Is not as easy as that, tide times and amplituded vary wildly from year to year for any given date. This is due to the fact that orbits are elliptical and the earths spin is at a tilt and also wobbles. So exact relative position is rarely repeated and impossible to predict- without newtonian physics. And yes , we can predict where the moon will be for thousands of years into the future, down to the millimeter, using basic newtonian physics.

Is our understanding of gravity perfect? No. Gravitational therories break down at the quantumn scale, this is true. However, observational data shows that the newtonian model is highly accurate at our scale. This is why we have sattelites, areoplanes, raines and cars. Because the math derived from newtons laws predicts the motion of objects so well, we can use them to predicably engineer the tech we use daily. If they didnt work, how come planes fly, satellites can be launched into orbit, and why tide tables are perfectly accurate?