What is the distance of the Earth's orbit around the Moon?

I realize the Earth and the Moon both orbit around their shared center of mass, and that in the case of the Earth and Moon this center is "inside" the Earth. However, I'm looking for an approach to determine the distance the Earth travels in one "orbit around the moon" (as small as it may be).

• The title of your question assumes that your frame of reference is fixed to Moon. Then, the radius of Earth's orbit around Moon is the same as that of Moon's orbit around Earth. Following from this, the circumference of Earth's orbit around Moon is also the same as that of Moon's orbit around Earth. If you mean that your frame of reference is the centre of mass of Earth+Moon system, then [Steve Linton's answer][astronomy.stackexchange.com/a/25378] is adequate. – garyF Mar 5 '18 at 11:45
• @garyF - Re-read the question. – Hot Licks Mar 5 '18 at 13:35
• If anyone knows of an animation that shows the Earth and the moon both moving correctly, I'd love to see that. Seems like the Earth is always stationary. – JPhi1618 Mar 5 '18 at 15:54
• Found this video which shows the motion pretty well. Also the Wiki article on barycenter has some basic animations. – JPhi1618 Mar 5 '18 at 16:37
• @JPhi1618 You'd need a pretty high resolution frame to show it clearly, as the scale of the Earth's motion is quite small compared to the separation. – dmckee Mar 5 '18 at 18:23

The orbits are not too far from circular, so the Earth travels about $2 \pi$ times that each month, so a little under 30000km.