DescriptionEpicycles were introduced by Ptolemy in the 2nd century AD as a way of modelling the apparent motion of the sun, moon and planets across the sky. Although remarkably successful for the time, the model was later made more complex as an attempt to reconcile it with more accurate measurements. Eventually it was supplanted by the heliocentric model and Kepler's Laws. The project will investigate the mathematics describing the motion of celestial bodies across the sky, also known as spherical astronomy. Besides a comparison of epicycles and Keplerian motion, there are many potential avenues you may wish to explore: the prediction of sunrise and sunset times, the `equation of time' describing the difference in times predicted by sundials and clocks, the effects of the earth's precession and refraction on observations etc, using Lagrangian/Hamiltonian mechanics and orbital perturbation theory. PrerequisitesThere are no special prerequisites for the project, although those with 2H Mathematical Physics may wish to explore perturbations to Keplerian motion.ResourcesPerhaps the best introduction to the mathematics of epicycles is to be found in the article by Fitzpatrick: A couple of treatments of spherical astronomy which can be found in the Library are and some introductory material can also be found at Another source on epicycles and the ancients which is quite mathematical can be found atSome information on Lagrangian/Hamiltonian mechanics of the solar system can be found in |
email: Peter Bowcock