Back
Università del Molise (Campobasso – Italia)
GIREP Seminar
2003
Newton’s universal gravitation theory founds on the basic assumption that every bit of matter attracts every other bit of matter. Even though the widespread belief that the mathematical expression of Newton’s law results from the settlement of the experimental observations of planets motion on the background of Kepler’s laws, more properly it should be viewed as a straightforward issue of the embedment of Newton’s former statement in to the Euclidean and absolutistic space-time. In this paper, I suggest a heuristic derivation of Newton’s statement analytical form drawn from a critical reading of the Principia. Basically, the work is aimed to show to the students of the early years at University Science Courses to what extent basic assumptions about space-time structures in which mechanical phenomena are described affect the ultimate analytical form of the gravitation law and to what degree they restrict its applicability. Emphasis is laid to the observation that time does not appear in the Newton’s law neither explicitly nor implicitly. Despite his sizeable epistemic and philosophical implications, such a fault did not hamper a firmly establishment of the law, chiefly because of the smallness of the numerical errors arising from its application to the planetary scale. This point is spelled out through some simple numerical examples. Finally, the quest of a more efficient gravitational theory (like, for example, Einstein’s general relativity) is shown to be the need to overcome the logic-mathematical restrictions dictated from the Newtonian formalization more than the attempt of an improvement of the numerical reliability of the model.