon relative to the Earth and the Sun. Imagine two lines extending from Earth to the Sun and the Moon, if the angle at Earth is 90 degrees, the moon appears half full to the people on the side of the Earth that can see it. If that angle is 180 degrees, it’s full. Zero degrees is a new moon. The reason the phases last all night is because the moon rotates ~27 days, therefore changing its relative position to the sun only slightly in a night.

A lunar eclipse occurs during a full moon and the Earth, Moon and Sun are aligned. causing the Earth to cast a shadow on the Moon. This doesn’t happen every Moon rotation because the Moon’s orbit is slightly off.

[sokoloff]

You can fairly well demonstrate this to yourself with a dark room, a single lamp, and a soccer/basketball.

Put the light at one wall center, the ball in the middle, and walk around the ball. You can see the new, quarter, full, quarter ball lit up just as you can from Earth. (Naturally, the sun is too close in this example, so the shadow lines won’t be as crisp.)

[masonic]

They're related only in the sense that a lunar eclipse can only happen at full moon, and a solar eclipse can only happen at new moon.