At what speed does the Earth wobble around the EarthMoon center of m?

About 9 miles per hour. The sidereal period of the Moon's orbit around the Earth is 27 and 1/3 days. The center of m of the Earth and Moon is about 1,000 miles from the center of the Earth, the cirference is about 6,300 miles . The Earth wobbles around this in 27 and 1/3 days (655 hours)