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Earth-Moon distance

This question is addressed to those on the list (e.g. G3RUH, W3IWI, etc.) 
who are experienced and wise about orbital mechanics. It is not exactly 
amateur satellite stuff, but I expect to find more wisdom on this list than 

I am working up a set of orbits notes for use in an introductory college 
physics course. One of our exercises is calculating the orbital period of a 
two-body system. The usual equation, assuming circular orbits, is (please 
excuse the clunky mathematical notation):

T*T = (2*pi)*(2*pi)*r*r*r/G(M+m).

My problem is making this equation give good results when I apply it to 
the Earth-Moon system. The correct average period should be 27.322 days, 
but this answer requires r = 384,750 km. This is not satisfactory, because 
every reference lists the mean Earth-Moon distance as 384,400 km.

Am I expecting too much from this simple formula? Can someone show me 
my error or point me to some good references?

John Gibson

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