# Earth-Moon distance

• Subject: [amsat-bb] Earth-Moon distance
• From: John Gibson <GIBSON@xxxxxxxx>
• Date: Fri, 22 Oct 1999 11:03:18 -0400 (EDT)

```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
elsewhere.

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
no8V@amsat.org

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