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Apollonius of Perga (3rd century BC) realized that this cyclical variation could be represented visually by small circular orbits, or epicycles, revolving on larger circular orbits, or deferents. Hipparchus (2nd century BC) calculated the required orbits. Deferents and epicycles in the ancient models did not represent orbits in the modern sense ...
Book III describes his work on the precession of the equinoxes and treats the apparent movements of the Sun and related phenomena. Book IV is a similar description of the Moon and its orbital movements. Book V explains how to calculate the positions of the wandering stars based on the heliocentric model and gives tables for the five planets.
For the ratios of the radii of the outer planets' deferents to radius of the Earth, the Commentariolus gives 1 13 ⁄ 25 for Mars, 5 13 ⁄ 60 for Jupiter, and 9 7 ⁄ 30 for Saturn. For the ratios of the radii of their deferents to the radii of the larger of their epicycles, it gives 6 138 ⁄ 167 for Mars, 12 553 ⁄ 606 for Jupiter, and 11 ...
The epicycles of the planets in orbit around Earth (Earth at the centre). The path-line is the combined motion of the planet's orbit (deferent) around Earth and within the orbit itself (epicycle). Around 210 BCE, Apollonius of Perga shows the equivalence of two descriptions of the apparent retrograde planet motions (assuming the geocentric ...
Noted critics of the equant include the Persian astronomer Nasir al-Din Tusi who developed the Tusi couple as an alternative explanation, [10] and Nicolaus Copernicus, whose alternative was a new pair of small epicycles for each deferent. Dislike of the equant was a major motivation for Copernicus to construct his heliocentric system.
Philolaus (4th century BCE) was one of the first to hypothesize movement of the Earth, probably inspired by Pythagoras' theories about a spherical, moving globe. In the 3rd century BCE, Aristarchus of Samos proposed what was, so far as is known, the first serious model of a heliocentric Solar System, having developed some of Heraclides Ponticus' theories (speaking of a "revolution of the Earth ...
Size of deferents, epicycles Only ratio between radius of deferent and associated epicycle determined; absolute distances not determined in theory Interior planets: Average greatest elongations of 23° (Mercury) and 46° (Venus) Size of epicycles set by these angles, proportional to distances Interior planets Limited to movement near the Sun
These oscillations generally occur on a once-monthly or twice-monthly time-scale. The line of its apses precesses gradually with a period of roughly 8.85 years, while its line of nodes turns a full circle in roughly double that time, 18.6 years. [29] This accounts for the roughly 18-year periodicity of eclipses, the so-called Saros cycle ...