Does Newtonian physics work everywhere in the universe, or only in a local frame?

Physics is like trying to find which set of addends gives you four: two plus two, three plus one, and the square root of sixteen all reach four, so the real work is diagnosing which one truly fits the problem. Newton diagnosed the earth's equatorial bulge and much else by assuming absolute space, and his famous bucket experiment is the root of it: when the spinning water climbs the sides of the bucket, he reasoned that the surrounding space must itself be motionless and absolute, so that a body moving through it can be said to move in a straight line. He then extended that absolute, non-rotating space to the whole universe, which forced the conclusion that the stars only appear to circle us because the earth rotates. But two hundred years later Ernst Mach pointed out that Newton had no right to assume the universe is absolute and cannot rotate; to claim that is to be a metaphysician, not a physicist. Once you drop that assumption, both systems become mathematically viable: Newton's earth rotating in fixed space, or a fixed earth with the universe rotating around it, where our equation is not just F equals ma but F equals ma plus the centrifugal, Coriolis, and Euler forces, which in our system are real forces, not mere effects. Only one can be true, and the empirical evidence, the Michelson-Morley result and the cosmic microwave background, leans toward the fixed earth. You can see the flaw in Newton concretely in the galaxy rotation curves: every spiral galaxy rotates about ten times too fast for F equals ma, so rather than admit the equation is wrong they invented dark matter, the missing mass they have never been able to find, as a patch to keep Newton's core equation alive. The rotating-universe forces supply the answer instead.