What Is Galileo's Argument For The Movement Of The Earth?

In the discourse involving Galileo’s findings and theories, there has been much reference to the works of the pagan Aristotle. While his genius is indisputable, his ignorance is also evident in matters of which we have newfound knowledge. Consequently, his writings on such subjects as astronomy must be considered only under heavy scrutiny. This scrutiny reveals, as shall be demonstrated, Galileo’s rectitude in supporting the Copernican model of the movement of the Earth.
Aristotle presents several arguments to explain and defend his proposition of an immobile Earth. These arguments, however, tend to be based on abstract hypotheses rather than empirical evidence. In fact, the idea of the corruptibility of the Earth in mutual exclusion from the perfection of that outside the Earth, an idea fundamental to his arguments, is itself rather unfounded. Aristotle makes this claim with little evidence, only that the celestial bodies appear to be spherical and unchanging and move in a circle about the Earth, and that

Aristotle’s beliefs suggest that the observable directly vertical fall from a height is evidence of Earth’s immobility, for, surely, a moving Earth would move under the falling object, changing its path from a straight line. What Aristotle overlooks here is the circular motion already in the object as an Earthly object. We have all observed, as a marble rolls off the edge of the table, it does not land directly at the foot of the table; it retains its horizontal motion to fall a distance from the table. In the same way, an object dropped from a height retains the motion granted to it by the Earth’s rotation, to move at the same speed as the Earth, falling precisely below where it was dropped, or rather, to the new position of the Earth. While we, as we move with the Earth, see the object fall straight down, an unbiased observer would see the object fall with horizontal movement equal to that of the Earth below