Newton-Machian analysis of Neo-tychonian model of planetary motions

Abstract

The calculation of the trajectories in the Sun-Earth-Mars system will be performed in two different models, both in the framework of Newtonian mechanics. First model is well-known Copernican system, which assumes the Sun is at rest and all the planets orbit around it. Second one is less-known model developed by Tycho Brahe (1546-1601), according to which the Earth stands still, the Sun orbits around the Earth, and other planets orbit around the Sun. The term "Neo-tychonian system" refers to the assumption that orbits of distant masses around the Earth are synchronized with the Sun's orbit. It is the aim of this paper to show the kinematical and dynamical equivalence of these systems, under the assumption of Mach's principle.