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A detailed description of the many Tychonic and semi-Tychonic planetary systems that were proposed is given in Schofield (1981).

28 Quoted from Blair (1990). 29 Quoted from Thoren (1990) p. 327.

Tycho's discovery of the variation is described in detail in Thoren (1967b).

managed to produce displacements of about 45' in the position of the Moon at the octants, while leaving the position of the Moon at the syzygies and quadratures unchanged. He modified further the traditional theory by making the centre of the larger epicycle (D in Figure 4.7) rotate around another small circle with a period of 1 year. This mechanism produced a change in longitude that oscillated between ± 11' over the period of 1 year. It is not known how Tycho came to discover this annual variation in the Moon's motion, but it was explained by Newton a century later as being due to the varying distance

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