And on the right, we have Ptolemy's attempt to explain retrograde motion with a fixed Earth, using epicycles. Both ideas (Copernicus' Sun-centered system, and Ptolemy's Earth-centered system) seem to work well. But the Sun-centered system is the true situation:
www.jimloy.com/cindy/ptolemy.htm www.jimloy.com/cindy/ptolemy.htm
These ideas concerning uniform circular motion and epicycles were catalogued by Ptolemy in 150 A.D. His book was called the "Almagest" (literally, "The Greatest"), and this picture of the structure of the Solar System has come to be called the "Ptolemaic Universe".
csep10.phys.utk.edu/astr161/lect/retrograde/aristotle.h... csep10.phys.utk.edu/astr161/lect/retrograde/aristotle.html
physique et optique avec Cabri Géomètre ... ; Ptolemy's Epicycle (CabriJava version) version française; Place the cursor on the figure to observe animation ... ( other CabriJava animations ); Click twice to erase the traces, then once to resume the animation.
www.sciences.univ-nantes.fr/physique/perso/cortial/bibl... www.sciences.univ-nantes.fr/physique/perso/cortial/bibliohtml/epiclc_ja.html
Ptolemy's Solar System ... Ptolemy and Retrograde Motion II ... Epicycles (2002)
youtube.com/watch?v=faqjmAoXpM4
Feb-11-05: Ptolemy & Epicycles ... The key elements are ... the epicycle to account for the retrograde...
jca.umbc.edu/~turner/105/chapter03/105_history.ppt_file... jca.umbc.edu/~turner/105/chapter03/105_history.ppt_files/slide0016.htm
Retrograde Motion, Animations and explanations; Models of Planetary Motion from Antiquity to the Renaissance; Almagest Ephemeris Calculator; Star Catalogue of Ptolemy; Ptolemy's Epicycles; Ptolemy on Astrolabes; Ptolemy on Sundials;
www.mlahanas.de/Greeks/PtolemyAstronomy.htm www.mlahanas.de/Greeks/PtolemyAstronomy.htm
However, Copernicus, like Ptolemy, also used circular orbits and had to resort to epicycles and deferents to explain retrograde motions. In fact, Copernicus was forced to use more epicycles than Ptolemy, i.e. a more complicated system of circles on circles.
zebu.uoregon.edu/~js/ast221/lectures/lec06.html
Lecture 3d. Ptolemy & Epicycles ... 3. Ptolemy solved this problem by inventing epicycles ... Ptolemy's predictions were only close to observations, and the configurations of epicycles and deferents needed continual revision as better data became available...
solar.physics.montana.edu/welsch/Phys101/lecture3d.html
Lecture 5 C. Retrograde motion & Epicycles ... On the other hand, from the WRONG geocentric viewpoint of Ptolemy, with everything orbiting Earth, one would believe any backward (E to W) motion to be actual, not just apparent! ... so Ptolemy invented epicycles so planets would actually move forward sometimes & backwards others:
solar.physics.montana.edu/welsch/Phys101/lecture5c.html
To better understand the retrograde motion of the planets, Ptolemy used epicycles (small orbits of the planets) within the larger orbit around the Sun. These epicycles seemed to fit the observations that he and other astronomers had recorded.
astronomy.wakaf.net/htm/ptolemy.htm astronomy.wakaf.net/htm/ptolemy.htm