# Re: Earth-Moon distance

• Subject: Re: [amsat-bb] Earth-Moon distance
• From: Norm McMillan <njmcmillan@xxxxxxxxxxx>
• Date: Sat, 23 Oct 1999 07:55:22 +1000

```John Gibson wrote:
>
> 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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The error is less than 1%!!! Considering the Earth as an oblate sphere
and the moons orbit as not truly circular would probably account for the
difference.

But then, I'm not an orbital mechanic!!!!!

Norm
VK2XCI

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