IIRC, the moon and earth kind of revolve around each other. Almost dual planets.
No. The barycenter is below the surface of the earth. The moon is a moon.
The ratio of mass of the earth to mass of the moon is 82.4, so the ratio of the distance from the center of the earth to the center of mass and the distance from the center of the moon to the center of mass is 1/82.4. So the distance from the center of earth to the center of mass will be 1/(82.4 + 1) * 387000 = roughly 4630 kilometers. Which means the center of mass lies under the surface of the earth.
The book Darwin’s Ghost (by Ateve Jones) tells us that ... “The Moon flew off its parent after a giant impact. Because it stayed small, cold and undisturbed it gives a better picture of the past than does its parent. A guick trip by the Apollo 11 mission was enough to date it. The Earth’s turmoil makes it harder to trace its own origin. Its oldest rocks, found in Greenland and Western Australia, are just under four billion years old.”