The ancient Greeks knew that the diameter of the Earth is small compared to the distance to the stars. For example, there is a legend that the god Hephaestus accidentally dropped his anvil on Earth. It took $\tau=9$ days for the anvil to eventually hit the ground. Estimate the “height of the sky”, in accordance to the beliefs of the ancient Greeks.

Assume $GM=4\times10^{14} \rm Nm^2kg^{-1}$

Source: Romanian NAAO 2014