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ForVenus, this gives a sidereal period of about224.7 days, whereas for Mercury we get just under 88 days.

Further discussion of the relative merits of Copernicus' and Ptolemy's theories, based on knowledge available in the sixteenth century, is given in Martin (1984).

Fig. 5.7. Copernicus' theory for Venus.

Copernicus' model for the motion of Venus is shown in Figure 5.7 and is, in fact, very similar in structure to that for a superior planet. The planet P again moves around a circle centred at C once every sidereal period, the point C rotating around a circle centred at O at twice the rate that the Earth E orbits the sun S. However, in this case the roles of the two circles are reversed, with the circle carrying the planet being the larger. Again, the Sun is displaced slightly from O. The point A in Figure 5.7 is the position of the Earth when it is at the greatest distance from the centre of the orbit of Venus. It is possible to perform a reduction to a geostationary model exactly as was done above for the superior planets, with the same conclusions. The circle centred at C and carrying the planet plays the role of Ptolemy's epicycle, and Copernicus obtained |CP| = 7193 (with |ES\ = 10000) where Ptolemy's model would imply a value of 7194. Ptolemy's value for the double eccentricity |EQ\ was 417, but Copernicus reduced this: 'Formerly it was all of 416 but now it is 350 as many observations show us.'

Copernicus' theory for the motion of Mercury (Figure 5.8) follows closely the arrangement for Venus with two key changes. The first difference is that when a = IESA = 0inthe model for Mercury, the point O lies between S"and

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