# The tested length scale of classical mechanics

I was reading this, and I am left wondering actually how good classical physics, Newtonian mechanics or general relativity, is in very large length scales, as an approximation?

Therefore, I would like to ask: to what scale, order of magnitude of length, classical mechanics is observationally/ experimentally verified? How is the observation done? $^{\dagger}$

P.S:I am trying to ask a question as well posed as I can, if you find any problems - please at least comment, such that I will learn.

$\dagger:$ I would like an answer that a well prepared physics undergrad can understand. (or at least, a master degree physics student)

Leaving that point aside and to give you a concrete example to illustrate how small quantum effects usually are lets take gravity and the Newtonian inverse square law as an example. First of all this law gets corrections from considering the more complete theory of General Relativity and this is often a very small effect. In the solar-system the correction is of the order of $10^{-5}$ and when we try to test gravity these are usually the corrections we try to measure. The quantum corrections are much much smaller. Just from dimensional analysis these can be estimated to be of the order
$$\frac{G\hbar}{r^2c^3} = \left(\frac{r_{\rm Pl}}{r}\right)^2$$
where $r_{\rm Pl} \sim 10^{-35}$m. In the solar-system this is a correction of the order of $10^{-80}$.