Isaac Newton, Robert Hooke and the mystery of the orbit
pp. 77-94
in: Décio Krause, Antonio A. Passos Videira (eds), Brazilian studies in philosophy and history of science, Berlin, Springer, 2011Abstract
The concept of "force" is formulated in Isaac Newton's Principia in a series of propositions that define "force" in terms of Galileo Galilei's theorem on the fall of bodies. We claim that the distinctive characteristic of the concept of force as it stands in the Principia is reminiscent of a method to treat non rectilinear orbits suggested to Newton by Robert Hooke.According to an opinion, Newton had a method to draw physical orbits prior to his interaction with Hooke, and he used this method to draw an orbit in a letter to Hooke; according to a different opinion, Newton used Hooke's method to draw the orbit. We draw it by three different methods of numerical computation: one corresponds to Hooke's method, another corresponds to the above mentioned prior method, and the third is a standard higher order method of numerical computation; these solutions are then compared with the solution obtained by Newton. The conclusion is that if Newton had any method whatever to draw curves, and if he made any mistake in the application of the method, this mistake would have been in the sense of diminishing the angle of the pericenter, and not of increasing it, as it is in Newton's drawing.
