In De Motu Animalium, Aristotle says there is an unmoved mover in the animal’s leg joint, and proceeds to a geometrical description of the axis of rotation of the joint. More famously, he says there is an unmoved mover in the apparent motion of the stars, and there too associates it with the geometrical axis of rotation. What is going on here? This is a good illustration of several points.
First, Aristotle is perfectly happy to use mathematics in natural science. (He just correctly thought early Greek arithmetic and geometry generally had little to contribute to the intelligibility of becoming, and correctly objected to superstitious Pythagorean enthusing in the Platonic Academy.)
Second, there is nothing mysterious about what he calls an unmoved mover. It refers to something that is in fact both observable and mathematically describable. (This is not the only way a concept can have value, but that is not the point here.)
Third, he calls the unmoved mover a “mover” in the sense that it is the descriptive law or form of the physical motion in question, not a driving impulse or force. In a similar move, Leibniz famously said God is the law of the series.