# Ptolemy's geocentric system of the universe

## The purpose of the program

The purpose of this program is to enable you to find out for yourself how good (or bad) Ptolemy's geocentric system of the universe was at 'saving the appearances' - i.e. predicting the positions of the planets in the sky.

## How it works

For each of three representative celestial object - the Moon; one of the inferior planets, Venus and one of the superior planets, Mars - the real orbit of the body is calculated using the known Keplerian parameters of the body. Your task is to simulate that orbit using the devices which Ptolemy (or Copernicus) allowed himself.

(I should mention one small proviso here, namely that for simplicity only the largest eccentricity has been incorporated into the calculation of the real orbit so in reality, Ptolemy would not have been able to achieve quite such a good fit as you can achieve. Also, bear in mind that with a click of your mouse you can test out a theory that would have taken Ptolemy months of calculation to check!)

## Main window

When you start the program the main window looks like this

The mode is initially set to Earth/Moon and the Moon is shown rotating round the Earth every 10 seconds approximately.

The Moon's orbit is slightly elliptical with an eccentricity of 5.5%. The large blue circle is called the deferent and is the starting point for simulating the actual orbit of the Moon and the simulated Moon will be seen orbiting around this circle.

At the bottom is a panel which shows the relative positions of the simulated Moon and the real Moon as seen from Earth. The lines are one degree apart

On the right are a number of sliders with which you can experiment. The sliders can be set to an accuracy of 1%. The nudge buttons to the side can be used to set the values more accurately.

Ptolemy used three devices to achieve a good fit between the predicted positions of the Moon and Planets and their observed positions.

- The eccentric deferent
- The equant
- The epicycle

To appy an eccentric deferent, move the 'Offset fraction' slider. A value of 10% will offset the centre of the deferent by 10% of its radius.

To apply an equant, click on the equant checkbox. This makes the planet orbit at a constant speed round a point which is an equal distance on the opposite side of the centre. The position of the equant is shown in violet.

To add an epicycle, adjust the 'Epicycle radius'. You also need to specify a frequency. Negatice frequencies rotate in the opposite direction to the rotation of the deferent.

All the percentages are in terms of the size of the deferent which is automatically set to be equal to the semi-major axis of the Moon's real orbit. (Since both Ptolemy and Copernicus had no way of measuring the actual size of any of the orbits, the size of the deferent is, in effect, arbitrary anyway.)

For further details of how to use the program, see the pages on the individual modes as follows: