When reading the Feynman Lectures (chapter 7, volume 1), Feynman was explaining the formation of tides on the Earth and said the following:
The moon does not just go around the earth, the earth and the moon both go around a central position, each falling toward this common position
I got confused by that statement. Does that mean that the 1st Kepler's Law actually means that a planet orbits around the center of mass and that this center of mass is the one located at one of the focus of the elliptical orbit? Or is the focus at the center of the massive body?
Moreover, if the Earth is orbiting around the sun, does that mean that it would be doing kind of small orbits in the large orbit? What I mean is that, if it is also orbiting around that center of mass from the Earth-Moon system, then its orbit around the sun would not be a perfectly elliptical path, it would be like going overall in an elliptical path but doing small circles through that path, right?
I would appreciate if someone can clear my doubts.