Question

How do Galileo inferred that objects in a vacuum fall with uniform acceleration, and that force is not neccessary to sustain horizontal motion?

Answer 1

It's simple because when you write the formula of gravitation that's F=GMm/r^2
And when you write the Newton's second law F=ma
Thus
GMm/r^2 = ma
The mass of the object gets cancelled out, thus the acceleration of the object towards the centre of the earth is irrespective of the mass, I mean the gravitational field is same for any object. That's in the TOTAL VACCUM,but if there is no vaccum then the upward dragging force makes the object to fall at different rates and time. The gravitational law accounts the centre part so horizontal motion is not in the account to even ask about, motion is towards the center not away from it