Here I present a set of animated diagrams representing Ptolemy's models of the planetary orbits.
Claudius Ptolemy was an Astronomer and Mathematician living in Egypt around 100-170AD. His most famous work is called the Almagest,"The Greatest", in which he describes a model of the Solar System in great detail.
The Almagest is complicated and based on ancient mathematics and date/time systems. Few people have read it, resulting in many false and over-simple explanations. I hope these animations will help to explain, and demonstrate the elegance of, Ptolemy's models.
Various translations of the Almagest have existed over the centuries and the diagrams here are based on Ptolemy's Almagest by G. J. Toomer, Duckworth, 1984 and A Survey of the Almagest by Olaf Pedersen (1974) revised by Alexander Jones, Springer 2011.
Ptolemy's stated intention was to extend and complement the works of earlier observers and philosophers. He used observations from the Babylonian Astronomical Diaries going back over 800 years together with those of Greek philosophers and his own measurements made in Alexandria.
The models are based on Greek philosophy where it was held that the planets must move in "uniform circular motions, since these are proper to the nature of divine beings...". Clearly there is difficulty in representing planetary orbits in this way. Ptolemy used circles but compromised over the positioning of the circles and the uniform motion.
In each model, the Earth is in the centre of the Universe and consists of the spheres of earth, water, air and fire as described by Aristotle. All planets, including Sun and Moon, orbit round the Earth.
Ptolemy used the Ecliptic as his reference plane and the Vernal Equinox as his reference point. Coordinates of planets are described in terms of longitude round the ecliptic from the equinox and latitude north or south of the ecliptic.It was known that the equinox moves about about 1 degree per century relative to the stars, but it was believed this was due to the stars moving, not the equinox.
Each planet has its own model and each model has a similar scale. Ptolemy did not try to lay out all the models in a complete solar system. In fact he was not sure in what sequence the planets should appear. All the models have a radius of 60 "partes", where a "parte" is an arbitrary unit of measurement.
Ptolemy also published a work called the Planetary Hypothesis which is sometimes regarded as a supplement to the Almagest. In this work, Ptolemy made some small adjustments to the parameters of the orbits and some major changes to the way latitude is calculated.
I have adopted these new values and theories to the extent they are described in Pederson(1974). In particular the theories of latitude represent a much more realistic representation of orbital inclination than those in the Almagest.
Each model is presented as an animated diagram on the left and scrollable text on the right
A set of tools above the diagram allow to stop/start, zoom in/out, tilt, rotate and control speed.
Mouse drag can be used to shift the diagram so you can examine different areas in detail.
The animation code is written in Javascript, developed using Netbeans, and deployed on the Interplanetary File System (IPFS) using Fleek.
The source is available on Github as is a PDF document describing the models in more detail.