A mathematical model for a didactic device able to simulate a 2D Newtonian gravitational field

摘要

In this paper we propose a mathematical model to describe a theoretical device able to simulate an inverse-square force on a test mass moving on a horizontal plane. We use two pulleys, a counterweight, a wire and a smooth rail, in addition to the test mass. The tension of the wire (i. e. the attractive force on the test mass) is determined by the position of a counterweight free to move on a rail placed under the plane. The profile of the rail is calculated in order to obtain the required Newtonian force. Details of this calculation are reported in the paper, and numerical simulations are provided in order to investigate the stability of the orbits under the effect of the main friction forces and other perturbative effects. This work points out that there are some criticalities intrinsic to the apparatus and gives some suggestions about how to minimize their impact.