Re: Tidal forces?
You're misreading that Wikipedia article. Yes, R_M appears in one of their equations, but only because that's the one that compares their densities, rather than their masses directly. In the case we're considering here, the density and radius are changing, but the mass is staying relatively constant. Radius of the Sun doesn't enter into it. The only situation where it's relevant to the gravity field when comparing spherical bodies is when you'd be within one of them.
ETA: See also Wikipedia on the shell theorem, https://en.wikipedia.org/wiki/Shell_theorem . It's pretty much what you were saying in your penultimate paragraph.
Biting the hand that feeds IT
