This news just in from a Feynman lecture   http://www.feynmanlectures.caltech.edu/II_42.html     "Suppose we take the earth as an example and forget that the density varies from point to point—so we won’t have to do any integrals. Suppose we were to measure the surface of the earth very carefully, and then dig a hole to the center and measure the radius. From the surface area we could calculate the predicted radius we would get from setting the area equal to 4πr24πr2. When we compared the p