Simulating Kepler’s Geocentric Mars Orbit

Abstract

The word ’Geocentric’ comes from the Greek word Γεωκεντρικό which is a compound word composed from two words: “γεω” means Earth and “κεντρικό” means centric. Geocentric aspect, appears for the first time in ancient Greece. Pythagoras had formulated the geocentric system with the Earth at the center of the Universe surrounded by the orbiting planets with Sun included. Later Greek ancient astronomers, trying to explain the weird planetary motion in the sky, introduced the epicyclic theory.33The epicyclic theory was well formulated by Hipparchus and Apollonius. Using this theory the two famous Greek astronomers managed to explain the weird planetary motion on the sky. This theory states that the geocentric planetary motion could be considered as a combination of circular motions. Today this idea is quite sensible if we consider that the geocentric motion could be perceived as synthesis of two independent motions; one is the rotation of the planet around the Sun and the other is the apparent rotation of the Sun around the Earth. Someone could say that the heliocentric motion is hidden inside the geocentric planetary path as one of two superimposed motions. This logical conclusion is supported by F. Hoyle Hoyle (1975) who states “We know that the difference between a heliocentric theory and a geocentric theory is one of relative motion only, and that such a difference has no physical significance.” In other words Geocentrism isn’t completely wrong excluding only the arbitrary claim that the Earth is fixed and immobile at the center of the Universe.Geocentrism lasted many years until Nicolaus Copernicus at the middle of 15th century, proposed the heliocentric system by transferring the reference origin from Earth to Sun. Although Copernican model was capable explaining the geocentric orbits of planets with negligible eccentricity, it failed to give a convincing explanation in cases of planets with considerable eccentricity like Mars. The lack of symmetry in Mar’s trajectory led Kepler to discover that planet’s orbits weren’t circular, as it was already believed, but elliptical. According to (Evans, 1998, p.431) Kepler said “I therefore once again think it to have happened by divine arrangement, that I arrived at the same time in which he was intent upon Mars, whose motions provide the only possible access to the hidden secrets of astronomy, without which we would remain forever ignorant of those secrets.” In this article we are trying to simulate the process followed by Kepler, studying the apparent geocentric Mar’s orbit which triggered him to discover elliptical planetary orbits.The relation between heliocentrism and geocentrism is highlighted during this study. Besides, this aspect is mentioned by David R. Topper...But this fact is then sometimes generalized to positing that geocentrism and Heliocentrism are equivalent, that they are the same geometrically or mathematically or even exactly the same; in a phrase, there is an isomorphism between them... Topper (2007) The methodology which was used, in the whole process, relies on mathematical modeling. This approach is based mainly on dynamic position change over time, which the interactive mathematic software GeoGebra can generously provide. The end of this historical approach shows that the heliocentric view was revealed throughout a geocentric model, proving the equivalence of these two different aspects. Finally the theoretical numerical results of this study seem to be in full agreement with the astronomical records of that era with minimal discrepancies.