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

TL;DR

This paper compares the Newtonian trajectories of the Copernican and Neo-tychonian planetary models, demonstrating their kinematical and dynamical equivalence under Mach's principle.

Contribution

It introduces a Newtonian analysis of the Neo-tychonian model and shows its equivalence to the Copernican system based on Mach's principle.

Findings

Both models produce equivalent planetary trajectories.

The Neo-tychonian model can be reconciled with Newtonian mechanics.

Mach's principle underpins the equivalence of these models.

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.