We all see the same moon at the same time, but because of the time differences, we see the moon at different times. In reality, we all see the moon at the same time… Both New and Full Moon are very specific instances of time when the Moon is at a specific location in its orbit around the Earth. This moment in time doesn’t care what time zone anyone on Earth is located in either! Astronomers use a standard called Universal Coordinated Time, which is the time at Greenwich England. Everyone else on earth is in a time zone that is some offset from this coordinated time. On the East Coast of the United States for example, the time zone is 5 hours earlier (or 4 hours during Daylight Savings Time) than it is in Greenwich while people living in California are another 3 hours displaced for their local time. This makes civil life make more sense as sunset is “about” 5 O’clock for everyone because the time zones flow all the way around the Earth, and this keeps the Sun ins “about” the same place for everyone during their same times of day. Have you ever seen a television show advertised to come on at 8pm Eastern, but 7pm Central? Time zones at work, the broadcast is at the same time for everyone, but their local time zones, or offsets from Greenwich are different. This is why New Moon might be at 1am for someone on the East coast, but at 10pm the previous day for someone on the West coast. It’s the same moment in time, but because of civil time zones (and our round Earth), our local clocks are different. https://www.moongiant.com/fullmoons/2019/
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