Newtonian–Machian analysis of the
neo-Tychonian model of planetary
motions
Luka Popov
Department of Physics, University of Zagreb, Bijeniˇcka cesta 32, Zagreb, Croatia
E-mail:
lpopov@phy.hr
Received 5 December 2012, in final form 6 December 2012
Published 31 January 2013
Online at stacks.iop.org/EJP/34/383
Abstract
The calculation of the trajectories in the Sun–Earth–Mars system is performed
using two different models, both in the framework of Newtonian mechanics.
The first model is the well-known Copernican system, which assumes that the
Sun is at rest and that all the planets orbit around it. The second is a less wellknown
model, developed by Tycho Brahe (1546–1601), according to which the
Earth stands still, the Sun orbits around the Earth, and the 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...
...5. Conclusion
The analysis of planetary motions has been performed in the Newtonian framework with the
assumption of Mach’s principle. The kinematical equivalence of the Copernican (heliocentric)
and the neo-Tychonian (geocentric) systems is shown to be a consequence of the presence of
pseudo-potential (4.4) in the geocentric system, which, according to Mach, must be regarded
as the real potential originating from the fact of the simultaneous acceleration of the Universe.
This analysis can be performed on any other celestial body observed from the Earth. Since the
Sun and Mars are chosen arbitrarily, and there is nothing special about Mars, one can expect
to obtain the same general conclusion.
There is another interesting remark that follows from this analysis. If one could put the
whole Universe in accelerated motion around the Earth, the pseudo-potential corresponding
to pseudo-force (4.2) will immediately be generated. That same pseudo-potential then causes
the Universe to stay in that very state of motion, without any need for exterior forces acting
upon it.