Geocentric Model of the Solar System

Introduction

The Astronomical geocentric model or geocentrism,

often denited by the Ptolemaic system is a very ancient terminology of the Universe with Earth at the center. Under the geocentric model, the Sun, Moon, stars, and planets all orbit the Earth. The geocentric model was the predominant description of the cosmos in many ancient civilizations, e.g., those of Aristotle in Classical Greece and Ptolemy in Roman Egypt.

There were some observations that supported the idea that Earth was the center of the Universe:

First, from anywhere on Earth, the Sun appears to revolve around Earth once per day. Whereas the Moon and the planets have their own motions, they also appear to revolve around Earth about once per day. The stars appeared to be fixed on a celestial sphere rotating once each day about an axis through the geographic poles of the Earth.

Again, Earth seems to be not moving from the perspective of an earthbound observer.. it feels solid, stable, and stationary.

Ancient Greek, and Roman, and the philosophers usually combined the geocentric model with a spherical Earth, in contrast to the older flat-Earth model implied in some mythology. The ancient Jewish Babylonian sources pictured a flat Earth with a dome-shaped, rigid canopy called the firmament placed over it. However, the ancient Greeks believed that the motions of the planets were circular and not elliptical, a view that was not challenged in Western culture until the 17th century, when Johannes Kepler postulated that orbits were heliocentric ones, as for his 1st law of planetary motion. In 1687 Newton showed that elliptical orbits could be derived from his laws of gravitation.

The astronomical predictions of Ptolemy's geocentric model, developed in the 2nd century CE, served as the basis for preparing astrological and astronomical charts for over 1500 years. The geocentric model held sway into the early modern age, but from the late 16th century onward, it was gradually superseded by the heliocentric model of Copernicus, Galileo, and Kepler.

Astronomy in Greece

The geocentric model entered Greek astronomy and philosophy at an early point; it can be found in pre-Socratic philosophy. In the 6th century BC, Anaximander proposed a cosmology with Earth shaped like a section of a pillar (a cylinder), held aloft at the center of everything. The Sun, Moon, and planets were holes in invisible wheels surrounding Earth; through the holes, humans could see concealed fire. About the same time, Pythagoras thought that the Earth was a sphere , by the observations with similarities eclipses, but not at the center..  they believed that it was in motion around an unseen globe of fire. Later these views were combined, so most educated Greeks from the 4th century BC on thought that the Earth was a sphere at the center of the universe.

Ptolemaic model

Although the basic tenets of Greek geocentrism were established by the time of Aristotle, the details of his system did not become standard. The Ptolemaic system, developed by the Hellenistic astronomer Claudius Ptolemaeus in the 2nd century AD finally standardised geocentrism. His main astronomical work, the Almagest, was the culmination of centuries of work by Hellenic, Hellenistic and Babylonian astronomers. For over a millennium European and Islamic astronomers assumed it was the correct cosmological model. Because of its influence, people sometimes wrongly think the Ptolemaic system is identical with the geocentric model.

Ptolemy argued that the Earth was a sphere in the center of the universe, from the simple observation that half the stars were above the horizon and half were below the horizon at any time (stars on rotating stellar sphere), and the assumption that the stars were all at some modest distance from the center of the universe. If the Earth was substantially displaced from the center, this division into visible and invisible stars would not be equal.

Motion of planets according to Ptolemy

In the Ptolemaic system, each planet is moved by a system of two spheres: one called its deferent; the other, its epicycle. The deferent is a circle whose center point, called the eccentric and is removed from the Earth. The original purpose of the eccentric was to account for the difference in length of the seasons , such as, the northern autumn was about five days shorter than spring during this time period, by placing the Earth away from the center of rotation of the rest of the universe. Another sphere, the epicycle, is embedded inside the deferent sphere. A given planet then moves around the epicycle at the same time the epicycle moves along the path marked by the deferent. These combined movements cause the given planet to move closer to and further away from the Earth at different points in its orbit, and explained the observation that planets slowed down, stopped, and moved backward in retrograde motion, and then again reversed to resume normal, or prograde, motion.

The deferent-and-epicycle model had been used by Greek astronomers for centuries along with the idea of the eccentric, just a little off-center from the Earth, which was even older. Unfortunately, the system that was available in Ptolemy's time did not totally matched the  observations, even though it was considerably improved over Hipparchus' system. Most noticeably the size of a planet's retrograde loop, mainly  for the plantet Mars, would be smaller, and sometimes larger, than expected, resulting in positional errors of as much as 30°. To resolve the problem, Ptolemy developed the equant. The equant was a point near the center of a planet's orbit which, if you were to stand there and watch, the center of the planet's epicycle would always appear to move at uniform speed, and all other locations would see non-uniform speed, like on the Earth. By using an equant, Ptolemy claimed to keep motion which was uniform and circular, although it departed from the Platonic ideal of uniform circular motion. The resultant system, which eventually came to be widely accepted in the west, seems unwieldy to modern astronomers; each planet required an epicycle revolving on a deferent, offset by an equant which was different for each planet. It predicted various celestial motions, including the beginning and end of retrograde motion, to within a maximum error of 10°, considerably better than without the equant.

The model with epicycles is in fact a very good model of an elliptical orbit with low eccentricity. The well known ellipse shape does not appear to a major extent when the eccentricity is very low, but the offset distance of the "center" as the Sun, and is very much observable  even with low eccentricities as possessed by the planets.

It has been proven, in fact, that the Copernican, Ptolemaic and even the Tychonic models provided identical results to identical inputs. They are computationally equivalent. It wasn't until Kepler demonstrated a physical observation that could show that our sun is directly involved in determining an orbit that a new model was required.

The Ptolemaic order of spheres from Earth outward is:

  ● Moon

  ● Mercury

  ● Venus

  ● Sun

  ● Mars

  ● Jupiter

  ● Saturn

  ● Fixed Stars


Ptolemy did not invent or work out this order, which aligns with the ancient Seven Heavens cosmology related to mythology, common to the major Eurasian cultural traditions. It also follows the decreasing orbital periods of the Moon, Sun, planets and stars.