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Stellar parallax was first measured, long after the invention of the telescope, in the 1830s (see note 7, p. 357). The first direct experimental confirmation of the motion of the Earth actually came from a quite different source - the discovery of the aberration of starlight in 1728 (see p. 307).

of the axis of the Earth remains constant with respect to the fixed stars - and so Copernicus introduced a third rotation about a line perpendicular to the orbital plane through the centre of the Earth that he called the 'motion of the inclination' and which was equal and opposite to the second, so that the axis of the Earth does not rotate. In fact, the rotation rates in Copernicus' scheme were only approximately equal, the rotation of the axis of the Earth being slightly greater than its annual rotation rate so as to account for the precession of the equinoxes. Since the axis of the Earth is, in effect, wobbling, Copernicus advocated the use of the fixed stars, rather than the equinoxes, as the correct frame of reference for the description of astronomical phenomena.

Nowadays, we are not constrained to think of Copernicus' second rotation as if the Earth were attached rigidly to a revolving sphere, and so it is more natural to think of the motion of the Earth, at least as far as we have discussed it so far, as being made up of the daily rotation about its axis, its annual motion around the Sun, and the slow rotation of its axis about the poles of the ecliptic once every 26 000 years or so.

Because of the discrepancy between Ptolemy's value for precession (1° in 100 years) and those of others (1° in 66 years according to al-BattanTand 1° in 71 years according to Copernicus), and the discrepancy between the values of the obliquity used by ancient and Islamic astronomers (23° 51' 20" according to Ptolemy and 23° 35' according to al-Battani), Copernicus believed that these quantities were variable:

When [Hipparchus] was scrutinizing the length of the year more intensely, he found that as measured with reference to the fixed stars, it was longer than when measured with reference to the equinoxes or solstices. Hence he thought that the stars too had a motion in the order of the zodiacal signs, but a very slow motion which could not be perceived immediately. Now however, with the passage of time it has become absolutely clear Moreover the motion is found to be nonuniform Besides, another marvel of nature supervened; the obliquity of the ecliptic does not appear as great to us as it did before Ptolemy Now the measurement of this motion and the explanation of its variation were not known to earlier [astronomers]. The reason is that the period of its revolution is still undiscovered on account of its unforeseeable slowness. For in so many centuries since it was discovered by mortal man, it has completed barely 1/15 of a circle. Nevertheless, so far as I can, I shall clarify this matter by means of what I have learned about it from the history of the observations down to our time.

Following the long-standing tradition begun by Thabit ibn Qurra, but with virtually no evidence to support the view, Copernicus believed that these two

28 Copernicus On the Revolutions, III, 1.

Fig. 5.3. Copernicus' theory of precession.

functions were oscillatory functions of time and, because the value for precession appeared to have a minimum around the time of al-BattanTbut no such minimum was observed in the obliquity, Copernicus chose to make the period of the obliquity exactly twice the period of variation in precession, the latter being 1717 years. Copernicus measured the obliquity as 23° 28' 24" and, even though the data did not support his argument, he claimed that the maximum and minimum values of e over its 3434 year cycle were 23° 52' and 23° 28', respectively. All the tables in On the Revolutions that are dependent on the value of e are computed for e = 23° 28' with a correction column provided to enable the user to adjust for larger values of e.

The actual mechanism that Copernicus used to model the variations in precession and obliquity is shown in Figure 5.3. A uniform rate of precession corresponds to a steady revolution of the north pole N around the pole of the ecliptic E as shown inFigure 5.3(a), and in this model the obliquity ofthe ecliptic, being determined by the distance | EN | ,is constant. The various theories of trepidation that were proposed by Islamic astronomers used, in effect, a polar epicycle with the mean north pole N rotating around E and the actual north pole rotating about a small circle centred at IN, as shown in Figure 5.3(b), and in this case the periods of variation of precession (determined by the angle NEN) and of the obliquity (determined by the distance | EN |) are the same. But Copernicus wanted a mechanism by which the period of the distance | EN| was twice that of ZNEN, and the one he came up with is shown in Figure 5.3(c). Instead of moving around a circle centred on N, the north pole follows a figure-of-eight-type path built up from two perpendicular oscillations: the motion parallel to EN is controlled by the angle 0 and the inner circle, whereas the motion perpendicular to this line is governed by the angle 20 and the outer circle.

In fact, things are rather more complicated than this because these figures should be drawn on a sphere rather than on a flat surface, but Copernicus argued that the motions are small enough for the approximation not to lead to noticeable errors. Copernicus used the equivalent of the Tuslcouple to produce the two rectilinear motions required, so that everything was built up from uniform circular motions. Interestingly, Nasir al-Din al-Tuslhad suggested earlier that his mechanism might be used for just such a purpose:

The same method may also be used for trepidation and for the movement of the obliquity in latitude for the ecliptic orb if the fact of these two motions and their

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