Kepler's laws and empirical observation

Earth ($5.97\times10^{24}\,\text{kg}$) and Moon ($7.35\times10^{22}\,\text{kg}$) separated by $3.84\times10^8\,\text{m}$: $$F = 6.67\times10^{-11}\frac{(5.97\times10^{24})(7.35\times10^{22})}{(3.84\times10^8)^2} \approx 1.98\times10^{20}\,\text{N}$$

Orbital mechanics, satellite trajectories, tidal predictions

Valid for point masses or spherical distributions