For the early astronomers, the errors of Mercury's position were huge. Copernicus may never have seen it, reporting no observations of his own for it, and remarked: 'This star tormented me, with its many twistings and toilings, in trying to explore its motions' (4). Kepler at the start of his career confessed: 'Certainly this is the one planet which most of all disgraces the reputation of astrologers, and confounds the whole theory of things on high' (5). In Galileo's time, the tables of Mercury available could err by ten degrees. In the horoscopes he prepared, it was often out by two or three degrees (6).
Earth and Mercury
The Golden Section solves their relative orbits and their relative sizes
A single pentagram, embodying the proportion known as the Golden Section, both spaces Earth and Mercury's mean solar orbits and sizes their relative physical bodies with 99% accuracy. Coincidences between the proportions of two planets' physical sizes and their mean orbits occur only twice in the solar system, and both involve Earth: between Earth and Mercury, and between Earth and Saturn. Coincidentally, Mercury and Saturn are the innermost and outermost of the medieval planets. The Golden Section is shown above defined by the arm-crossing of a pentagram (see Appendix 2.1 - the Golden Star). The unit "oo" means "our orbits" so that 1 oo = 149.5979 million km.
Mercury's Three Halos
In which Venus's Orbit is determined from Mercury's by just three circles
In this simple construction, a circle is drawn which represents Mercury's mean solar orbit. Three equal circles are drawn from the first circle with radii such that they touch each other like three coins. The circumcircle (containing circle) around these three touching circles then represents Venus's mean heliocentric (sun-centred) orbit with an astonishing 99.9% accuracy. This is an easy solution to remember and can be practised in restaurants or at home; it can also be discovered drawn up in the tracery of many church windows. It is important to remember that Venus and Mercury swapped positions in the order of things as a result of the shift to the heliocentric cosmos.