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Like everything else in astronomy, "it varies". Most cycles are sinusoidal; they go up and down at varying rates. When it is at the top or bottom of the cycle, it's hardly changing at all. When it is at the middle of the cycle, it can change pretty quickly.

I'm going to refer you to the Online Nautical Almanac, and you can look up the magnitude of the change for the day you're interested in. Let's look up today, August 10, 2013.

Today, 8/10/2013, it looks like the Moon's declination is moving south at about 10.7 minutes per hour. But by 8/15/13, the Moon's declination will be moving south at only 2.5 minutes per hour.

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Related Questions

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