[Calavar]

That's also true for, say, electromagnetism. The strength of the force follows the inverse square law, so the acceleration applied on an charged object depends not only on the intensity of the charges but also the distance between the two charges. The only difference between classical gravity and electromagnetism (in a mathematics sense) is that gravitational "charge" is mass, which means the mass term of the accelerated object can be canceled out since it is on both sides of the equation. For an object with a fixed mass (like the earth), that means you can say the acceleration is purely a function of distance rather than distance and mass of the other object. But I don't see how that makes the acceleration term invalid or implies that gravity doesn't actually cause acceleration.

[tsimionescu]

This is because classical gravity is wrong. The easiest way to notice this is to build an accelerometer, and show that while it is in freefall towards the Earth, it measures the same reading as it does while it is in space far away from any massive body. However, when it is resting on a table on the earth, it will measure an acceleration away from the table, upwards. The same direction of acceleration it will measure if put on a rocket in the direction of movement of the rocket.

You yourself are such an accelerometer. The feeling you get while falling is the same feeling you'd get if you lived on the International Space Station. If you wanted to add a module on the ISS to make you feel just like on earth, you'd a module that generates a force on your feet up towards you head, not a force that pushes on your head up towards your feet.

So, Newton's universal force of attraction is quite clearly wrong, and there is no equivalent force in reality.