How the gravitational constant $G$ is determined?

Question

We know the gravitational constant is $G=6.67545 \times 10^{-11} m^3 kg^{-1} s^{-2}$. But how this value is determined at first?

Answer 1

The gravitational constant has been experimentally measured. Wikipedia has a brief but quite nice article on the history of measurements of $G$. The first measurement was made in 1798 (yes, that long ago!) by Henry Cavendish, who measured the gravitational force between lead spheres. The force from small masses is exceedingly small, but with sensitive equipment it can be measured.