Open AccessLA LEGGE GRAVITAZIONALE DELL’INVERSO DEL QUADRATO NEI PRINCIPIA DI NEWTON
Author(s) -
Antonio Giorgilli,
Niccolò Guicciardini
Publication year - 2021
Publication title -
rendiconti. classe di scienze matematiche e naturali
Language(s) - English
Resource type - Journals
eISSN - 2384-986X
pISSN - 1974-6989
DOI - 10.4081/scienze.2021.768
Subject(s) - inverse square law , square (algebra) , section (typography) , philosophy , calculus (dental) , physics , mathematics , gravitation , classical mechanics , geometry , computer science , medicine , dentistry , operating system
We revisit the question concerning the accuracy of the inverse-square gravitational law, as raised in section IX, book I of Newton’s Principia, and in some sections of book III. We argue that the problem has been thoroughly discussed and basically solved by Newton himself. We point out in particular the relations with the well-known Bertrand’s theorem. Bertrand approached the same problem in more abstract terms. We remark, however, that much of Bertrand’s proof is essentially contained in Principia.