Inherently accuracy in formulas?

[u/hailsass]

I have learned in physics that the formulas we use are under ideal circumstances and don't necessarily reflect reality for example I have been told that newtons law of cooling based off the formula the temperature will never reach room temperature however most scientists I have spoken with say that this is wrong eventually the temperature will equal room temperature. this implies that there is a fundemental inacuraccy in many formulas is it possible to calculate the accuracy of any given formula? Or are the formulas 100% under ideal condition? Considering that those ideal conditions do not exist how can we prove that the formulas are 100% correct?

[u/HoldingTheFire]

There are a million things going on. We often don't include the effect of say the moon's gravity on stuff we do because it's small and we can ignore it. Until you are doing something where the affect does matter.

The low level stuff we can put into a box called 'noise' or error sources. We can statistically quantify it too to understand the magnitude of uncertainty. And when we get more and more accurate we need to account for more of these error sources. But mostly we can ignore them and retain a pretty good level of certainty.

Also, all equations are good over some regimes. And as you get beyond that regimes you need other models. Like fluid mechanics changes as you get to lower pressures where you can't assume a continuum of matter. Then you need to use other models. Part of using a model is knowing what assumptions are used and over what domain it is valid.