I believe that’s the same for every planet. And every moon. For every orbit.

Its just that the barycenter is inside the more massive object when one is much more massive than the other. Not that this makes much of a difference to anything.

I mean, sure, but that’d be like saying I’m pulling the earth towards me when I jump.
You don’t have to jump, you’re already doing it. Some of us more than others… *Looks in mirror and hangs head
Isn’t that canceled out by the pushing you do when you start to jump?
Yeah, but then I pull it back as I’m falling.
If you have ever done a handstand then you have lifted over your head the weight that the entire mass of the earth has in your own gravitational field.