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All of it though not at the same time.

At any point in time, it is a little over a half.

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Q: What fraction of the earth surface is illuminated by the sun?
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What is the efffect of rotation of the earth when facing the sun?

The illuminated patch on the earth's surface drifts westward relative to a fixed point on the earth as the earth spins eastward.


How much of the total surface of the Moon is illuminated by the Sun when it is at quarter phase?

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At any time, half of the entire Moon's surface is illuminated.


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Since the Earth is a Spheroid shape, (not a true sphere) 50% of its surface is illuminated by the Sun, at any given moment.


Is the moon always dark on one side?

No. The Moon is orbiting the Earth, but is illuminated by the Sun. About half of the Moon's total surface is illuminated by the Sun at any one time. As the Moon orbits the Earth, the same side always faces the Earth. The phases of the Moon represent the part of that face that is lighted on that particular day. We cannot see the far side of the Moon, but it will have the remaining part of the illuminated one-half.


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How much of the moon is illuminated by the sun at each position as the Moon's orbits earth?

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Like the Earth, the Moon is a sphere which is always half illuminated by the Sun, but as the Moon orbits the Earth we get to see more or less of the illuminated half.