How long does it take the moon to complete an entire phase change?thanks
http://en.wikipedia.org/wiki/New_moon#Determining_new_moons:_an_approximate_formula
If you are in a science class you need to learn how do do your own research. Get to it!
Lunar months are quite variable in length for several reasons including the fact that the earths orbit around the sun is elliptical and not circular. According to the web page http://scienceworld.wolfram.com/astronomy/Lunation.html
between 1900 and 2100 the lunation or period between new moons will have varied from 29 days 6 hours and 35 minutes and 29 days 19 hours and 55 minutes. The figure usually given for the mean length of a lunar month is 19 days 12 hours and 43 minutes.
There isn't an exact answer. The moons position is one of the hardest to
calculate. Google"lunar ephemerides" and "evection".
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