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If the moon is in waning gibbous phase, where would you look in the sky to see the moon at 10pm

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The phase has nothing to do with position, only the amount of moon visible, the point in the sky is based on the time of day, day of the month, (also varies)and location on the earth. on the east coast the moon at 10 will be in the middle of the southern sky

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This is incorrect. Since the Earth rotates under the moon it is at the same place above the horizon at any particular time. For instance, when full it is directly opposite the sun, so it is overhead at midnight no matter where you are on earth. At half full and waxing it is overhead at 6PM, etc.
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eastern horizon

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I don't think it would be visible at that time. A waning moon in the last quarter would rise around midnight.

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