La forma della Terra: una lezione sulla gravit\`a Newtoniana

Abstract

We suggest a lecture on Newtonian gravity, discussing how the use of the scientific method allows to rule out some of the models for the shape of Earth leaving a spherical Earth as the only possibility, in agreement with empirical observation. In particular, we suggest to focus on a physical quantity, namely the gravitational acceleration, that can be both computed theoretically and measured in experiments. Rather than insisting on the numerical code for the evaluation of the gravitational acceleration -- that can be computed anyway in any numerical analysis course -- we want to focus on the formal setting of the problem, emphasizing the importance of having a mathematical formulation capable of quantitative predictions, present the result and discuss it both qualitatively and quantitatively, comparing it with daily experience. We let the student notice that assuming a non-spherical Earth would result in a parallel component of the gravitational acceleration, in disagreement with measurement; moreover, in case we consider a disk-shaped Earth we show that this parallel component becomes more and more important as the boundaries of Earth are approached by an observer. Finally, we make quantitative predictions on how this abnormal component of the gravitational force would affect the free fall motion. We think that the topics discussed here can be presented both in high school and university classes of general physics, as well as in introductory classes about the scientific method.