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Three or four weeks ago I was outside showing my neighbors how cool the moon was through a 'backyard' telescope in broad daylight (~8PM PDT). It was 3/4 of the way across the sky (setting behind the houses behind us.) Two weeks later the moon was not even up yet at 8PM. The planets I've been watching (Jupiter, Saturn, Mars) are all rising and setting a little earlier each day as I would expect.

Why did the moon abruptly change its position in the sky a couple of weeks ago?

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Compared to the planets the moon changes it's rise and set times very quickly. Using the calculator on this page it can be seen that if one were looking at the sky on May 1st, 2014 from Irvine, California the moon set at 10:08PM (which at 8PM would have had the moon most of the way across the sky as noted in the question.)

The moon rises and sets approximately one hour later each day. So, by May 14th the moon did not even rise until nearly 8PM - which also correlates with the observations noted above.

Contrasting that with the other context point made in the OP, using this page we can see that on May 1st Saturn rose at 8:07PM and on May 14th rose at 7:11PM.

So while the moon changes its rise a set times by almost an hour each day, the planets change much more slowly by comparison, in this case only 56 minutes over two weeks.

If one weren't continually watching the moon's progression it would appear to abruptly change positions when comparing it to the planets' movements.

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That is good, for a question like this it is best if you figure it out for yourself, as you have done. Well done. –  Jeremy May 18 at 20:01
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The moon orbits the Earth in roughly 29 days. So in 14 days, it would be on the other side of the Earth.

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The moon didn't abruptly change position, it is gradually and continually changing position. You've obviously never really noticed what it is doing until now. You would really benefit from getting a planetarium application for your PC or device and adjusting the time base to see how everything moves. You'll get a much better understanding of the mechanics of it all, why the moon goes through phases, and why it rises and sets at different times.

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