Kepler's 2nd Law states that the area swept by the line joining the Sun and the Earth is constant per unit time. And here the Sun is at fixed position. (first statement)
How about the area swept by the line joining the earth and the center of mass (or by the line joining the sun and the center of mass)? (second statement)
I went over the derivation and it seems that, based on constant angular momentum of the reduced mass, one can only prove the "first statement". However, I also see that in binary stars, this law is applicable to individual star in the system about the center of the mass e.g.
So is the second statement also correct? How to prove it (or deduce from the first statement)?