Refutability – Newtonian Mechanics

In honor of Rabbi Michael Avraham
Hello,
I saw an idea from the Rabbi regarding the question of whether the basic principle of evolution, the survival of the fittest, can be refuted. Following these words, I was inspired to discuss Newtonian mechanics and I mean Newton’s three laws. Can mechanics be refuted? Let’s take the law of conservation of momentum. The law of conservation states that if the system is not subject to an external force, then the total momentum in the system is conserved. If it were shown that we did an experiment and the total momentum was not conserved, we would not say that the law of conservation of momentum is not valid, but that there is an external force acting on the system. Maybe we would start looking for this force, maybe we would come to the conclusion that it is a “real” or Delambret force, but we would not claim that the law of conservation is not valid. The same goes for the law of conservation of energy.
The same thing will essentially happen to any experiment in mechanics, we will perform an experiment that will predict a certain kinematics of the system, if that kinematics is not obtained, it is said that there is an additional force or an additional unknown mass, etc. I am a student at the Technion and a physics professor here told me that I was right and that this is one of the problems that physics is facing today regarding dark matter/dark energy.
Another question, is Newtonian mechanics in its current form necessary? That is, Newtonian mechanics links the concept of force to acceleration. Could I create another complete mechanics that links the concept of force to velocity? I admit that this would be very inconvenient and computationally cumbersome mechanics, it would give me time-varying forces and other inconvenient phenomena. But if this is indeed possible, it turns out that Newtonian mechanics, mainly in the second law, only gives us language and nothing more.
If this is true, I still don’t think that mechanics as a whole is irrefutable, but only the three laws. For example, when I state that the acceleration of gravity on the edge of the Earth is 9.8, this is a definitely refutable claim. However, on second thought, where does that come from? Can’t I say that the acceleration of gravity is 10 and there is an unknown force that gives me -0.2? I think not, and here I think there should be a distinction between a fundamental inability to refute, as I mentioned regarding the three laws, and regarding this claim that I just made excuses for why it doesn’t have to be like that, etc. And by the way, there really is a change in the gravitational field, a tiny change, between those who are closer to the sun on the globe and the other side because of the centrifugal force of the sun.
Another point, I don’t think that Newtonian mechanics is completely irrefutable because relativity supposedly refuted it. I think it assumes 2 things, continuous time and Euclidean geometry of space and that’s where it can be refuted. But the three laws overall define the concept of force, define a language, on which we clothe the forces of nature.
Indeed, the importance of mechanics, even if it is just a language, is that it helps us quantify causality in physics, and that it is incredibly convenient for calculation.
And if we mentioned Delembert forces, what is the Rabbi’s opinion about Newton’s Hadley experiment and Mach’s principle? That professor introduced him to me following the conversation we had. At the end of the conversation, although he agreed with me, he claimed that this is the difference between physics and philosophy, that in physics what is important is that things work. Although he agreed that it is an important principle.