Let's get back to Sawicki's model though, again referring to his fig.1.

Point O is 1AU from the sun and it takes 365.3 days to complete an orbit so we can work out a(c) (centripetal acceleration), at O, using a(c) = w^2 r - it comes to 5.9303e-03 ms^-2. We also know the solar mass (1.989e30 kg) so we can work out a(g) (gravitational acceleration), at O, using a(g) = GM/d^2 - it also comes to 5.9303e-03 ms^-2. At point O therefore centripetal and gravitational acceleration are the same.

Point F is farther from the sun at 1AU+ 1 earth radius but it's period is the same at 365.3 days. Repeating the above calculations, using this increased distance, gives a(c) = 5.9306e-03 ms^-2 and a(g) = 5.9298e-03 ms^-2. Solar gravity is less than the centripetal acceleration, which means that (at point F) the sun in not able to supply all the acceleration required - something else is making up the difference.

Stop and think about this, we started looking for the force (acceleration) that pulls the tidal bulge at F up, but after doing 3 simple calculations we find that we really need a force (acceleration) to pull it down. Not an outward force, an inward force - the same as the sun's gravity.

Good isn't it? and it makes a lot more sense