There is more to Newton's gravity than just that.No it's true for any object, not just point masses. You don't need to know the distribution of mass on a planet to use Newton's Law of gravity do you, - You only locate it's centre of mass and treat it just like a point mass. Newtons gravity law would be incredibly complicated otherwise wouldn't it
True, but in this case, the simplification simplifies-away the effect that we're discussing.And any physics problem is vastly simplified by analysing the motion of the centre of mass of the system.
No, it is more complicated than you realize. See all of the above posts about tidal locking. If what you were saying were true, there'd be no such thing as tidal locking. Heck, there'd be no such thing as tides if we could only consider the objects as point masses! To calculate tidal forces you, at the very least, need to consider a dumbell-shaped object with two point masses.The solution is actually very simple and I think you people are making it sound very difficult. It's not.
2/3 of the way down this page is a diagram showing the vector resultant fore doesn't pass through the CoM:
Here's a discussion of where the torque comes from:
Resulting torque: Since the bulges are now displaced from the A-B axis, A's gravitational pull on the mass in them exerts a torque on B. The torque on the A-facing bulge acts to bring B's rotation in line with its orbital period, while the "back" bulge which faces away from A acts in the opposite sense. However, the bulge on the A-facing side is closer to A than the back bulge by a distance of approximately B's diameter, and so experiences a slightly stronger gravitational force and torque. The net resulting torque from both bulges, then, is always in the sense which acts to synchronise B's rotation with its orbital period, leading inevitably to tidal locking. [/qutoe]