What is the distance of the Earth's orbit around the Moon?
The mass of the Earth is about 81 times that of the Moon and the distance between their centres of mass is typically 384 400 km, so the centre of mass will be about 1/82 of this distance from the centre of mass of the Earth, which is about 4700km. 

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