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c the line connecting the planet to the centre of its epicycle (CP in Figure 3.13, p. 77) remain parallel to the Earth-Sun line ES which by definition revolves at a rate of 1 revolution per year. However, had &>c + &>p been different from unity, this would have caused no problem for Ptolemy - he could simply have made CP rotate relative to ES at the appropriate rate. Hence, for Ptolemy, the fact that &>c + &>p is the same for all the superior planets is simply a coincidence -part of God's grand design. Not for Copernicus, though. In his theory, each superior planet rotates around the Sun at the rate &>c and the Earth rotates around the Sun once each year. The angular speed associated with the synodic period of each planet (i.e. the rate at which it orbits the Earth) is then necessarily

For the inferior planets, the simplification in terms of the number of ad hoc assumptions provided by the Copernican theory is more obvious, since it is the zodiacal period of those planets that is 1 year, and this is immediately implied by placing the Earth in orbit around the Sun between Venus and Mars.34 In the heliocentric system, the orbital (sidereal) periods Ts of Venus and Mercury must be calculated from their observed synodic periods Tp. The synodic period of Venus is the time between successive inferior conjunctions, and so if the Sun, Venus and the Earth lie in a straight line at t = 0, they next do so (in the same order) at t = Tp. If we measure time in years, the Earth makes Tp orbits of the Sun in this time and so Venus must make 1 + Tp revolutions. It follows that the rate at which Venus orbits the Sun is 1/ Tp + 1 revolutions per year, and thus,

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